Vortex-merger statistical-mechanics model for the late time self-similar evolution of the Kelvin–Helmholtz instability

The nonlinear growth, of the multimode incompressible Kelvin-Helmholtz shear flow instability at all density ratios is treated by a large-scale statistical-mechanics eddy-pairing model that is based on the behavior of a single eddy and on the two eddy pairing process. From the model, a linear time growth of the mixing zone is obtained and the linear growth coefficient is derived for several density ratios. Furthermore, the asymptotic eddy size distribution and the average eddy life time probability are calculated. Very good agreement with experimental results and full numerical simulations is achieved. (C) 2003 American Institute of Physics.