Prediction of resolvent mode shapes in supersonic turbulent boundary layers

• Published in: The International journal of heat and fluid flow Vol. 85; p. 108677
• Main Authors: Dawson, Scott T.M., McKeon, Beverley J.
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 01.10.2020
• Subjects: Coherent structures; Compressible flows; Large scale motions; Nonmodal stability analysis; Resolvent analysis; Turbulent boundary layers; Coherent structures; Resolvent analysis; Large scale motions; Compressible flows; Turbulent boundary layers; Nonmodal stability analysis
• ISSN: 0142-727X; 1879-2278
• DOI: 10.1016/j.ijheatfluidflow.2020.108677

•Resolvent analysis of supersonic boundary layers to study large scale motions.•Amplification mechanisms for large scale motions similar to incompressible flows.•Effects of compressibility largely due to changes in mean properties.•Streamwise velocity and temperature components predicted from scalar equation.•Shape of resolvent mode components predicted analytically. 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.