Numerical and Asymptotical Study of Three-Dimensional Wave Packets in a Compressible Boundary Layer

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Conference Proceeding

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A three-dimensional wave packet generated by a local disturbance in a two-dimensional hypersonic boundary layer flow is studied with the aid of the previously solved initialvalue problem. The solution can be presented as a sum of modes consisting of continuous and discrete spectra of temporal stability theory. Two discrete modes, known as Mode S and Mode F, are of interest in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectra are analyzed numerically for a hypersonic flow. A comprehensive study of the spectrum is performed, including Reynolds number, Mach number and temperature factor effects. A specific disturbance consisting of an initial temperature spot is considered, and the receptivity to this initial temperature spot is computed for both the two-dimensional and three-dimensional cases. Using the analysis of the discrete and continuous spectrum, the inverse Fourier transform is computed numerically. The two-dimensional inverse Fourier transform is calculated for Mode F and Mode S. The Mode S result is compared with an asymptotic approximation of the Fourier integral, which is obtained using a Gaussian model as well as the method of steepest descent. Additionally, the three-dimensional inverse Fourier transform is found using an asymptotic approximation. Using the inverse Fourier transform computations, the development of the wave packet is studied, including effects due to Reynolds number, Mach number and temperature factor.

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