Wave Back-Interaction on Inviscid Shear Flows.
MASSACHUSETTS INST OF TECH CAMBRIDGE FLUID DYNAMICS RESEARCH LAB
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The nonlinear interaction between a slowly varying wavetrain and an inviscid shear flow is treated by a Whitham-type averaging of the oscillations over a rapidly varying phase variable and integration over the modal cross-space of the basic fluid-dynamical conservation laws. The modulation equations so derived together with a kinematic requirement for wave conservation govern coupled nonlinear changes between wave and mean flow variables, and extend Whithams ideans for irrotational mean flows to waves riding on inviscid shear flows. the key idea in the analysis is an additional Stuart-Watson type shape assumption for the mean flow to account for wave-induced distortions to the basic shape of the mean velocity profile. The Ansatz used is based on the local picture furnished by inviscid, nonlinear normal mode theory, this description being representative of truly slowly varying flows. Some applications are given and some possible physical consequencies of the theory are discussed. Author
- Numerical Mathematics
- Fluid Mechanics