### 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 language | English |
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Pages | 14881-14892 |

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

Other | 43rd AIAA Aerospace Sciences Meeting and Exhibit |
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Country | United States |

City | Reno, NV |

Period | 10/01/05 → 13/01/05 |

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### Cite this

*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.

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

Research output: Contribution to conference › Paper

TY - CONF

T1 - Three-dimensional wave packet in a hypersonic boundary layer

AU - Forgoston, Eric

AU - Tumin, Anatoli

PY - 2005/12/1

Y1 - 2005/12/1

N2 - 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.

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.

UR - http://www.scopus.com/inward/record.url?scp=30744453535&partnerID=8YFLogxK

M3 - Paper

AN - SCOPUS:30744453535

SP - 14881

EP - 14892

ER -