Turbulent mixing in shallow water Turbulent mixing in shallow water basins; parameterization ofbasins; parameterization ofvertical turbulent exchange vertical turbulent exchange

coefficientcoefficient

1919thth Congress of Mechanics Congress of Mechanics

2626thth August 2009 August 2009

A.I.Sukhinov, E.V. Alexeenko, A.E.Chistyakov,A.I.Sukhinov, E.V. Alexeenko, A.E.Chistyakov,

B. Roux, P.G. Chen, S. MeuleB. Roux, P.G. Chen, S. Meule

Modeling of turbulence as an Modeling of turbulence as an important mechanism in shallow important mechanism in shallow

water basinswater basins Turbulence in shallow water basins plays Turbulence in shallow water basins plays

important role in many processes of important role in many processes of hydrodynamics such as: transport and hydrodynamics such as: transport and mixing heat, salt, momentum and mixing heat, salt, momentum and suspended and dissolved mattersuspended and dissolved matter

Turbulent fluxes of material occur as a Turbulent fluxes of material occur as a result of correlated, small-scale fluctuations result of correlated, small-scale fluctuations in current velocity and the transport in current velocity and the transport quantity itselfquantity itself

Shallow water basinsShallow water basins

The Azov sea, South of RussiaThe Azov sea, South of RussiaLength of water basin Length of water basin from the west to the from the west to the east/ from the south to east/ from the south to the north :the north : 350 350 kmkm // 250 250 kmkm Maximum depth: Maximum depth: 15 15 mm

Length of water basin Length of water basin from the west to the east/ from the west to the east/ from the south to the from the south to the north :north : 1919 kmkm // 1818 kmkm Maximum depth: 9.2Maximum depth: 9.2 mm

The Etang de Berre, South if FranceThe Etang de Berre, South if France

we are mainly interested by shallow water basins which can be roughly characterized by the we are mainly interested by shallow water basins which can be roughly characterized by the condition: condition: kh < 1 (2π h< λ), where where k -wave number of the wave, -wave number of the wave, h - height of the water column, - height of the water column, λ - wave length. - wave length.

Average depth of the Azov sea is about 8 m, for Etang de Berre - 6 m, what correspond to Average depth of the Azov sea is about 8 m, for Etang de Berre - 6 m, what correspond to wave length – 40m . According to satellite photos wave lengths are not more than this value. wave length – 40m . According to satellite photos wave lengths are not more than this value.

Expeditions in the Lagoon Etang de BerreExpeditions in the Lagoon Etang de Berre

• Three expeditions (20Three expeditions (20  Sept.Sept.  2006, 2006, 2828  Sept.Sept.  2006 and June 2008) was 2006 and June 2008) was executed by REC ofexecuted by REC of  thethe  SouthSouth  ofof  Russia Russia inin  cooperation withcooperation with  L3M/CNRSL3M/CNRS  laboratory laboratory (the group of Prof. B. Roux) and(the group of Prof. B. Roux) and  SIBOJAI SIBOJAI Environmental Service in the Etang de Environmental Service in the Etang de Berre and Etang de Bolmon. Berre and Etang de Bolmon.

ADCP Workhorse ADCP Workhorse 600 Sentinel600 Sentinel• Depth range 70 Depth range 70

m.m.• Frequency 600 Frequency 600

kHz.kHz.• Measure Measure

precision precision 0,25%0,25%

Numerical simulation of turbulent coefficientNumerical simulation of turbulent coefficient (two methods are considered)(two methods are considered)

1/ 22 2

2( )U V

c zz z

Pulsations of velocity components was spread out in Taylor series: 2 2

2

( ) ( )( ) ( ) ..... ( )

2!x

x

lU z U zu z U z l U z

z z

( )( ) x

U zu z l

z

( ) ( )x ZZx

U z U zu w l w K

z z

2 2

2

( ) ( )( ) ( ) ..... ( )

2!y

y

lV z V zv z V z l V z

z z

( )( ) y

V zv z l

z

( ) ( )y ZZy

V z V zv w l w K

z z

2 2( ) ( )ZZx ZZyK z K z

1) method of Monin1) method of Monin::

2) method of Belotserkovskii2) method of Belotserkovskii::

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Coefficient (mCoefficient (m22/s)/s)

1-st method1-st method 2-nd method 2-nd method

Distributions of the coefficient of Distributions of the coefficient of vertical turbulent exchange vertical turbulent exchange

blue lineblue line – –result of numerical simulationresult of numerical simulation, , red dash linered dash line – – result of measurementsresult of measurements

Point 2 Point 5 Point 6

Parameterisation of Belotserkovskii was included as a module in Parameterisation of Belotserkovskii was included as a module in Azov3d-model for calculation evolution of 3D currents in shallow water Azov3d-model for calculation evolution of 3D currents in shallow water basins.basins.• Results of modeling were compared with results of measurements Results of modeling were compared with results of measurements during expedition in the lagoon Etang de Berre in September 2006during expedition in the lagoon Etang de Berre in September 2006

Coefficient (mCoefficient (m22/s)/s)

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MARS3DMARS3D

boundary value problem for boundary value problem for lagoon lagoon Etang de BerreEtang de Berre

MARS3D for Etang de Berre (Caronte inflow, EDF, Western Wind)MARS3D for Etang de Berre (Caronte inflow, EDF, Western Wind)vector fieldsvector fields (palette – square of module of horizontal velocity)(palette – square of module of horizontal velocity)

Model of Mars3d adopted to shallow water basins and based on solving equationsModel of Mars3d adopted to shallow water basins and based on solving equations::Navier-Stokes equationsNavier-Stokes equations

+Boussinesq approximation+Boussinesq approximation+ hydrostatic assumption for pressure+ hydrostatic assumption for pressure+ parameterization of turbulent viscosity+ parameterization of turbulent viscosity+ equations of thermodynamics+ equations of thermodynamics

calculation in calculation in σσ-coordinate adopted to free surface -coordinate adopted to free surface and bottom vertical gridand bottom vertical grid

Barotropic flowBarotropic flow Near free surface flowNear free surface flow Near bottom flowNear bottom flow

Evolution of general barotropic Evolution of general barotropic currents in the lagooncurrents in the lagoon

One day after the begining of simulationOne day after the begining of simulation Two days after the begining of simulationTwo days after the begining of simulation

Three days after the begining of simulationThree days after the begining of simulation

Numerical vector fields Numerical vector fields superpossuperposed ed withwith results of expedresults of expediition in September 2006 tion in September 2006 Qualitatively we have similar directions of currents in the place of the main Qualitatively we have similar directions of currents in the place of the main

vortexvortex

Vertical profiles of horizontal velocity components are similar with Vertical profiles of horizontal velocity components are similar with measurements in 4 control points (station - 2, 5, 6, 7) from 8. This result measurements in 4 control points (station - 2, 5, 6, 7) from 8. This result means, that we need to calibrate configuration and also to do more means, that we need to calibrate configuration and also to do more measurements for having data in more points of the lagoon Etang de Berremeasurements for having data in more points of the lagoon Etang de Berre

Measured currentsMeasured currentsnear the free surface – red arrowsnear the free surface – red arrows, , near the bottom – yellow arrowsnear the bottom – yellow arrows

Mars3D cMars3D currents urrents near near the the free surfafree surfaccee

Mars3D cMars3D currents urrents near near the bottom surfacethe bottom surface

1122

33

44

55 66

77

88

Quantitative comparison of approachesQuantitative comparison of approaches of Mars3Dof Mars3D with results of expedition with results of expedition

With Belotserkivskii approximationWith Belotserkivskii approximation With Prandt approximationWith Prandt approximation With Mellor-Yamada approximation (2 eq.)With Mellor-Yamada approximation (2 eq.)

near the free surfacenear the free surface near the free surfacenear the free surface near the free surfacenear the free surface

near the bottomnear the bottom near the bottomnear the bottom near the bottomnear the bottom

Application of model Mars3D Application of model Mars3D with parameterization of vertical with parameterization of vertical

turbulent exchange turbulent exchange Configuration of Mars3d with Belotsercovskii Configuration of Mars3d with Belotsercovskii

parameterizaton of vertical turbulent exchange parameterizaton of vertical turbulent exchange was applied for research structure of currents in was applied for research structure of currents in the lagoon Etang de Berre for understanding and the lagoon Etang de Berre for understanding and solving ecological problem in this lagoon.solving ecological problem in this lagoon.

After installation in the EDF-Channel hydroelectric-After installation in the EDF-Channel hydroelectric-station, big volumes of fresh water are entering station, big volumes of fresh water are entering during last 50 years in the waters of the lagoonduring last 50 years in the waters of the lagoon

This change affected ecology of the lagoon.This change affected ecology of the lagoon. TThere here wawas a strong desalination s a strong desalination during last 50 during last 50

years and many aquatic plants disappeared near years and many aquatic plants disappeared near coastline coastline

TIDE, WIND and EDF-inflow + parameterization of vertical TIDE, WIND and EDF-inflow + parameterization of vertical turbulent exchange in one simulationturbulent exchange in one simulation

Barotropic currents associated with fast propagating waves (tide Barotropic currents associated with fast propagating waves (tide waves) waves)

wind – mistral N-NW 5 m/s, EDF-inflow (200 mwind – mistral N-NW 5 m/s, EDF-inflow (200 m33/s)/s)

Point of Berre (zoom)Point of Berre (zoom)TIDE, WIND and EDF-inflow in one simulationTIDE, WIND and EDF-inflow in one simulation

Barotropic currents associated with fast propagating waves (tide Barotropic currents associated with fast propagating waves (tide waves) waves)

wind – mistral N-NW, EDF-inflow (200 mwind – mistral N-NW, EDF-inflow (200 m33/s)/s)

Near the boundary where aquatic plants during last 50 years disappeared we can see intensive currents which could destroy flora of these places

Point of BerrePoint of Berresuperposition of barocurrents and zones of Zoosteres superposition of barocurrents and zones of Zoosteres

corresponding to data of 1944, 1992, 2004corresponding to data of 1944, 1992, 2004 (GIPREB) (GIPREB) for NW-wind (mistral)for NW-wind (mistral)

Simulation in the Point of BerreSimulation in the Point of Berre(resolution 1 m)(resolution 1 m)

Bathymetry of the Point de Berre (1m resolution), received during

expedition measurements in the June 2009 by GPS (CEREGE, Samuel Meulé )

Point of BerrePoint of Berrecurrents in the layer near the bottom currents in the layer near the bottom

(20-40 cm from the bottom)(20-40 cm from the bottom)