Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer

Eric Forgoston, Anatoli Tumin

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

1 Citation (Scopus)

Abstract

An initial-value problem is formulated for a threedimensional wave packet in a hypersonic boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. 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 since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically, and the following features are revealed: (1) the synchronism of Mode S with acoustic waves at low wave number is primarily twodimensional; (2) at high angles of dis turbance propagation, Mode F is no longer synchronized with entropy and vorticity waves; (3) at high angles of disturbance propagation, the synchronism between Mode S and Mode F no longer leads to a Mode S instability, and at even higher angles of disturbance propagation, Mode S and Mode F are not synchronized.

Original languageEnglish
Title of host publication34th AIAA Fluid Dynamics Conference and Exhibit
StatePublished - 1 Dec 2004
Event34th AIAA Fluid Dynamics Conference and Exhibit 2004 - Portland, OR, United States
Duration: 28 Jun 20041 Jul 2004

Publication series

Name34th AIAA Fluid Dynamics Conference and Exhibit

Other

Other34th AIAA Fluid Dynamics Conference and Exhibit 2004
CountryUnited States
CityPortland, OR
Period28/06/041/07/04

Fingerprint

Hypersonic boundary layers
Initial value problems
Synchronization
Wave packets
Boundary layer flow
Laplace transforms
Vorticity
Fourier transforms
Entropy
Acoustic waves

Cite this

Forgoston, E., & Tumin, A. (2004). Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer. In 34th AIAA Fluid Dynamics Conference and Exhibit (34th AIAA Fluid Dynamics Conference and Exhibit).
Forgoston, Eric ; Tumin, Anatoli. / Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer. 34th AIAA Fluid Dynamics Conference and Exhibit. 2004. (34th AIAA Fluid Dynamics Conference and Exhibit).
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title = "Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer",
abstract = "An initial-value problem is formulated for a threedimensional wave packet in a hypersonic boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. 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 since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically, and the following features are revealed: (1) the synchronism of Mode S with acoustic waves at low wave number is primarily twodimensional; (2) at high angles of dis turbance propagation, Mode F is no longer synchronized with entropy and vorticity waves; (3) at high angles of disturbance propagation, the synchronism between Mode S and Mode F no longer leads to a Mode S instability, and at even higher angles of disturbance propagation, Mode S and Mode F are not synchronized.",
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Forgoston, E & Tumin, A 2004, Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer. in 34th AIAA Fluid Dynamics Conference and Exhibit. 34th AIAA Fluid Dynamics Conference and Exhibit, 34th AIAA Fluid Dynamics Conference and Exhibit 2004, Portland, OR, United States, 28/06/04.

Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer. / Forgoston, Eric; Tumin, Anatoli.

34th AIAA Fluid Dynamics Conference and Exhibit. 2004. (34th AIAA Fluid Dynamics Conference and Exhibit).

Research output: Chapter in Book/Report/Conference proceedingConference contributionResearchpeer-review

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AU - Tumin, Anatoli

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N2 - An initial-value problem is formulated for a threedimensional wave packet in a hypersonic boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. 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 since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically, and the following features are revealed: (1) the synchronism of Mode S with acoustic waves at low wave number is primarily twodimensional; (2) at high angles of dis turbance propagation, Mode F is no longer synchronized with entropy and vorticity waves; (3) at high angles of disturbance propagation, the synchronism between Mode S and Mode F no longer leads to a Mode S instability, and at even higher angles of disturbance propagation, Mode S and Mode F are not synchronized.

AB - An initial-value problem is formulated for a threedimensional wave packet in a hypersonic boundary layer flow. The problem is solved using a Laplace transform with respect to time and Fourier transforms with respect to the streamwise and spanwise coordinates. 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 since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically, and the following features are revealed: (1) the synchronism of Mode S with acoustic waves at low wave number is primarily twodimensional; (2) at high angles of dis turbance propagation, Mode F is no longer synchronized with entropy and vorticity waves; (3) at high angles of disturbance propagation, the synchronism between Mode S and Mode F no longer leads to a Mode S instability, and at even higher angles of disturbance propagation, Mode S and Mode F are not synchronized.

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Forgoston E, Tumin A. Initial-value problem for three-dimensional disturbances in a hypersonic boundary layer. In 34th AIAA Fluid Dynamics Conference and Exhibit. 2004. (34th AIAA Fluid Dynamics Conference and Exhibit).