Resolvent analysis of spatially developing hypersonic boundary layers: A study of freestream acoustic waves

The Resolvent analysis is applied to a hypersonic streamwise developing zero pressure gradient boundary layer (ZPGBL), where-in we focus on the study of freestream propagating pressure waves. The Resolvent analysis is a reformulation of the Navier-Stokes (NS) where we linearise around a 2-D mean state (function of streamwise and wall-normal direction) and consider the non-linear terms to be an unknown forcing to the linear terms, thus obtaining a linear model. We compare the freestream propagating waves obtained as responses from the resolvent to those that were obtained as an optimal linear response from the resolvent analysis around the 1-D mean flow (function of wall-normal direction alone) by Bae et al. (J. Fluid Mech., vol. 883, 2020, pp. 336-382, pp. A29). These freestream propagating acoustic waves were derived as solutions to the 1-D Linearized NS equations for a ZPGBL by Mack (California Inst of Tech Pasadena Jet Propulsion Lab, 1984.). Further, the findings of Mack have been found to be consistent with experimental and subsequent numerical observations. In the present study, we analyze the effects of the streamwise development of the hypersonic boundary layer on the freestream propagating waves and study how spatial dependence affects the generation of these waves.