Mathematical foundations for mean flow stability analysis

Abstract eng:
This presentation provides theoretical foundations for the use and meaning of a stability analysis around a mean flow. Considering a Reynolds decomposition of the flow field, the Fourier transform of the fluctuation field is found to be equal to the product of the resolvent operator by a turbulent forcing term. If the dominant singular value of the resolvent is much larger than all others, then the Fourier transform of the fluctuation field is directly related to the dominant optimal response mode of the resolvent. In the case of weakly non-parallel flows, the spatial structure of this mode may be approximated by a local spatial stability analysis based on parabolized stability equations (PSE). Results are illustrated for the case of a turbulent backward facing step.

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