Turbulence consists of irregular movements ofthe molecules in a fluid, through which mechanicalenergy is transmitted and decayed. Through this me-chanism, transport of heat and of materials in solu-tion is accelerated along the respective gradients.

This appears simply enough, although a rigor-ous approximation to the physics of turbulencemay appear rather discouraging. To the biologist,the energy involved in turbulence is obviouslymaterial and responsible for the maintenance ofecosystems. This may seem less than obvious whenecologists often have been guilty of neglectingessential energy inputs by fixation on photosynthe-sis and to transfers of energy delivered from it toother trophic levels. Other energy sources active onearth that contribute as well to the organization andmaintenance of ecosystems have been neglected

systematically, as is obvious in the case of vascularterrestrial vegetation, where energy of transpirationmediates the input and translocation of water andnutrients and quantitatively widely exceeds theenergy of photosynthesis. Furthermore human civ-ilization, besides food, uses increasing amounts ofenergy from many sources. Turbulent energy inaquatic environments may be relatively compared,at least, with transpiration energy in terrestrialecosystems.

Primary producers in open waters are very small,and never build the relatively persistent structuralframe of terrestrial vegetation. Phytoplanktonassimilates in a top layer, usually 40-80 m thick, andthe formed organic matter enters a food chain thatextends to maximal depths. Turbulent energy, most-ly originated by the interaction between atmosphereand water at the surface, plays an essential role inreturning the nutrients from the levels and placeswhere they tend to accumulate, chiefly in deep

TURBULENCE AND MARINE LIFE 109

SCI. MAR., 61 (Supl. 1): 109-123 SCIENTIA MARINA 1997

LECTURES ON PLANKTON AND TURBULENCE, C. MARRASÉ, E. SAIZ and J.M. REDONDO (eds.)

Turbulence and marine life*

RAMON MARGALEF

Departament d’Ecologia, Facultat de Biologia, Universitat de Barcelona. Avda. Diagonal 645, 08028 Barcelona. Spain.

SUMMARY: The decay of the mechanical energy of waves, currents and tides generates turbulence that propagates down-wards, diffuses nutrients and influences in different ways the movement of organisms. Light and turbulence combine in cre-ating local conditions for primary production. Mechanical properties of organisms (size, shape, production of mucilages)interact under different regimes of turbulence. Turbulence is a main factor in determining the stratification of populations.Organisms manipulate turbulence with results that could have positive selection value. It is suggested that many organicconstructions, like the limbs of copepods, provided with setae, rather than as filters, function as manipulators of the turbu-lent regimes at a small scale, in ways that increase the effectivity of feeding currents, introducing longitudinal asymetries inthe turbulent currents, in a way that could allow to speak of a “turbulence valve”.

Key words: Mixing, nutrients, pelagic life, plankton, phosphorus, Redfield ratio, sinking, turbulence valve.

*Received December 15, 1995. Accepted March 7, 1996.

water, to illuminated layers again. This role of tur-bulence covers wide spectra of wave length andpower.

Much less energetic turbulence is unavoidablygenerated by the swimming of the organisms andthrough the feeding currents that animals generate.Here it becomes a mixed benefit, and leads both tothe use of turbulence in the detection of prey andenemies, as well as to the development of ways ofconcealment or to the broadcast of false informa-tion, selected as it limits the probabilities of beingcaught. In summary, the role of turbulence in aquat-ic life is so important that Ambühl (1960) couldwrite “There is no life without water, and there is nolife in water without turbulence in water”.

Both surroundings, the atmosphere and the water,are fluid and turbulent: Water is a practically incom-pressible liquid, air is a compressible gas. These dis-parate mechanical properties are the sources ofimportant differences. But turbulence always sensi-bly accelerates transport along the gradients.

Mechanical turbulent energy is necessary to thecontinued life of plankton. Benthic life is capable ofredirecting circulation and developing turbulence ina large scale (like in corals), but also generating,controling and using turbulence very effectivelyover smaller scales (Riisgard and Larsen, 1995).

Life of plankton and its dependence on turbulenceprovides an excellent example of how evolution grad-ually takes control of environmental forces. Turbu-lence results from (entropic) dissipation of mechani-cal energy that works in a fluid. Water is a barely com-pressible liquid of relatively high density, supportsmechanically the organisms and as a solvent of excep-tional properties is the carrier of materials and pro-vides an excellent substrate for mechanical and chem-ical interaction among aquatic organisms (Fig. 1).

Dissolved and suspended materials diffuse ormove along any gradient of decreasing concentra-tion, from places where they are added to placeswhere they are consumed, and turbulence acceler-ates the flow. In oceans and lakes, surface waves arean important source of turbulence; turbulence isgenerated also in internal surfaces with shear,between overlaying water masses of different densi-ty or between the water and the bottom.

Living beings are, in part, dissipative systems, andin part selforganizing systems, and turbulence in thesurrounding fluids around contributes to dissipation ofheat and of momentum and in special to displacementof selected molecules. Between layers of contrastingsalinities, the so called “salt fingers” result from dif-ferences in the diffusivities of heat and of solutes, andcreate asymmetrical boundaries of peculiar properties.

110 R. MARGALEF

FIG. 1. – A general sketch of the interaction between light and mechanical energy in the oceanic environment.

Turbulent oscillations cover a wide scale of size,in an irregularly hierarchical pattern as expressed bythe few rhymed lines attributed to L. F. Richardsonand repeated ad nauseam: “Big swirls have littleswirls that prey on their velocity, and little swirlshave lesser swirls and so on ... to viscosity”. Vis-cosity, the tendency of molecules to adhere togethersets a limit to turbulence; it depends on the nature ofthe fluid and on conditions like temperature.

The decay of energy in the production of irregu-lar movements has been rationalized through sever-al theoretical models that imagine the way trajecto-ries modify with the passage of time, down to mol-ecular level. From its molecular composition alone,at “regular” temperatures, water would be expectedto behave as a gas; but it is a liquid, because its mol-ecules are more densely packed than a preliminarytheoretical approach could predict, held together insmall groups by secondary hydrogen bridges. Theaverage size of each one of such molecular clustersdepends on temperature and perhaps also on otherconditions. This is not without consequences for thedegree of hydration of living matter and certainlyalso in the dependence of viscosity and turbulencefrom temperature.

Adequate observations of small motions requiretracers and become difficult and even impossible atthe smallest scale, and some of the acceptedassumptions have been acquired in a deductive andprobably incorrect way. Only the recent develop-ment of sophisticated equipment apt to collect andanalyze large amounts of information about move-ments of the fluids over small scales of time and ofspace, keep a promise of empirical progress(Imberger, l994).

In stationary situations in which decay is com-pensated by a constant input of energy - that mightcome, eventually, from surface waves - , the localspectra of turbulence may remain relatively constantfor a while. The supplied energy may come withorbital movements of water, such as those generatedby the waves raised by wind in the surface, whichmomentum propagates downwards. The spectra ofthe movements of small parcels of water shift overtime and space, periods may split and movementsthat formerly were regular end in confused turbu-lence. On average, wavelengths and amplitudesdecrease and frequencies may go up, in a genuinelyirreversible and entropic process, in which a widespectrum of motion is alway present. Trains ofwaves can reflect and meet again and interfereamong them, being out of phase, after travelling dif-

ferent paths. The prevailing notions for explainingobserved or supposed regularities have been basedon analogy and dimensional analysis. It was expect-ed that chaos might provide a complementary con-ceptual frame. Indeed, one of the pioneers of the sci-ence of chaos, Lorenz (1963), got a start into chaostheory through the consideration of thermal turbu-lent convection in the atmosphere.

Indeed, chaotic behaviour has been observed orsuspected in nature or in experiments, sinceReynolds (1883), who studied flow by means ofstreaks of colored fluid interspersed in a stream, andin different situations. There is a particular value ofthe mean velocity of the fluid, that depends on thediameter of the pipe or of the channel, and, ofcourse, on the nature of the fluid, below which theflow is smooth (“not chaotic”) and disturbances arerapidly obliterated. If speed goes up, the flowbecomes increasingly sensitive to disturbances,however small, and for higher speeds the rectilinearregime breaks down completely. Energy is drainedfrom the larger scales of motion to smaller scales,until viscosity of the fluid sets a limit. Viscosity is,indeed, one fundamental property, characterizingthe “fluid machine of turbulence”.

It was inferred from Reynolds that the “uppercritical velocity”, separating the smooth rectilinearflow from the aparition of eddies and generaliza-tion of flow irregularities, could be related to thekinematic coefficient of viscosity (ν, of dimensionL2T-1). The diameter of the pipe, multiplied by theflow speed and divided by the coefficient of kine-matic viscosity, yields a dimensionless number, theReynolds’ number, Re, expression of the ratio ofthe inertial to the viscous forces, with a criticalvalue around 1000; above such value, flow is per-ceived as turbulent. The coefficient of kinematicviscosity is temperature dependent (it decreaseswith increasing temperature). In experiments withwater, viscosity can be easily increased by coolingor adding mucilage.

An analogous and parallel measure of the behav-iour expressed by the Reynolds’ number, and goingunder the same name, has been adapted to charac-terize the expected regularities in the movement offree particules or mobile organisms immersed in afluid: this particular form of the Reynolds number ismade equal to VL/ν or ρVL/µ. V is speed in cm s-1

and ν is the coefficient of kinematic viscosity, ofdimension cm2 s-1, its unit being the stokes; µ is thecoefficient of dynamic viscosity, of dimensions gcm-1 s-1 , the unit being the poise; νρ=µ (ρ stands for

TURBULENCE AND MARINE LIFE 111

density). This practical Reynolds’ number is below0.1 for a phytoplankton cell that sinks slowly inwater, and half a million or more for a swimmingfish. In these examples, laminar flow is supposed tobrake the supply of nutrients to the phytoplankton,and turbulent flow, in which eddies absorb muchenergy, will surely slow down the potential speed ofthe fish. For convenience in particular applications,it might be acceptable to compute analogousReynolds’ numbers on the distances between theradii in any filtration device, or, in particular situa-tions, with reference to the definite thickness of aliquid layer.

A, a symbol for Austausch, the German word forexchange, is used for actually observed speeds in theturbulent transmission or diffusion of heat, salinity,or momentum (specified adding to A the appropriatesubindex, θ, s, v), and has the same dimensions asdynamic viscosity, µ. As expected, its numericalvalues when refering to properties with no return,like heat and motion, are larger than values referingto properties in which transmission happens bothways, with partial return, like in the forwarding ofsalts, gases and nutrients in solution. Most frequentactual values at sea go from much less than 1 g cm-

1 s-1 in the well stratified water during the warm sea-son, to 3-50, in the same units, in agitated waters;these numbers refer to the vertical direction. Waterstratification by density makes horizontal diffusionmuch easier, as less energy is involved in effectivemixing along the horizontal plane. Austausch num-bers, Ax, refered to the horizontal are often 100-1000 times larger than those mesured along the ver-tical (Az).

SCALES OF INTERACTION BETWEEN TURBULENCE AND PLANKTON

Turbulent mixing in oceans and lakes, principal-ly under the action of wind, brings back nutrients tothe surface and restarts the cycle. The work done canbe appreciated in different ways. If, to begin with,the water was stratified by density, large scale mix-ing raises the center of gravity along the vertical.Work done is equal to the product of the total massM by the vertical distance between the two consec-utive positions of the center of gravity (E) and theacceleration of gravity (g). This total work, gME,replaces nutrients to the illuminated layers, allowingbiological production to proceed. This is an exampleof large scale mixing (Fig. 2).

A much larger fraction of available energy isusually dissipated just in mixing over small andsmaller distances, although the biological resultsmay be as significant as in the precedent exampleof large scale mixing. The wave spectrum of tur-bulence shifts naturally along time towards short-er wavelengths, and dissipates and practicallywould stop if no more momentum were injected.If Az is the value of “Austausch” along the verti-cal, and dV/dz the change of sinking speed alongthe vertical, the vertical diffusion of mechanicalenergy will be Az(dV/dz)2. The irreversible dis-persal or diffusion of mechanical energy and tem-perature is unavoidable and in absolute value ishigher (more increase of entropy) than diffusionof materials in solution, because a fraction of suchmaterials can always and eventually travel back, afeat that is not possible concerning heat (heat can-not flow from a cold to a warmer body) ormomentum. In consequence, as already stated,vertical diffusivity for movement is higher thanvertical diffusivity for nutrients, and in the sea,the ratio Az/Am, or Av/Am, with reference to thevertical axis z, may be between 5 and 50. Oneconclusion is that turbulent diffusion is somewhatparsimonious or not as effective as it would bedesirable, in the task of supporting the fertility ofthe top levels of the seas, by replenishing themwith nutrients from below.

The path described by a freely suspendedorganism does not exclude randomness, in a degreethat depends on turbulence and on the capacity ofthe organism to orient itself in relation to light, togravity, and any other possible cue or stimulus, andto control its own speed and trajectory in relationwith them. A simple approach is to suppose a ran-dom walk and to subdivide it into small steps. Theexpected lineal distance between both endpoints(D) separed by N steps of length L is D=LNk,where k expresses a fractal property; k=1 for astraight path, k→0 in a path that keeps turningaround inside a small volume. Intermediate valuesare expected in the normal aquatic environmentsand they depend on turbulence. The non uniformi-ty of turbulence, as well as the directionality ofexternal stimuli (light, gravity) make clear thatmovements along the vertical may be and usuallyare much more internally influenced or determinedthan drifting around along an horizontal plane,which is characterized by higher values for turbu-lence and by the lack of directional stimuli. Thefractal walk in this example is supposed to be

112 R. MARGALEF

decomposed in relation to the three dimensions:k2=kx

2+ky2+kz

2. This approach is useful to introducethe analysis of vertical migration, and helps tounderstand the random shifts in the horizontalplane that are associated with such migration.

Oceanographers and biologists are impatientwith and critical of the current theoretical modelsand expect much from expansion of empiricalresearch in the field (Lazier and Mann, 1989). Tur-bulence (or non turbulence) close to small solidbodies is expected to take the form of laminarshear. The existence and metabolism of very smallcreatures poses many problems to fluid dynamics,real or imaginary. The image of tiny things of 1-2µm swimming happily and confidently, is alwayshaunting to the observer.

Electrical charges of the membrane (eventual-ly pushing the cells along the environmental gra-dients of electrical potential) might influence neg-

atively the aggregation of assimilating cells intofood balls. Experimentally, small living organ-isms can be displaced electrophoretically betweenelectrodes with a speed that is also related to theintensity with which they assimilate. One ques-tion poses itself: would filter-feeding be moreeffective at night, when electrical charges in thesurface of autotrophic organisms may be sup-posed to drop?

On the basis of theoretical constructions,including dimensional analysis, a decay of turbu-lent energy over small spaces is commonly sup-posed to follow a law of a -5/3 power. This is dis-cussed in other companion contributions, and for abiologist one of the most important unresolvedquestion may be the possibility of having intermit-tences left, that is, small volumes at rest, whichcould serve perfectly as spaces where agregation ofmucilages might easily happen.

TURBULENCE AND MARINE LIFE 113

FIG. 2. – Schematic representation of typical oceanic situations in function of vertical flow and of turbulence. Energy involved inupwelling of deep water or in simple mixing of water enhances primary production, in a degree proportional to the supplied extra energy.In the lower part of the figure, input of energy is assumed to increase from right to left (Redraw from Margalef, 1974 and Watt, 1973).

This supposed basic spectrum might be expandedover to larger scales in an attempt to comprise in thesame broad pattern, the clumping or patchiness that isrevealed in most statistical studies on the large scaledistribution of plankton organisms. The particularreasons for the distributions are rarely clear. Anyway,a previous logarithmic transformation of the originalconcentration of organisms simplifies the analysisand the presentation of distributions in terms of num-bers of cells or concentrations of pigments, alongtransects from a moving ship. On an arithmetic scale,such transects would show a “mountain range” pro-file, compatible, when projected on an horizontalplane, with discontinuous high density patches dis-persed over a less populated background extensionthat tend to coalesce into a continuous reticulum.Considerable expectations have been placed on theadoption of generalized spectral distributions in ecol-ogy (Platt and Denman, 1975). But it would be hardto believe that an identical power rule holds over verylarge areas, as local hydrodynamic accidents upsetcontinously the assumption of uniform turbulence.The only valuable general conclusion is that theseand many other considerations that assume only theuniformity of ratios and slopes may provide reasonsfor a generalized use of logarithmic transformation oforganism concentrations.

Natural distributions extend over space andtime and always are the outcome of changes asym-metrical in space - discontinuous patches over areticulated main ground - and irreversible in time,alternating gradually and often slowly increasingwith catastrophic drops. Indeed plankton dynam-ics and the resulting plankton distributions,expressed over time and space, fit reasonably wellwith the I/F noise generation and distribution, withan inverse and logarithmic relationship betweenthe intensity of disturbance (measured by the ener-gy involved) or the size of the resulting “patch” ofplankton (I) - that provide an expression of theenergy involved - and the frequency (F) withwhich patches or disturbances of a defined classoccur.

Such distributions are consistent with the exis-tence of small areas that are energy rich, developingstrong turbulence, biologically very active or veryproductive, and not necessarily persistent (althoughoften they develop repeatedly in the same places),always contrasting and set against surfaces increas-ing in extension as they become less and less pro-ductive and comprise water masses that are morestratified or less turbulent.

Heterogeneity, often refered as patchiness, at allthe scales is real in plankton distributions and, asassumed in precedent comments, consists in spaceswith high plankton density relatively discontinuousand included in a network or background with a lowerdensity of life and less turbulent water. Several mech-anisms account for their ocurrence, among them theone described by Levin and Segel (l976). One of themconcerns primary irregular distribution of small eddiesin response to wind; over any large area, asymmetry isintroduced by composition of random eddies with therotation of Earth, as deep-water ascends and fertilizesthe center of such cyclonic eddies that exceed a mini-mal size, thus generating a set of discontinuous spotscharacterized by high productivity under localupwellings, in contrast with the anticyclonic gyreswhich centers may be descending and anyway remainless distinct and often less productive or containorganisms that are more adapted to survive in sinkingwater masses. Also, anticyclonic eddies might blendtogether more easily than cyclonic ones.

Most of above considerations converge in mak-ing it likely that more turbulent and biologicallymore productive patches may lie enclosed in a sortof low turbulence reticulum. Such patterns, withdifferent scales and different intensities, areexpected to manifest themselves in most sectionsavailable for spectral analysis (Platt and Denman,1975). Observation from space is opening newpossibilities for obtaining evidence, much neededto validate or to refute the significance of themechanisms refered to, and the repetitions downto the smallest scales, apt to accomodate the socalled “microbial loop”.

For application at very small scales, mixinglength (I) refers to the theoretical length of the aver-age path followed by any small parcel of water untilit is assimilated and adopts the momentum of thesurrounding fluid. From the basic relation

ρ[I(dV/dz)]2 = Av(dV/dz)

one gets

I = (Av/[ρ(dV/dz])1/2

where ρ is density of water. The concept of mixinglength might be helpful to understand plankton biol-ogy, at millimetric scales, between 0.5 and 10 mm,if the actual structure of turbulence, with intermit-tencies or not, were known, and adopted in the rightway to improve this expression.

114 R. MARGALEF

If the distances between recognizable or taggedparticles were measured in a continuous way, theywould be found not constant and usually increas-ing. If their mutual distances increase exponential-ly and indefinitely along time, the powers in thefunctions that describe succesive positions may beassimilated to exponents or numbers of Lyapunov,that appear to have a useful meaning in differentecological contexts; for instance in relation tochanges in the numerical importance of popula-tions of coexisting species. Besides, Lyapunovexponents are often associated with chaotic behav-ior of the evolving turbulent systems.

PLANKTON BIOLOGYIN RELATION TOLARGE SCALE TURBULENCE

Most work done on turbulence is disorderedand irreversible, and has to be written down in theaccount of entropy - the dissipative part of theecological machine. The speed of degradation ofenergy in turbulence increases with temperature.Viscosity of water opposes turbulence, but viscos-ity is effective only over small distances. In theopen sea, turbulence is a part of a vast dissipativematrix, and contributes to feed the self-organiza-tive systems in it: the living organisms of plank-ton. Vertical organization is better developed andpreserved when turbulence is low and close to thetwilight zone, that is also an actual store of biodi-versity, that behaves like the seed bank of a forest.It is sustained and enriched by the results of thesuccessive blooms in the more turbulent levels ofthe photic zone. Thus, dynamics of diversitybecomes associated with distribution of turbu-lence and acceleration, and the preservation ofgenetic biodiversity happens mostly in less turbu-lent environments, including sediments.

Energy, most of it from wind, sets water in motion.Total work is reflected in the vertical shift upwards(E) of the center of gravity of the water column whengradients of stratification decrease. This increasespotential gravitatory energy, and turbulence energy isadded in the amount of Az(dV/dz)2 per unit volume.The symbol g is the acceleration of gravity, dV/dz isthe vertical gradient of current speed, Av is turbulentviscosity and Az is turbulent diffusivity. Av(dV/dz)2 islarger than gEAz. Strong vertical gradients in hori-zontal speed and Ax appear associated with thermo-clines and other density gradients.

Viscosity is a function of temperature; at 30˚Cviscosity is approximatively half, and at 75˚ onefourth, of its value at zero degrees. In consequence,at higher temperature, water has more capacity tocontain small scale turbulence. Hydrostatic pressureis less important as a modifying factor.

In oceans and lakes there is a competitive coursebetween penetration of turbulence and penetrationof light, from which issue many important aspects ofphysical and chemical stratification and production.This is very clear when comparing (1) the fluid sys-tem of open water with (2) an algal mat or stroma-tolite in which high viscosity (mucilage) dampensthe turbulence and places the sharp chemical bound-aries inside a narrow band. Biochemical gradients asexpressed in redox potentials may be in ratios up toone to a million in the respective situations (plank-ton:algal mats). Many other valuable generalizationson these aspects, that obviously are related to theorigins and fundamental constraints on the processof organization of the biosphere, are ameanable toexperimental approach.

The first quantitative approximations to popu-lation dynamics and to the study of interactionsbetween populations of different species (demog-raphers: Lotka, Volterra) ignored space. Indeed,space was introduced in the ecological models bymarine biologists, as a consequence of their wishto take into account sinking organisms in more orless turbulent water. In part it was the considera-tion of turbulence that made ecologists think aboutthe need to improve the early and traditionalLotka-Volterra models.

Gordon A. Riley provided an important and mostwelcome stimulus, and in several contributions -especially in a joint paper with Stommel and Bumpus(1949) - presented and justified a wise and stimulat-ing model. Here are sketched: a) the expression orig-inated by Riley, and below, b) a recent version of it inmore modern and proper notation, that substantiallyembodies the same concepts (Delhez et al., 1993), buttries not to be limited to a single column of water.Sinking relates to the first derivative of vertical distri-bution and turbulence tends to take out secondaryirregularities and relates to the second derivative.

a)dN/dt = rN – gNZ – V dN/dz + Ad2N/dz2

total cell consumption sinking turbulentchanges division by diffusion

zooplankton

proper Lotka andVolterra dynamics

TURBULENCE AND MARINE LIFE 115

N = phytoplanktonr = rate of increaseg = grazing by animals V = vertical speedA = turbulent diffusionz = vertical dimension

b)δy/δt = Qy – ∇ (v y) – ∇

y = state variablet = timev = velocity vectorQy = rate of production-destruction of y∇ = three-dimensional nabla operator

= turbulent flux of y

Turbulent exchange (A, Φ) disperses and redis-tributes the populations, contributing to recolonize aspace in which population density might be drivendown by sinking. Simultaneously, mixing at allscales, brings back nutrients to the illuminated lay-ers. The equilibrium conditions shift continuouslyand intensity of turbulence in combination with pen-etration of light may become decisive in this respect.Its role is defined also by depth, down to which sur-face waters mix vertically, a depth that in shallowshores is limited, a condition helped very much inevolving from the preliminary approximations(Gran and Braarud, 1935) to the present model.

The same basic assumptions were suggestive(Margalef, l978) of the important role of terms ofthe form A ([d2S/dx2] + [d2B/dx2]) that could beinterpreted as the product of turbulence (Aus-tausch, A) by an expression of the covariancebetween different factors of production, like bio-mass (B) and substrate or nutrient concentration(S). This hint suggested the need to look moreclosely at possibly relevant literature for furtherinspiration and it was found that von Smoluchovs-ki (1918), working with colloidal systems, was ledto accept that reaction speed depends both on thelocal diffusivity or turbulence (A) and on the over-lap or covariance in the spatial distribution ofavailable potential reactants (C) [See also Kelzer(1982) and Kopelman (1988)]. In its tentativeadaptation to ecosystems, the expression of suchpoints of view could produce:

energy of mixing covariance in theproduction (P) = Austausch × distribution of factors

turbulence of production

Light cannot be displaced by mechanical work(by turbulence) and belongs to an independentframe. Light or any analog of it was not relevant inthe problem that von Smoluchovski (1918) wantedto attack.

Simple derivation in relation to time yields anabridged suitable description of ecological succes-sion:

dP/dt = C (dA/dt) + A (dC/dt)

All these models allow subdivision into smallercompartments in a way that might show also if, andhow, the concepts of new production and recycledproduction can be separated.

In very general terms, these different approachesturn around the basic concept of systems in which(turbulent) diffusion, including sinking, and reac-tions (primary production, grazing), are determi-nant. In the same group comes the KISS model(Skellam, l951; Kierstead and Slobodkin, 1953), andit surprises the aquatic ecologist to see that even thedevelopers of the theory of dissipative systems(Nicolis and Prigogine, 1989) never refer toattempts from physicists and oceanographers, madeknown between 1918 and 1949 and oriented to dealwith this very general problem of self-organizationand pattern formation based on diffusion and reac-tion. Instead they hint only at Turing (1952) as amost distinguished precedent.

SHAPE AND SIZE AS PASSIVE ADAPTATIONS TO SURVIVAL IN TURBULENT ENVIRONMENTS

The consideration and analysis of the presumptiveevolutionary play between nutrient absorption, swim-ming and environmental turbulence becomes fascinat-ing (Margalef, 1978). Passive sedimentation of phyto-plankton is an always present risk, as it takes cells outof the photic zone towards situations of likely poorillumination, although, it can bring the cells in contactwith water enriched in nutrients. In the presence ofmoderate and high turbulence, swimming adaptationssuch as are only possible in very small organisms, can-not matter much anyway. The problem is how to com-pensate the losses that sedimentation causes in thepopulations through an increased input of the nutrientsenhanced by turbulence, that would allow the popula-tions to increase at a rate capable of compensating andeven exceed the loss of cells suffered. Non-motile

Φ̃y

Φ̃y

116 R. MARGALEF

x

diatoms thrive frequently under turbulent conditions,as well as coccolithophorids that have lost functionalflagella and are, besides, lested by calcareous coccol-iths. All these organisms and many others are ratherheavy and naturally may tend to sink; in turbulentwater such abilities could not make a serious differ-ence. But in stratified and less turbulent water it paysto invest energy in swimming and so to be able toposition the cells in the most favourable situations, anoptimization that could be useless in turbulent water.Intensity of mixing and nutrient supply in the photiclayers are decisive factors.

Turbulence, assuring renewal of the layers ofwater in contact with phytoplankton cells, and oftenassociated with larger scale water movements,becomes a critical factor in the selection and evolu-tion of the species. Size and shape of cells determinethe surface/volume ratio. Organisms in the size classof approximately 1 µm should become prisoners ofviscosity and their potential opportunities to assimi-late and multiply are perhaps more restricted thanwas imagined at the time of the discovery of therichness and ubiquity of picoplankton.

For sizes above those of bacteria and smallcyanophytes, the relations between size and shape ofthe cells and colonies, and viscosity, turbulence andnutritive capacity of water have attracted the attentionof several authors (Munk and Riley, 1952; Gavis,1976; Margalef, 1983; Lazier and Mann, 1989, andmany others). In an open and creative approach,Gavis (1976) combines several likely components offitness under a compound index P, without dimen-sions, that may be taken as a measure of the prospec-tive evolutionary success of any strain or lineage.Thus, competition between stocks or species mightdepend on shape, size, nutritional efficiency, etc., thatis, on the different factors that enter in the computa-tion of the said index.

Rearrangement of the terms in the original Gavis(1976) expression results in:

P = K’(Ks/Vmax) × (dø) × [A+(1/2)øV]kinetics size and shape environment

K’ = constantd = sizeA = turbulence, cm2 s-1

Ks, Vmax = constants that refer to absorption kineticsø = coefficient of shape:

=1 for the sphere<1 for other shapes

V = sinking speed

The persistence of a population depends on prop-erties of the organisms in relation to environmentqualities, supply of nutrients, and mechanical forcesin the environment responsible for turbulence. Ageneral conclusion might be (Carlson, 1962) thateven with an efficient motility, it is possible toimprove the conditions of nutrition through adapta-tion or manipulation of properties of the environ-ment. There is a speed range in which benefits maytop the energy investment. Improvement seemsalways possible along some definable evolutionarypaths.

Lazier and Mann (1989) argue, very reasonably,that turbulence over small scales is not well under-stood, and that anyways, active movement or sink-ing of the cells may be more important; conversely,turbulence may erode away the so called microzones(Mitchell et al., 1985), with accumulated excretathat may give support to “microbial loops”. Thereare known instances of accelerated growth under theinfluence of increased turbulence, introduced in thecultures in the form of bubbling (Aguilera et al.,1994). But not much descriptive information isavailable on the mechanics of motion of small fla-gellates (Melkonian, l992), and the nature and even-tual help provided by the flow close to the cells isbarely known. Coanoflagellates and other peculiartypes of organisms pose other unanswered ques-tions. Diverging solutions (strategies) might havebeen adopted in the evolution of many kinds ofsmall flagellates and of dinoflagellates.

Dinoflagellates possess an undulating flagellumsunk in the girdle that keeps the cells turning, oftenworking against the resistance opposed by the flat-tening of the whole cell or by the expansions or out-growths added to the cell body, that also is oftenstrongly asymmetrical: the necessary result of suchconstruction principles is to have an acceleratedflow of water over the cell body, that surelyimproves the chances for absorption. An interestingdesign includes a small cell body and longappendages that extend over a large space and mayanchor the cell in a relatively fixed position againtssmaller turbulent eddies that “wash” the surface ofthe cells (Ceratium vultur, C. trichoceros, Ceratoco-rys horrida, Triposolenia, Amphisolenia, Dinoph-ysis miles, Thalassiothrix longissima, T. antarctica,Chaetoceros, Bacteriastrum, etc.).

The correspondence between the hydrographicconditions prevailing in the different seasons ofthe year and the syndromes of adaptation of theorganisms most frequent under such situations,

TURBULENCE AND MARINE LIFE 117

helps to explain one important part of the season-al dynamics of phytoplankton (Margalef, 1978).Turbulence, Austausch, may play, thus, a principalrole in the alternative dominance of diatoms ordinoflagellates.

THE ROLE OF SECRETIONS IN THE WAY TO THE OBLITERATION OF TURBULENCE

Sheets of mucilage that cover the cells of phyto-plankton, and that have been excreted by them,

118 R. MARGALEF

FIG. 3. – Examples of shapes in planktonic dinophytes that increase cell surface washing, even in conditions of low turbulence.

increase the viscosity of water so much that positiveconsequences of turbulence must become stronglydampened by the mucilaginous cover. Mucilaginoussheets are common around small aquatic organisms,and not only in algae of different groups, chiefly infresh-water, but also around ciliates (Ophrydium)and rotifers (Collotheca, Conochilus). Phaeocystis,and species and forms of Chaetoceros, Thalas-siosira, Nitzschia, and a few others often appear sur-rounded by jelly-like covers. In the polar oceans,comparable secretions are common around theorganisms of the pack, initially submerged in a brinethat can be enriched in nutrients, after the separationof grains of solid ice. Such organisms, mostlydiatoms, may appear, consequently, covered by, andincluded in, a reticulum of water made more consis-tent by mucilage, as clearly observed in samples col-lected in the Antarctic by Marc Steyaert in the fifties.Such samples were preserved in alcohol, which ledto the coagulation of the mucilaginous reticulum sur-rounding and enclosing the cells.

It would seem that the presence of such mucilagi-nous sheets would limit diffusion, although it isknown that bacteria can move faster through liquidsmade more viscous by long molecules, and thatsome kinds of molecules can travel faster than usualdue to the support provided by polysaccharides.

Surficial mucilaginous secretions over the bodyof larger animals, like fishes, could help to iron outthe irregularities that generate turbulence and absorbmomentum. An equivalent adaptation operating in alarger scale is the flexibility and easy accomodationof the surface of larger animals, a positively select-ed feature that reduces resistence encountered incruising through fluids. Such properties are wellknown in the skins of cetacea and are provided bythe soft feathers over the body of birds.

In the first stages of production and accumulationof mucilages in water, probably some relation has tobe found with the availability of spaces at relativerest, or of intermittency in turbulence. Any specula-tive model about eventual organization of move-ments in turbulence and their changes along aprocess of decay, should accomodate eventual sub-models accounting for the availability of spaces atrelative rest, where mucilage accretes with morefacility. But the acceptance of spaces at rest couldpose some difficulties for the general acceptance ofthe models of turbulence in the style of Kolmogorov.

The most simple explanation for the presence ofmucilaginous covers is that carbon assimilation con-tinues when there is light, even if the more limitant

nutrients (chiefly P) are not available. Under suchconditions, cells do not multiply, but long moleculesof carbon compounds are given off. Coccolithopho-rids, in equivalent situations, that is, under highavailability of calcium carbonate, fabricate andthrow away an extra number of coccoliths.

If such explanations hold, it makes sense to viewthe secretion of mucilage, in the first place, as a sortof “birth control device”, in the sense that mucilagi-nous sheets slow down diffusion - from turbulent toslow lineal diffusion regime. The extruded organicmolecules, that contain carbon molecules might beanalogous to the excess sugar excreted by aphidsand other homoptera when feeding on plant juicesthat contain “an excess” of carbon compounds. Asthere is apparently no brake to stop photosynthesiscompletely, assimilation of carbon compounds con-tinues to run, mainly during the long days and inshallow environments, like in North Sea or in thenorthern part of the Adriatic during the summer(Martin et al., 1995; Mingazzini and Thake, l995).In general, presence of mucilages is associated withhighly productive conditions, often a consequenceof human impact. In summary it seems reasonable toassociate production of mucilages with exhaustionof phosphate and rapidly increasing light availabili-ty - longer days, shallow waters.

Perhaps one can find a valid analogy in many ter-restrial plants of arid places. In summer, these plantscontinue to assimilate carbon, which they give off inmolecules of terpenes and isoprene. Perhaps also ananalogy can be made in growing wood that is cheapbecause it is poor in chemical elements others thanC, O, H. It is stated that isoprene production alonemay siphon off 2% of the carbon fixed by photosyn-thesis in terrestrial plant communities (Mlot, l995).As in such situations fires may be encouraged, itseems a bit difficult to find an utilitary explanation,except in the sense of destroying competitors,inflicting on them damage more important or moredefinitive than on oneself. In other situations, com-pounds that do not contain essential nutrients, likesaponins, may have a value of defence and one can-not but remember spit-bugs, surrounded by a wateryfluid rendered viscous by saponins, and well popu-lated by microorganisms of many species.

Evolutive adoption of a precise shape and sizemay increase survival of plankton under defined con-ditions and, inside a group, may open the possibilitiesfor ecological segregation among different species.The cells and colonies of the species of Chaetoceros,Bacteriastrum and Corethron, according to the length

TURBULENCE AND MARINE LIFE 119

and disposition of bristles, operating in environmentsthat show a wide spectrum of turbulence, anchor andturn with eddies of larger or of smaller size, accord-ing to the dimension subtended by the appendages,and this may be the origin of ecological segregation.We know related species with the same null or smalllocomotory activity, that actually belong to different“ecological niches”, and some of them, like the coc-colithophorids mentioned in a precedent paragraph,have flagella, but often make no use of them.

An illustrative image of segregation in functionof the extension of the space used to anchor the cellor the colony can be obtained visualizing and com-paring a small boat that dances above the waves, anda large ship that is washed by the same waves, andequating them with what happens with small round-ed cells and, respectively, with organisms that sub-tend a larger volume, relatively anchored in itswater, through long and rigid expansions (like Cer-atium trichoceros); the appendices do not hinder theresults of turbulence that wash the surface of thecentral part of the cell. Also the expansions of a fewCeratia (C. platyceros, C. ranipes) provide largeabsorption surfaces, either for light (the first namedspecies) or for nutrients (the second one). Withoutdoubt, the relation between the spectrum of turbu-lence in water and the way an organism with itsappendices is anchored in the water may start orencourage ecological segregation and evolutionarydivergence, that perhaps was effective in the case ofthe two last reported species of Ceratium.

THE INTERPLAY BETWEEN STRATIFICATION,NUTRIENTS, LIGHT AND TURBULENCE

In microbial mats and stromatolites, illuminatedstructures are thin and dense, with high absorptionof light, and often a great part of the overlying wateris immobilized by mucilages, an indication thatabsorption of C, N and extrusion of their compoundscontinue, even in the practical absence of elementsallowing for cell division (mostly phosphorus). Thestrong gradient of redox potential, associated with agradient in nutrient availability, is close to the sur-face. A few mm below starts the reducing zone,where heterotrophic prokaryota dominate. This situ-ation contrasts with that described for water bodies,where penetration of light and of important turbu-lence determine less sharp structures in liquid andturbulent water, that extend over a vertical range ofdecameters. Changes in illumination and in vertical

mixing, these in function of (wind) turbulence andvariable thermal stratification, define productionand distribution of organisms.

Take the Western Mediterranean as an example.The most productive layer, where photosyntetic pig-ments are concentrated (although rarely above 1 mgchlorophyll per cubic meter) is found between 40and 60 m depth. Phosphorus is the limiting element,and its concentration above this level is extremelylow, down to undetectable. It is rapidly used, andstarving cells tend to sink. The cycle maintained byzooplankton consumption and return in the top lay-ers is not much effective and does not counteractseriously the losses due to net sedimentation.

In marine pelagic biology there is often questionof the Redfield ratio, that refers to the ordinary(atomic) relations between the basic elements C:N:Pin the body of the planktonic organisms. Its accept-ed value is 106:16:1, or expressed in total relativeweights as 100:17:2.4. Evolution of seaweeds and ofterrestrial plants has included a sensible increase ofthe carbon fraction that is incorporated in the sup-port and transport structures.

Phosphate seems to be always the limiting ele-ment, although for about 30 years, oceanographershave inexplicably forgotten it and centered attentionon N, of which water contains an extra large supplyin form of dissolved dinitrogen gas, that is availableto cyanobacteria or cyanophytes. One reason to pre-fer N was perhaps its protean behavior that facilitatesthe study of different paths of regeneration, but theresult has been to impair seriously the study ofmarine productivity. The reserve of phosphate, prac-tically all as orthophosphate, is considerable (morethan 40 mg P m-3 below 1000 m; in the Mediter-ranean less than one half of such concentration,about 15 mg P m-3), but in the photic layer the con-centration of available phosphorus, organic plusinorganic, is much lower and necessarily limiting.

The ratio N:P in Western Mediterranean water isa bit above the current proportions elsewhere and, inconsequence, only exceptionally, nitrogen may belimiting. One characteristic shared with theCaribbean, parts of the Pacific Ocean, and probablyin other extensive areas that so far have been poorlyexamined from this point of view, is the presence ofan almost continuous layer rich in nitrite (NO2

–), justbelow the limit of penetration of light of usableintensity and above the top of sensible concentra-tions of phosphorus. Myself and my former studentDolors Blasco (1971) have developed an interpreta-tion of this layer (concentrations 0.2-0.5 µM N) in

120 R. MARGALEF

the sense that it might result from the activity of phy-toplankton cells as they sink to a level in which cellsare still able to reduce available nitrate to nitrite, butin which light is insufficient to allow reduction andassimilation of nitrogen compounds to proceed. Thecells would let nitrogen escape, now in the form ofnitrite, which remains in solution in the environmen-tal water, forming a continuous layer. This layer mayshow some discontinuities or openings, as well asdifferences in its depth, a topography that seems tobe related to the horizontal distributions of the inten-sity of the operative agents (vertical movements,mixing, availability of phosphorus).

Ascending movements of water, mostly along theWestern coasts of the main continents, allow nutrientsaccumulated in deep water to cross the limit of lightsufficient for plant life and enter the photic zone,accelerating the process of primary production in thetop layers. With this aspect we rejoin one of the moststudied aspects of the biological oceanography, theupwelling areas that support important fisheries(Mann and Lazier, l99l and an extensive literature).

THE MANIPULATION OF TURBULENCE

Turbulence has conditioned evolution, and evolu-tion has found ways to adapt to turbulence and even tomanipulate it artfully. Some of the established rela-tions are notorious and particularized. I will never for-get an elegant presentation by Prof. Okubo - includinga mathematical description of the mechanics involved- about the reproductive behavior of a species of fish.After the female has spawned her eggs, the male, inthe apparent possession of a complete if unconsciousknowledge and control of hydrodynamics, extrudes ajet of sperm that, with the help of perfect moves ofbody and fins, take the form of a rotating torus in aposition that might optimize success in fertilization.Natural selection has often succeeded in combiningstructural contraptions and appropriate forms ofbehavior in the field of turbulence, subjected to thegeneral laws of hydrodynamics of water.

This may concern what is known as bioconvec-tion. Excellent examples are provided not only bythe generation of Bénard cells by swimming cells(or flying midges and mosquitos) or by the con-struction and use of quasi-exosomatic devices bymany tube and case dwelling organisms, amongwhich pelagic tunicates excel.

By swimming, an organism introduces deforma-tions and turbulence in the surrounding water. The

water absorbs a large fraction of the energy involvedand often a trail of eddies is generated. Evolution hasled to body shapes that presumably minimize the lossof locomotive energy in feeding such eddies that,moreover, may be undesirable, as they surely couldprovide signals to eventual predators. More generally,selection may led to the development of adaptationsthat allow interpretations of the turbulent trails in thesense of crypsis (played down or misguiding in direc-tion) or of aposematism (exaggerated and menacing).

It has been accepted that evolution has led to thegradual development of mechanically appropriatedprofiles, through at least two selective pressures…(1) the convenience to adopt a shape and a surfacequality that minimizes energy invested in swimming- fishes, already mentioned; and (2) in dampingdown or redirecting advertising trails, that mightattract predators. The study of the body shape offishes provides excellent examples of optimization.In smaller organisms, 0.1-2 mm, for relatively highspeeds (>1 cm s-1), Reynolds’ numbers fall in theturbulent region on which our interest is centered,and in this domain viscosity might work againstrenewal of the most close layers of water, a condi-tion that would seem not the best for the continuityof absorption and of life. The very reasonable con-siderations of Lazier and Mann (1989) point out thatpresent appreciation of such limitations might bemistaken.

There have undoubtably existed and continue tooperate a large number of trade-offs related to shapeand viscosity and concerning the relations betweenevolution, defence and competition. The techniques ofSchlieren show how movement of the legs of cope-pods often leave a trail that forms an angle with theactual trajectory of the body, which posterior partmigh help to erase or to confound trails, and such maybe the main or one of the functions of the furca. On theopposite or receiving end, there is the constant selec-tion pressure on predators to improve quality of pres-sure detectors and analyzers, and one exceptionalexample of such devices is the sword of an extraordi-nary creature, the sword-fish (Xiphias gladius) .

POSSIBLE ORGANIZATION OF HETEROGENEOUS REGIMES OF TURBULENCE OVER SMALL SCALES

One particular mechanism that has been relative-ly overlooked, probably because its reality and effi-ciency have to be more convincingly proved, could

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receive the name of “the turbulence valve”. Its real-ity has to be ascertained and confirmed and its bio-logical importance quantified, but it is likely that indifferent forms is present in many groups of organ-isms, and among them in many representative ofbenthos.

Imagine a small channel prepared for hydrody-namic experiments. Water with small particles insuspension -eventually food particles- flows freelyin an approximately laminar regime, between twolinearizing filters. If turbulence is mechanicallyinjected in the flow, as it may be through irregularpieces of flexible plastic material, kept freely swing-ing in the current, the flow losses linearity and par-ticles may deviate in their trajectories and concen-trate in definite spaces under lower turbulence andslower flow, close or in relation with the large scaleirregular conditions of turbulence that have beencreated. The particles are not driven away with thesame speed or by eventual accelerated veins of floworiginated in the new dynamic regime, so that den-sified clouds “make time” in selected volumes of theexperimental chamber. I do not know of any formaland adequate study of the dynamic lineal or turbu-lent processes involved that could be available orforthcoming. Such experiments might provide anaccess to a new or complementary interpretation ofmany complicated biological structures of unknownmeaning.

Imagine water carrying particles (food algae) insuspension that flows in an approximatively laminarregime through some filter consisting of limbs withsegments, setae and setulae, making a first mobilebarrier of the feeding system of a small creature.Food particles move without difficulty (they aresmaller than the spaces between setae or radii) inlaminar regime through the limbs or setae. If, aftercrossing the first barrier, turbulence is mechanicallyinjected or generated in the suspension, it mighthappen that the laminar flow forward, throughanother filter, or backwards through the same filterrecently crossed in a regime of laminar flow, cannotallow the passage of the particles in suspension, thatare thus separated. That would mean that particles,in the flow now made more turbulent, do not pass soeasily between radii and in consequence a majorityof the particles slow down or are retained and placedin a situation in which they fall under the influenceof some other hydraulic or perhaps mechanicalstructures that, after concentration, might lead totheir final ingestion by the master organism, equipedafter a long evolution with all the contraptions nec-

essary for the feat.Obviously, controlled currents around the body

of worms and crustaceans - perhaps less frequentlyaround other animals - are legion. That such a feat isnot unlikely seems obvious after the observation offilms on the movements of the mouth parts of cope-pods and trying to extrapolate the meaning of exper-iments in small hydrodynamic channels. Such a“turbulence valve” seems to be, I believe, possibleand acceptable, although I do not find it acceptedand much less adequately - that is, hydrodynamical-ly - described in the literature available to me.

Another reason for assuming tentatively theeffectiveness of this “turbulence valve”, or any otherequivalent contraption, appears when sighting thefilms purporting to demonstrate the feeding activi-ties in tethered copepods. They show in general anunbelievably low rate of effective captures, eventaking into account the slow speed of projection,inconsistent with the observation of the guts of“wild” animals, or with the measures of their metab-olism and with the theoretical amount of food nec-essary to keep them alive, and even with the usualestimates of the volumes of water swept clear. Thisis an argument that may carry some weight in favourof exploring neglected ways.

It is easy to anticipate some of the basic featuresthat such a valve of turbulence should have in dif-ferent animals - most of them, but not all of thempresumably arthropods and worms - that generatelaminar flows in water, then turn the flows turbulent,and the food particles in suspension seem to findspontaneously the way to the mouth or to some trav-eling band of mucus; in such situations very few ofthe potential parcels of food travel back and escape.

I recognize that there might be some difficultiesin accepting that a relatively linear and parallel flowof water with suspended particles goes rapidly, with-out slowing noticeably, or perhaps ever slightlyaccelerating a bit, through one external barrier ofsetae with setulae, only to be retained easily againstthe same or similar barriers in inverse trajectorieswhen flow has been made turbulent. More work is,of course, required to clarify the subject or fullyaccept this suggestion.

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