Energy dissipating structures produced by walls in two-dimensional flows at vanishing viscosity
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.
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⟩
Journal: Physical Review Letters
Date de publication: 01-01-2011