Dynamics of a turbulent layer generated by velocity jump

D. V. Strunin, A. J. Roberts


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.

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DOI: https://doi.org/10.21914/anziamj.v44i0.704

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ANZIAM Journal, ISSN 1446-8735, copyright Australian Mathematical Society.