Exact coherent structures in shear flows

由Deguchi & Hall（2014 a）开发的自由流相干结构理论在大雷诺数渐近极限下有效，将扩展到可压缩流并应用于射流。上述文献表明，在射流边缘可以支持一个非线性拟序结构，并且该结构在射流中心诱导出更大的条纹流。在可压缩效应的存在下，相干结构可以作为声辐射的源，并且很可能与可压缩射流的高频“尖叫”音有关。此外，在可压缩区域中，将研究能够支持其他类型的正则精确相干结构的涡波相互作用。可压缩剪切流对无粘不稳定性很敏感，而不可压缩剪切流是稳定的，因此在可压缩流中可能的涡波相互作用与不可压缩情况有很大的不同，这两个项目都涉及发展复杂的渐近程序，以将完整的非定常Navier Stokes方程简化为一个较简单的形式，其中相对简单的数值方法可以用来解决简化的问题。这项工作将适用于广泛的层流和湍流可压缩剪切流。

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.