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Statistical analysis of non-linearities in turbulence

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TURW04 - Wall-bounded turbulence: beyond current boundaries

Recent years have seen significant progress in the analysis of coherent structures in turbulent flows via an input-output framework, where non-linear terms, considered as “forcing”, drive a flow response through the resolvent operator, obtained by a linearisation of the Navier-Stokes system around the mean flow. This leads to models that often provide a good approximation of dominant coherent turbulent structures as the flow responses with maximal amplification by the resolvent. However, accurate quantitative agreement depends on the specific details of the forcing. In this presentation we will explore non-linear terms from simulations of turbulent channel flow and their connection to flow responses. The statistics of such non-linear terms are seen to have low rank, implying that coherent structures are driven by non-linear interactions that are also coherent; this is in contrast with the usual white-noise forcing assumption in linearised models. Non-linear terms are also seen to be approximately self-similar across a broad range of scales. Such properties provide directions to improve existing models of turbulent structures based on the linearised operator, and also to build accurate linear estimators for turbulent flows.

This talk is part of the Isaac Newton Institute Seminar Series series.

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