Prediction of resolvent mode shapes in supersonic turbulent boundary layers
This work applies resolvent analysis to compressible zero-pressure-gradient turbulent boundary layers with freestream Mach numbers between 2 and 4, focusing exclusively on large scale motions in the outer region of the boundary layer. We investigate the effects of Mach number on predicted flow structures, and in particular, look at how such effects may be attributed to changes in mean properties. By leveraging the similarity between the compressible and incompressible resolvent operators, we show that the shape of the streamwise velocity and temperature components of resolvent response modes in the compressible regime can be approximated by applying ideas from wavepacket pseudospectral theory to a simple scalar operator. This gives a means of predicting the shape of resolvent mode components for compressible flows without requiring the singular value decompositions of discretized operators. At a Mach number of 2, we find that accurate results are obtained from this approximation when using the compressible mean velocity profile. At Mach numbers of 3 and 4, the quantitative accuracy of these predictions is improved by also considering a local effective Reynolds number based on the local mean density and viscosity.
© 2020 Elsevier Inc. Received 13 April 2020, Revised 27 July 2020, Accepted 9 August 2020, Available online 3 September 2020. The authors thank H. Jane Bae for insightful comments and suggestions on an earlier version of this manuscript, and X. Wu for generously sharing his incompressible turbulent boundary layer DNS data. This work was supported by the Air Force Office of Scientific Research [Grant No. FA9550-16-1-0232], program manager Ivett Leyva. CRediT authorship contribution statement: Scott T. M. Dawson: Conceptualization, Methodology, Software, Validation, Formal analysis, Investigation, Writing - original draft, Visualization. Beverley J. McKeon: Conceptualization, Methodology, Resources, Writing - review & editing, Supervision, Project administration, Funding acquisition. The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.