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Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity

Abstract : We perform numerical experiments of a dipole crashing into a wall, a generic event in two-dimensional incompressible flows with solid boundaries. The Reynolds number (Re) is varied from 985 to 7880, and no-slip boundary conditions are approximated by Navier boundary conditions with a slip length proportional to Re(-1). Energy dissipation is shown to first set up within a vorticity sheet of thickness proportional to Re(-1) in the neighborhood of the wall, and to continue as this sheet rolls up into a spiral and detaches from the wall. The energy dissipation rate integrated over these regions appears to converge towards Re-independent values, indicating the existence of energy dissipating structures that persist in the vanishing viscosity limit.
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https://hal.archives-ouvertes.fr/hal-01022604
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Submitted on : Thursday, January 13, 2022 - 11:18:50 AM
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physrevlett.106.184502.pdf
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Distributed under a Creative Commons Attribution 4.0 International License

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Romain Nguyen van Yen, Marie Farge, Kai Schneider. Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity. Physical Review Letters, American Physical Society, 2011, 106, pp.184502. ⟨10.1103/PhysRevLett.106.184502⟩. ⟨hal-01022604⟩

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