A three-dimensional wave packet generated by a local disturbance in a hypersonic boundary layer flow is studied with the aid of the previously solved initial-value problem. The solution to this problem can be expanded in a biorthogonal eigenfunction system as a sum of discrete and continuous modes. 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 previous analysis of the discrete and continuous spectrum, we numerically compute the inverse Fourier transform. The two-dimensional inverse Fourier transform is found for Mode S, and the result is compared with the asymptotic approximation of the Fourier integral. Due to the synchronism between Mode F and entropy/vorticity modes, it is necessary to deform the path of integration around the associated branch cut. Additionally, the inverse Fourier transform for a prescribed spanwise wave number is computed for three-dimensional Mode S.
|Number of pages||12|
|State||Published - 1 Dec 2005|
|Event||43rd AIAA Aerospace Sciences Meeting and Exhibit - Reno, NV, United States|
Duration: 10 Jan 2005 → 13 Jan 2005
|Other||43rd AIAA Aerospace Sciences Meeting and Exhibit|
|Period||10/01/05 → 13/01/05|