Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity |
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Authors: | Nguyen van Yen Romain Farge Marie Schneider Kai |
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Institution: | LMD-CNRS-IPSL, école Normale Supérieure, Paris, France. |
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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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