Turbulent mixing in shallow water basins parameterization of vertical turbulent exchange coefficient

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Turbulent mixing in shallow water basins
parameterization ofvertical turbulent exchange
coefficient

• 19th Congress of Mechanics
• 26th August 2009

A.I.Sukhinov, E.V. Alexeenko, A.E.Chistyakov, B.
Roux, P.G. Chen, S. Meule
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Modeling of turbulence as an important mechanism
in shallow water basins

• Turbulence in shallow water basins plays
  important role in many processes of hydrodynamics
  such as transport and mixing heat, salt,
  momentum and suspended and dissolved matter
• Turbulent fluxes of material occur as a result of
  correlated, small-scale fluctuations in current
  velocity and the transport quantity itself

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Shallow water basins
we are mainly interested by shallow water basins
which can be roughly characterized by the
condition kh lt 1 (2p hlt ?), where k -wave
number of the wave, h - height of the water
column, ? - wave length. 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.
The Azov sea, South of Russia
The Etang de Berre, South if France
Length of water basin from the west to the east/
from the south to the north 350 km / 250 km
Maximum depth 15 m
Length of water basin from the west to the east/
from the south to the north 19 km / 18 km
Maximum depth 9.2 m
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Expeditions in the Lagoon Etang de Berre

• ADCP Workhorse 600 Sentinel
• Depth range 70 m.
• Frequency 600 kHz.
• Measure precision 0,25

• Three expeditions (20 Sept. 2006, 28 Sept. 2006
  and June 2008) was executed by REC
  of the South of Russia in cooperation
  with L3M/CNRS laboratory (the group of Prof. B.
  Roux) and SIBOJAI Environmental Service in the
  Etang de Berre and Etang de Bolmon.

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Numerical simulation of turbulent coefficient
(two methods are considered)?
1) method of Monin
Pulsations of velocity components was spread out
in Taylor series
1-st method 2-nd method
2) method of Belotserkovskii
Decreasing of free surface level
Coefficient (m2/s)?
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Distributions of the coefficient of vertical
turbulent exchange

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

Point 2
Point 5
Point 6
Decreasing of free surface level
Decreasing of free surface level
Decreasing of free surface level
Coefficient (m2/s)?
blue line result of numerical simulation, red
dash line result of measurements
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MARS3Dboundary value problem for lagoon Etang
de Berre
Model of Mars3d adopted to shallow water basins
and based on solving equations Navier-Stokes
equations Boussinesq approximation
hydrostatic assumption for pressure
parameterization of turbulent viscosity
equations of thermodynamics calculation in
s-coordinate adopted to free surface and bottom
vertical grid
MARS3D for Etang de Berre (Caronte inflow, EDF,
Western Wind)? vector fields (palette square of
module of horizontal velocity)
Barotropic flow
Near free surface flow
Near bottom flow
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Evolution of general barotropic currents in the
lagoon
One day after the begining of simulation
Two days after the begining of simulation
Three days after the begining of simulation
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Numerical vector fields superposed with results
of expedition in September 2006

• Qualitatively we have similar directions of
  currents in the place of the main vortex
• Vertical profiles of horizontal velocity
  components are similar with 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 measurements
  for having data in more points of the lagoon
  Etang de Berre

Measured currents near the free surface red
arrows, near the bottom yellow arrows
Mars3D currents near the free surface
Mars3D currents near the bottom surface
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5
6
3
8
2
1
7
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Quantitative comparison of approaches of Mars3D
with results of expedition
With Belotserkivskii approximation
With Prandt approximation
With Mellor-Yamada approximation (2 eq.)
near the free surface
near the free surface
near the free surface
near the bottom
near the bottom
near the bottom
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Application of model Mars3D with parameterization
of vertical turbulent exchange

• Configuration of Mars3d with Belotsercovskii
  parameterizaton of vertical turbulent exchange
  was applied for research structure of currents in
  the lagoon Etang de Berre for understanding and
  solving ecological problem in this lagoon.
• After installation in the EDF-Channel
  hydroelectric-station, big volumes of fresh water
  are entering during last 50 years in the waters
  of the lagoon
• This change affected ecology of the lagoon.
• There was a strong desalination during last 50
  years and many aquatic plants disappeared near
  coastline

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TIDE, WIND and EDF-inflow parameterization of
vertical turbulent exchange in one
simulationBarotropic currents associated with
fast propagating waves (tide waves) wind
mistral N-NW 5 m/s, EDF-inflow (200 m3/s)
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Point of Berre (zoom)TIDE, WIND and EDF-inflow
in one simulationBarotropic currents associated
with fast propagating waves (tide waves) wind
mistral N-NW, EDF-inflow (200 m3/s)
Near the boundary where aquatic plants during
last 50 years disappeared we can see intensive
currents which could destroy flora of these places
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Point of Berresuperposition of barocurrents and
zones of Zoosteres corresponding to data of 1944,
1992, 2004 (GIPREB) for NW-wind (mistral)
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Simulation in the Point of Berre(resolution 1
m)
Bathymetry of the Point de Berre (1m
resolution), received during expedition
measurements in the June 2009 by GPS (CEREGE,
Samuel Meulé )
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Point of Berrecurrents in the layer near the
bottom (20-40 cm from the bottom)