Dynamics of a turbulent layer generated by velocity jump

Abstract

We study a growing turbulent layer generated by the shear between half-spaces of fluid moving with different velocities. The $K$-$\ell $ Kolmogorov theory of turbulence is used, with the closure relation being proportionality of turbulent spatial scale to layer thickness. We show that the turbulent layer exhibits complete self-similarity, that is self-similar dynamics that are independent of initial conditions. A criterion of stability of self-similar regimes is deduced in a simple analytical form. The value of a coefficient entering the closure relation is estimated by matching experimental data.