Stochastic receptivity of laminar compressible boundary layers: an input-output analysis
Résumé
This study extends the input-output framework for the receptivity analysis of an incompressible boundary layer introduced by Ran et al. (Stochastic receptivity analysis of boundary
layer flow Phys. Rev. Fluids. 4, 093901, 2019) to the laminar adiabatic supersonic case.
Spatially distributed in the wall-normal direction, a delta-correlated Gaussian noise is considered as input, both including the velocity and temperature fields. Similarly, components
of the resulting velocity and/or temperature fields are chosen as outputs. To study effects on
the boundary layer the measurements of the output are restricted within the δ 99 boundary
layer thickness implying, however, that effects like acoustic radiation to the freestream are
outside the scope of the present analysis. The main goal of the study is twofold: First, to
demonstrate the potential of the chosen approach by comparison with familiar results; second, to extend the current state of knowledge in the compressible regime in selected points
by exploiting the extended capabilities of the chosen framework. To this end, the importance of the different inputs – especially the temperature effects – for the amplification of
two-dimensional, oblique flow structures and streaks are discussed. Furthermore, the influence of first and second Mach modes (not present in the incompressible regime) is identified
within the stochastic framework for the first time and results are discussed in the light of
previous receptivity analyses where the output is restricted to a single mode. By varying
the spatial distribution of the forcing, the dependence of the receptivity on the wall-normal
position, where the forcing is introduced, is illustrated and discussed.
Finally, dominant coherent structures are identified by evaluating the first singular vector
of the correlation matrix (POD modes). By analyzing the dependence of both forcing and
response POD modes on the choice of the measured component, further insight is provided
about the contribution of temperature fluctuation to the stochastically maintained variance
of the system.
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