Receptivity of high-speed boundary layers to kinetic fluctuations

Receptivity of high-speed boundary layers in calorically perfect gas is considered within the framework of fluctuating hydrodynamics introduced by Landau and Lifshitz ("Hydrodynamic Fluctuations," Soviet Physics, JETP, Vol. 5, No. 3, 1957, pp. 512-513) for a one-component fluid. It is assumed that kinetic fluctuations manifest themselves in the governing equations through "stochastic forcing" by a random stress tensor and by a random heat flux. The stochastic forcing generates unstable modes in boundary layers. By solving the kinetic-fluctuation receptivity problem, the root-mean-square amplitudes of instability are expressed in terms of correlations for the random stress tensor and heat flux stemming from the fluctuation-dissipation theorem. The results indicate that the boundary-layer flow is most susceptible to kinetic fluctuations in the critical layer, and the receptivity occurs near the lower branch of the neutral stability curve for the considered instability. Although the initial amplitudes of the unstable modes generated by kinetic fluctuations are small, they go through a significant amplification toward the nonlinear region and may lead to laminar-turbulent transition. The root-mean-square amplitudes of kineticfluctuation-induced instability are expressed in a compact analytical form, which does not contain any empirical quantities. This opens up an opportunity to estimate the upper bound of the transition Reynolds number in the framework of a physics-based amplitude method. The results are consistent with the previous theoretical findings indicating that kinetic fluctuations at a microscopic scale can trigger a macroscopic phenomenon: laminarturbulent transition in boundary-layer flows.