Timoshin, SN; Smith, FT; (1997) Vortex/inflectional-wave interactions with weakly three-dimensional input. J FLUID MECH , 348 247 - 294. 10.1017/S0022112097006447.

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Abstract

The subtle impact of the spanwise scaling in nonlinear interactions between oblique instability waves and the induced longitudinal vortex field is considered theoretically for the case of a Rayleigh-unstable boundary-layer flow, at large Reynolds numbers. A classification is given of various flow regimes on the basis of Reynolds-stress mechanisms of mean vorticity generation, and a connection between low-amplitude non-parallel vortex/wave interactions and less-low-amplitude non-equilibrium critical-layer flows is discussed in more detail than in previous studies. Two new regimes of vortex/wave interaction for increased spanwise lengthscales are identified and studied. In the first, with the cross-scale just slightly larger than the boundary-layer thickness, the wave modulation is governed by an amplitude equation with a convolution and an ordinary integral term present due to nonlinear contributions from all three Reynolds-stress components in the cross-momentum balance. In the second regime the cross-scale is larger; and the wave modulation is found to be governed by an integral/partial differential equation. In both cases the main-flow non-parallelism contributes significantly to the coupled wave/vortex development.

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