The experiments were carried out at the Hydraulics Laboratory of University “Roma Tre”, in a 3.0 m

long transparent Perspex channel with a 0.2 m wide and 0.3 m deep rectangular cross-section

(Fig.1). A vertical sliding gate is placed in the channel at a distance x0 from the left wall to form a

lock. The right side of the channel is filled with fresh water with density ρ0, whereas the lock is filled

with saline water with density ρ1, both sides filled up at same depth, h0. A controlled quantity of dye

is added to the water in the lock to provide flow visualization.

Fig. 1 Perspex channel. a) perspective view and b) longitudinal view.

When the gate is suddenly removed, a gravity current is established by the dense fluid flowing

under the fresh water. The evolution of the gravity current is recorded by a CCD video camera with

a frequency of 25 Hz kept at a fixed position 5.8 m from the channel. The illumination was made by

means of artificial light. The instantaneous density field of the current was assessed through an

image analysis technique applied to the video frames. These, with 768 x 576 pixel points, were

subsequently converted into gray scale matrices and then converted into instantaneous density

fields of the current through a nonlinear calibration method. Eight different lock-exchange tests

were preformed varying the initial density of the saline water, the water depth and bed roughness.

Herein we present the results for only one experiment (run D1 in the table below).

Table 1 Description of the lock-exchange experiments

The experiments were carried out at the Hydraulics Laboratory of University “Roma Tre”, in a 3.0 m

long transparent Perspex channel with a 0.2 m wide and 0.3 m deep rectangular cross-section

(Fig.1). A vertical sliding gate is placed in the channel at a distance x0 from the left wall to form a

lock. The right side of the channel is filled with fresh water with density ρ0, whereas the lock is filled

with saline water with density ρ1, both sides filled up at same depth, h0. A controlled quantity of dye

is added to the water in the lock to provide flow visualization.

Fig. 1 Perspex channel. a) perspective view and b) longitudinal view.

When the gate is suddenly removed, a gravity current is established by the dense fluid flowing

under the fresh water. The evolution of the gravity current is recorded by a CCD video camera with

a frequency of 25 Hz kept at a fixed position 5.8 m from the channel. The illumination was made by

means of artificial light. The instantaneous density field of the current was assessed through an

image analysis technique applied to the video frames. These, with 768 x 576 pixel points, were

subsequently converted into gray scale matrices and then converted into instantaneous density

fields of the current through a nonlinear calibration method. Eight different lock-exchange tests

were preformed varying the initial density of the saline water, the water depth and bed roughness.

Herein we present the results for only one experiment (run D1 in the table below).

Table 1 Description of the lock-exchange experiments

ANALYSIS OF THE ENTRAINMENT ON LOCK-EXCHANGE GRAVITY CURRENTS

H.I.S. NOGUEIRA1, C. ADDUCE2, E. ALVES3, M.J. FRANCA1,4

1University of Coimbra & IMAR-CMA, Coimbra, Portugal (hnogueira@dec.uc.pt)2 University of Rome “Roma Tre”, Rome, Italy

3 National Laboratory of Civil Engineering, Lisbon, Portugal4 New University of Lisbon & IMAR-CMA, Caparica, Portugal

Density or gravity currents are geophysical flows driven by density differences within a fluid, which

can be caused by temperature differences, dissolved substances or particles in suspension.

Oceanic fronts and turbidity currents in lakes and reservoirs are examples of gravity currents

occurring in masses of water. The latter may occur as a result of human intervention (release of

mineral waste, dredging operations) or spontaneously in nature (flood events, earthquakes) in

natural lakes and in the deep ocean, with significant morphological impacts. The understanding of

the mechanisms involving these large-scale phenomena is thus of extreme importance for the

development of prevention measures against their eventual adverse effects.

In the total mass conservation equation, the entrainment rate of the ambient fluid through the upper

interface becomes a source term requiring a closure model. The entrainment rate may be modeled

as a function of the buoyancy velocity and a characteristic density, and it is usually evaluated

through empirical relations.

Density or gravity currents are geophysical flows driven by density differences within a fluid, which

can be caused by temperature differences, dissolved substances or particles in suspension.

Oceanic fronts and turbidity currents in lakes and reservoirs are examples of gravity currents

occurring in masses of water. The latter may occur as a result of human intervention (release of

mineral waste, dredging operations) or spontaneously in nature (flood events, earthquakes) in

natural lakes and in the deep ocean, with significant morphological impacts. The understanding of

the mechanisms involving these large-scale phenomena is thus of extreme importance for the

development of prevention measures against their eventual adverse effects.

In the total mass conservation equation, the entrainment rate of the ambient fluid through the upper

interface becomes a source term requiring a closure model. The entrainment rate may be modeled

as a function of the buoyancy velocity and a characteristic density, and it is usually evaluated

through empirical relations.

1. Introduction1. Introduction

2. Experimental procedure2. Experimental procedure

The evaluation of the current density distribution was based on Hacker et al.

(1996) technique, which relates light intensity through the current with

concentration of dye present in the flow; this later is considered linearly correlated

with salt concentration within the current body. A calibration procedure was carried out

for each run and for each single pixel to establish the relation between the amount of

dye in the water and the values of gray scale in the frames representing light

intensities. Assuming a direct relation between the amount of dye and the density of

the current, it is thus possible to infer density values at any given pixel and at any

given instant from its instantaneous gray scale value. The estimation of pixel density is

made by means of a cubic interpolation applied to the local calibration curve (Fig. 2).

The evaluation of the current density distribution was based on Hacker et al.

(1996) technique, which relates light intensity through the current with

concentration of dye present in the flow; this later is considered linearly correlated

with salt concentration within the current body. A calibration procedure was carried out

for each run and for each single pixel to establish the relation between the amount of

dye in the water and the values of gray scale in the frames representing light

intensities. Assuming a direct relation between the amount of dye and the density of

the current, it is thus possible to infer density values at any given pixel and at any

given instant from its instantaneous gray scale value. The estimation of pixel density is

made by means of a cubic interpolation applied to the local calibration curve (Fig. 2).

3. Calibration method3. Calibration method

RUNS D1 D2 D3 D4 H1 R1 R2 R3

ρ1 (kg/m3) 1015 1030 1045 1060 1030 1030 1030 1030

h0 (m) 0.20 0.20 0.20 0.20 0.25 0.20 0.20 0.20

ε (mm) 0 0 0 0 0 3.0 10 25

4. Results4. Results 2D Density fields2D Density fields

5. Discussion5. Discussion

This research was supported by the Portuguese Science and Technology Foundation through the

research project PTDC/ECM/099752/2008 and the research grant SFRH/BD/48705/2008.

Financial supportFinancial support

4. Results4. Results Entrainment rateEntrainment rate

The aim of the present work is to experimentally investigate the

entrainment rate of ambient fluid into the region of current

head of unsteady density currents performed by lock-

exchange releases of saline water into a fresh water tank.

The aim of the present work is to experimentally investigate the

entrainment rate of ambient fluid into the region of current

head of unsteady density currents performed by lock-

exchange releases of saline water into a fresh water tank.

a)a)

. 1 . 2 . 3 . 4

. 6. 5 . 7 . 8

Fig. 4 a) Front position, b) front velocity, c) head length, d) mass of the head, e) local and convective terms of MCE and f) entrainment coefficient.Fig. 4 a) Front position, b) front velocity, c) head length, d) mass of the head, e) local and convective terms of MCE and f) entrainment coefficient.

The mass conservation equation (MCE) is presented below in the integral form for a moving and

deforming control volume defining the current head. As our main goal is to estimate the entrainment

rate of ambient fluid into the current head, the convective term, representing the fluxes through the

boundaries in the MCE, was divided in two, representing mass fluxes through the internal and

external boundaries, respectively.

The mass conservation equation (MCE) is presented below in the integral form for a moving and

deforming control volume defining the current head. As our main goal is to estimate the entrainment

rate of ambient fluid into the current head, the convective term, representing the fluxes through the

boundaries in the MCE, was divided in two, representing mass fluxes through the internal and

external boundaries, respectively.

Fig. 3 shows the development of the current captured in three instants and the

corresponding normalized instantaneous density fields . Kelvin-Helmholtz

type instabilities are quite visible at the mixing layer of the current and exhibit a

quasi stationary behaviour. Since the head of the current is a region of higher density,

the criteria used to characterize and isolate this region was based on the product

between the local density, vertically averaged, and current height: .The

upstream limit of the head, and therefore the head length Lf, were defined taking the

position of the local minimum of the function near the front.

Fig. 3 shows the development of the current captured in three instants and the

corresponding normalized instantaneous density fields . Kelvin-Helmholtz

type instabilities are quite visible at the mixing layer of the current and exhibit a

quasi stationary behaviour. Since the head of the current is a region of higher density,

the criteria used to characterize and isolate this region was based on the product

between the local density, vertically averaged, and current height: .The

upstream limit of the head, and therefore the head length Lf, were defined taking the

position of the local minimum of the function near the front.

Lf

KH Billow

Fig. 3 Photos of the current acquired in run D1 and corresponding density fields.

t = 19.6 s

t = 27.6 s

t = 35.6 s

t * = 16.8

t * = 23.7

t * = 30.6

Fig. 2 Example of images used for calibration and corresponding calibration curve obtained for one central pixel of the image represented in the frames by a white dot.Fig. 2 Example of images used for calibration and corresponding calibration curve obtained for one central pixel of the image represented in the frames by a white dot.

•experimental datalinear regression

csint

csext

cv

txhtx ,,

txhtx ,,

𝜌∗ሺ𝑥,𝑧,𝑡ሻ= 𝜌ሺ𝑥,𝑧,𝑡ሻ− 𝜌0𝜌1 − 𝜌0

a)a)

b)b)

c)c)

d)d)

e)e)

f)f)

The front velocity (Fig.4b) was obtained from the front position xf(t) by its derivative in time using

centred finite differences of 2nd order. Front velocity decays linearly, besides the oscillations, which

is in accordance with the shape of the x*f plot (Fig. 4a). As the current advances, the front motion is

characterized by repeated cycles of stretching+break (Fig. 4c and 4d), where mass detachment

from the head towards upstream, into the current body, is observed. This cyclic behaviour (with

period of roughly T* = 1.8) influences consequently the MCE terms (Fig. 4e) and in the entrainment

coefficient (Fig. 4f). Since the internal boundary flux term is positive, conservation of mass implies

that the remaining flux through the external boundary to be negative (inwards),

corresponding to entrainment of water into the current head. Fig. 4f) shows a decreasing

entrainment rate in time, as expected, converging asymptotically to a plateau at Ea = 0.

The front velocity (Fig.4b) was obtained from the front position xf(t) by its derivative in time using

centred finite differences of 2nd order. Front velocity decays linearly, besides the oscillations, which

is in accordance with the shape of the x*f plot (Fig. 4a). As the current advances, the front motion is

characterized by repeated cycles of stretching+break (Fig. 4c and 4d), where mass detachment

from the head towards upstream, into the current body, is observed. This cyclic behaviour (with

period of roughly T* = 1.8) influences consequently the MCE terms (Fig. 4e) and in the entrainment

coefficient (Fig. 4f). Since the internal boundary flux term is positive, conservation of mass implies

that the remaining flux through the external boundary to be negative (inwards),

corresponding to entrainment of water into the current head. Fig. 4f) shows a decreasing

entrainment rate in time, as expected, converging asymptotically to a plateau at Ea = 0.

0dSnudSnudVtDt

Dm

extcscscv

int

external boundary

internal boundary 0b0cs huEaflux

ext

local convective

tzx ,,*

ρ1 ρ0

Lock

Gate

h0

x0

x0

z

3.0 m

0.3 m

b)b)

Fig.4 shows the main results regarding the head dynamics, where length and time are normalized

as following , , being the buoyancy velocity.

Fig.4 shows the main results regarding the head dynamics, where length and time are normalized

as following , , being the buoyancy velocity.0b hgu '0f hxx * 0b hutt *