Exact coherent structures in shear flows

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The free-stream coherent structure theory developed by Deguchi & Hall (2014a), valid in the large Reynolds number asymptotic limit, will be extended to compressible flows and applied to jet flows. It was shown in the above paper that a nonlinear coherent structure can be supported at the edge of the jet, and the structure induces a much bigger streaky flow in the centre of the jet. In the presence of compressible effects the coherent structure can act as a source of acoustic radiation and might well be implicated in the high frequency 'screeching' tones of a compressible jet.In addition vortex-wave interactions capable of supporting other types of canonical exact coherent structures will be investigated in the compressible regime. Compressible shear flows are susceptible to inviscid instabilities when their incompressible counterparts are stable and so the likely vortex-wave interactions in a compressible flow will be quite different than the incompressible case.Both projects concern the development of sophisticated asymptotic procedures to reduce the full unsteady Navier Stokes equations to a simpler form where relatively simple numerical methods can be used to solve the reduced problem. The work will be applicable to a wide range of laminar and turbulent compressible shear flows.