Spectral transfers in two-dimensional anisotropic flow

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Abstract
Nonlinear transfers of kinetic energy and enstrophy in the unidimensional Fourier spectrum that is obtained in a two-dimensional shear flow are investigated. Detailed conservation laws reveal the existence of closed pairs of transfers that involve a source mode, a recipient mode, and an advecting mode, which mediates the interaction but is not directly affected by it. The methodology of spectral transfer diagnosis is applied in the study of two simple, linearly unstable, initially parallel shear flows, namely the Bickley jet and the hyperbolic-tangent shear layer. In each case, the transfer spectra are found to be dominated by wave–mean flow interactions and by downscale cascades that are associated with vortex mergers. Cascades are driven by the advective deformation of small eddies by the large-scale vortices (i.e., filamentation), and appear in the transfer function maps as local transfers driven by nonlocal interactions.