Dispersion due to Dispersion due to meanderingmeandering

Dean Vickers, Larry MahrtDean Vickers, Larry MahrtCOAS, Oregon State UniversityCOAS, Oregon State University

Danijel BelušićDanijel BelušićAMGI, Department of Geophysics, University of AMGI, Department of Geophysics, University of

ZagrebZagrebdbelusic@irb.hrdbelusic@irb.hr

OverviewOverview

IntroductionIntroduction (long) (long) Particle mParticle modelodel Dispersion due to mDispersion due to meanderingeandering Meandering vs. turbulenceMeandering vs. turbulence

Meandering introMeandering intro

Meandering = mesoscale wind Meandering = mesoscale wind direction variation direction variation

Usually recognized byUsually recognized by and studied in and studied in terms ofterms of its effects on dispersion in its effects on dispersion in stable weak-wind ABLstable weak-wind ABL

Unknown dynamicsUnknown dynamics

Turbulence vs. mesoscaleTurbulence vs. mesoscale

Modeling transient mesoscale Modeling transient mesoscale motionsmotions

Regional models, LES modelsRegional models, LES models,, etc etc.. do do not include the common transient not include the common transient mesoscale motions:mesoscale motions:

1.1. Not resolvedNot resolved

2.2. Physics missingPhysics missing

3.3. Eliminated by explicit or implicit Eliminated by explicit or implicit numerical diffusion.numerical diffusion.

Types of small mesoscale Types of small mesoscale motionsmotions

1.1. Gravity flows (sometimes Gravity flows (sometimes multiple flows superimposed)multiple flows superimposed)

2.2. Flow distortion by Flow distortion by tterrain/obstacleserrain/obstacles

3.3. Transient mesoscale motions Transient mesoscale motions (gravity waves, meandering)(gravity waves, meandering)

4.4. Nonstationary low-level jetsNonstationary low-level jets

5.5. SolitonsSolitons

Based on 14 eddy-correlation datasets, Based on 14 eddy-correlation datasets, the the strength of mesoscale motions are:strength of mesoscale motions are:

Not related to uNot related to u**, z/L, Ri or wind speed, z/L, Ri or wind speed Can be greater in complex terrain Can be greater in complex terrain

although less in thermally generated although less in thermally generated circulations.circulations.

Different types of mesoscale motions may Different types of mesoscale motions may have quite different dispersive behavior.have quite different dispersive behavior.

NOT PREDICTABLENOT PREDICTABLE

Effects on dispersionEffects on dispersion (1) (1)

Vv

To a first approximation, the variation of To a first approximation, the variation of wwind direction ind direction σσθθ is inversely proportional is inversely proportional to the mean wind speed:to the mean wind speed:

and is usually parameterized in models as:and is usually parameterized in models as:

V

const~

Indeed…Indeed…

Effects on dispersionEffects on dispersion (2) (2)

xV

const

xy

Therefore, Therefore, σσθθ (i.e. meandering) is (i.e. meandering) is significant only in weak windssignificant only in weak winds

The lateral dispersion is then:The lateral dispersion is then:

Effects on dispersionEffects on dispersion (3) (3)

Now, the parameterizations actually Now, the parameterizations actually state that the variability of cross-wind state that the variability of cross-wind component component σσvv is constant is constant not not completely true, but it is independent completely true, but it is independent of of V V and stabilityand stability

Effects on dispersionEffects on dispersion (4) (4)

tV

x

vy

vy

&

What does that actually mean?What does that actually mean?

The dispersion due to meandering does The dispersion due to meandering does NOT depend on wind speed and stability?!NOT depend on wind speed and stability?!

Effects on dispersionEffects on dispersion (5) (5)

Let’s compare the two expressions:Let’s compare the two expressions:

t

x

vy

y

Space or time??Space or time??

In time, the dispersion due to In time, the dispersion due to meandering does NOT depend on meandering does NOT depend on wind speed nor stability.wind speed nor stability.

Particle modelParticle model

Lagrangian stochastic particle modelLagrangian stochastic particle model Particle position updated as Particle position updated as

Xp(t+dt) = Xp(t) + (U+u’)dt Xp(t+dt) = Xp(t) + (U+u’)dt Turbulence described by a Markov Turbulence described by a Markov

Chain Monte Carlo process with one Chain Monte Carlo process with one step memory:step memory:

Wind field for particle modelsWind field for particle models

Observed from single mast (assume Observed from single mast (assume spatially homogeneous)spatially homogeneous)

Mesoscale modelMesoscale model LES modelLES model Observed using a tower network (this Observed using a tower network (this

study)study)

Observations CASES-99Observations CASES-99

Grassland in rural Kansas in OctoberGrassland in rural Kansas in October Seven towers inside circle of radius Seven towers inside circle of radius

300 m300 m 13 sonic anemometers 13 sonic anemometers 20-hz 20-hz

(u,v,w,T)(u,v,w,T) Site has weak meandering (ranked Site has weak meandering (ranked

88thth out of 9 sites studied) out of 9 sites studied)

CASES-99 networkCASES-99 network

Wind fieldWind field

High temporal resolution (no High temporal resolution (no interpolation required)interpolation required)

Meandering wind components and Meandering wind components and the turbulence velocity variances are the turbulence velocity variances are spatially interpolated in 3-D every spatially interpolated in 3-D every time steptime step

Meandering resolved!Meandering resolved!

Decomposition Decomposition

Velocity variances are partitioned into Velocity variances are partitioned into meandering and turbulence based on meandering and turbulence based on the time scale associated with the gap the time scale associated with the gap region in the heat flux multiresolution region in the heat flux multiresolution cospectra cospectra

Turbulence and meandering are Turbulence and meandering are generated by different physics and generated by different physics and have different influences on the plumehave different influences on the plume

AnimationsAnimations

Case studies showCase studies show

Spatial streaks and bimodal patterns in the Spatial streaks and bimodal patterns in the 1-h average distribution1-h average distribution

Double maximum patterns with higher C on Double maximum patterns with higher C on the plume edges and minimum C on plume the plume edges and minimum C on plume centerlinecenterline

Wind direction often jumps between Wind direction often jumps between preferred modes rather than oscillate back preferred modes rather than oscillate back and forthand forth

Time series are highly non-stationary even Time series are highly non-stationary even when 1-h average distribution is ~ Gaussianwhen 1-h average distribution is ~ Gaussian

Removing record-mean flowRemoving record-mean flow

Particles leave the tower network domain Particles leave the tower network domain too quickly with any significant mean too quickly with any significant mean wind, so the record-mean wind is removedwind, so the record-mean wind is removed

Removing mean wind has a huge impact Removing mean wind has a huge impact on the spatial distribution, however, it has on the spatial distribution, however, it has little impact on the travel-time little impact on the travel-time dependence of particle dispersion (verified dependence of particle dispersion (verified using particle simulator)using particle simulator)

This allows us to look at all the records This allows us to look at all the records including the stronger wind speedsincluding the stronger wind speeds

Measure of particle dispersionMeasure of particle dispersion

Travel time dependence of particle Travel time dependence of particle dispersion computed asdispersion computed as

σσxx22 = [(X = [(Xpp(t)(t) -- [X[Xpp(t)])(t)])22],],

where t is travel time and brackets denote where t is travel time and brackets denote an average over all particlesan average over all particles

E.g., for 1-h records there are 72,000 E.g., for 1-h records there are 72,000 samples of Xsamples of Xpp for all travel times for all travel times

σσxxyy = ( = (σσxx22 + + σσyy

22))½½

The entire dataset showsThe entire dataset shows

The meandering motions, not the turbulence, The meandering motions, not the turbulence, are primarily responsible for the horizontal are primarily responsible for the horizontal dispersion, and streaks, bimodal patterns and dispersion, and streaks, bimodal patterns and non-stationary time series are a consequencenon-stationary time series are a consequence

Meandering dominates in weak winds, strong Meandering dominates in weak winds, strong winds, stable and unstable conditionswinds, stable and unstable conditions

Tracer experiments cannot measure the Tracer experiments cannot measure the travel time dependence and therefore they travel time dependence and therefore they suggest that meandering is only important in suggest that meandering is only important in weak windsweak winds

ProblemsProblems

Horizontal dispersion is parameterized in Horizontal dispersion is parameterized in terms of turbulence, while terms of turbulence, while meandering meandering dominates horizontal dispersiondominates horizontal dispersion (and has (and has different properties than the turbulence)different properties than the turbulence)

Regional models under-represent Regional models under-represent meandering motionsmeandering motions

While While σσxxyy = f( = f(σσuvMuvM ) works well, such a ) works well, such a velocity scale is not available in models, velocity scale is not available in models, nor does it appear predictable, nor is it nor does it appear predictable, nor is it very useful since distributions are highly very useful since distributions are highly non-Gaussiannon-Gaussian