WKB theory for rapid distortion of inhomogeneous turbulence

A WKB method is used to extend RDT (rapid distortion theory) to initially i nhomogeneous turbulence and unsteady mean flows. The WKB equations describe turbulence wavepackets which are transported by the mean velocity and have wavenumbers which evolve due to the mean strain. The turbulence also modif ies the mean flow and generates large-scale vorticity via the averaged Reyn olds stress tensor. The theory is applied to Taylor's four-roller flow in o rder to explain the experimentally observed reduction in the mean strain. T he strain reduction occurs due to the formation of a large-scale vortex qua drupole structure from the turbulent spot confined by the four rollers. Bot h turbulence inhomogeneity and three-dimensionality are shown to be importa nt for this effect. If the initially isotropic turbulence is either homogen eous in space or two-dimensional, it has no effect on the large-scale strai n. Furthermore, the turbulent kinetic energy is conserved in the two-dimens ional case, which has important consequences for the theory of two-dimensio nal turbulence. The analytical and numerical results presented here are in good qualitative agreement with experiment.