Three-dimensionalization of freely-decaying two-dimensional turbulence

The three-dimensionalization of freely-decaying two-dimensional turbulence is studied numerically. Using two different basic states, it is shown that the hyperbolic instability of steady mixing layers generalizes to unsteady flow. The growth of three-dimensional (3D) perturbations is interpreted in terms of a “pressureless” analysis in which horizontal pressure gradients are neglected and the underlying physical mechanism is advective in nature. For a steady, pressureless base flow the (asymptotic) growth rate is exactly determined, in a few special cases, by variants of the so-called Weiss criterion; more generally, local growth rate estimates are obtained. For freely-decaying two-dimensional turbulence there is analogous behavior: while the 3D perturbation remains small the pressureless approximation holds at large horizontal scales and local growth rate estimates apply. The pressureless modes have a determining influence on the growth (the damping effect of the horizontal pressure gradient is small).