Three-dimensional wave packet in a hypersonic boundary layer

Eric Forgoston, Anatoli Tumin

Research output: Contribution to conferencePaperResearchpeer-review

2 Citations (Scopus)

Abstract

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.

Original languageEnglish
Pages14881-14892
Number of pages12
StatePublished - 1 Dec 2005
Event43rd AIAA Aerospace Sciences Meeting and Exhibit - Reno, NV, United States
Duration: 10 Jan 200513 Jan 2005

Other

Other43rd AIAA Aerospace Sciences Meeting and Exhibit
CountryUnited States
CityReno, NV
Period10/01/0513/01/05

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Hypersonic boundary layers
Wave packets
Inverse transforms
Fourier transforms
Initial value problems
Boundary layer flow
Vorticity
Eigenvalues and eigenfunctions
Synchronization
Entropy
Temperature

Cite this

Forgoston, E., & Tumin, A. (2005). Three-dimensional wave packet in a hypersonic boundary layer. 14881-14892. Paper presented at 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, United States.
Forgoston, Eric ; Tumin, Anatoli. / Three-dimensional wave packet in a hypersonic boundary layer. Paper presented at 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, United States.12 p.
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Forgoston, E & Tumin, A 2005, 'Three-dimensional wave packet in a hypersonic boundary layer' Paper presented at 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, United States, 10/01/05 - 13/01/05, pp. 14881-14892.

Three-dimensional wave packet in a hypersonic boundary layer. / Forgoston, Eric; Tumin, Anatoli.

2005. 14881-14892 Paper presented at 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, United States.

Research output: Contribution to conferencePaperResearchpeer-review

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AB - 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.

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Forgoston E, Tumin A. Three-dimensional wave packet in a hypersonic boundary layer. 2005. Paper presented at 43rd AIAA Aerospace Sciences Meeting and Exhibit, Reno, NV, United States.