Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
184 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
45 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

A shallow water model for magnetohydrodynamic flows with turbulent Hartmann layers (2006.03855v1)

Published 6 Jun 2020 in physics.flu-dyn

Abstract: We establish a shallow water model for flows of electrically conducting fluids in homogeneous static magnetic fields that are confined between two parallel planes where turbulent Hartmann layers are present. This is achieved by modelling the wall shear stress in these layers using the Prandtl's mixing length model, as did the authors of Albousssi`ere & Lingwood (Phys. Fluids, 2000). The idea for this new model arose from the failure of previous shallow water models that assumed a laminar Hartmann layer to recover the correct amount of dissipation found in some regimes of the MATUR experiment. This experiment, conducted by the authors of Messadek & Moreau (J. Fluid Mech. 2002), consisted of a thin layer of mercury electrically driven in differential rotation in a transverse magnetic field. Numerical Simulations of our new model in the configuration of this experiment allowed us to recover experimental values of both the global angular momentum and the local velocity up to a few percent when the Hartmann layer was in a sufficiently well developed turbulent state. We thus provide an evidence that the unexplained level of dissipation observed in MATUR in these specific regimes was caused by turbulence in the Hartmann layers. A parametric analysis of the flow, made possible by the simplicity of our model, also revealed that turbulent friction in the Hartmann layer prevented quasi-2D turbulence from becoming more intense and limited the size of the large scales.

Summary

We haven't generated a summary for this paper yet.