CNRS-NSF Workshop on
Three-dimensional Stratified and Sheared Turbulent Flows:
Comparison between DNS, LES and Observations

IPSL, Paris, December 19-20th, 2001


Marc Forestier
Laboratoire de Modelisation et de Simulation Numerique en Mecanique, Marseille, France

Numerical study of 3D wakes in stratified fluids, using a spectral multi-domain solver with a penalty method

A high accuracy numerical method associated with a fictitious domain approach has been developped in order to compute the far 3D wake of a obstacle embedded in an incompressible stably stratified fluid. We consider the Navier-Stokes equations in velocity and pressure formulation using the Boussinesq approximation for temperature. The spatial approximation is of spectral type and the method is based on a divergence-free multi-domain solver for velocity and temperature equations. The flow is assumed to be periodic in the z-direction. Thus, in homogeneous direction a Fourier-Galerkin method is used, coupled with a Chebyshev-Chebyshev collocation multi-domain method, streamwise. For the sake of stability, the convective terms associated with the mean flow velocity are handled implicitly. For such semi-open flows, the treatment of artificial outlet boundary is delicate : particularly low pertubative out-flow conditions are hence proposed. The last numerical point comes from the fact that when using spectral method of collocation type, it is difficult to take account of a complex shape. An original adaptation of the penalty method is then used to model the obstacle inside the computational domain. Finally, we show numerical results on the sphere wake in a fluid stably stratified by a thermal gradient. Calculations were carried out in water (Pr=7) for a Reynolds number equal to 300 for two states of stratification defined by the Richardson numbers 0.04 and 0.25 (Re and Ri based on the diameter). Then, these cases are investigated and compared with the one obtained when the temperature behaves like a passive scalar (Ri=0). It shows the collapse phenomenon and its consequences on the behaviour of the flow outside the viscous wake.

 

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