Energy dissipating structures in turbulent boundary layers

We present 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 $Rey$-independent values, indicating the existence of energy dissipating structures that persist in the vanishing viscosity limit. Details can be found in Nguyen van yen, Farge and Schneider, PRL, {\bf 106}, 184502 (2011).