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

Eric Forgoston, Anatoli Tumin

Research output: Contribution to journalArticle

26 Citations (Scopus)

Abstract

An initial-value problem is formulated for a three-dimensional wave packet in a compressible 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 in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow with Mach number M=5.6. The following features are revealed: (1) The synchronism of mode S with acoustic waves at a streamwise wave number α1;→0 is primarily two-dimensional; (2) at high angles of disturbance 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 is not accompanied by a mode S instability, and at even higher angles of disturbance propagation, mode S and mode F are not synchronized.

Original languageEnglish
Article number084106
Pages (from-to)1-14
Number of pages14
JournalPhysics of Fluids
Volume17
Issue number8
DOIs
StatePublished - Aug 2005

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compressible boundary layer
boundary value problems
disturbances
propagation modes
continuous spectra
synchronism
hypersonic flow
boundary layer flow
Mach number
wave packets
vorticity
high speed
entropy

Cite this

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abstract = "An initial-value problem is formulated for a three-dimensional wave packet in a compressible 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 in high-speed flows since they may be involved in a laminar-turbulent transition scenario. The continuous and discrete spectrum are analyzed numerically for a hypersonic flow with Mach number M=5.6. The following features are revealed: (1) The synchronism of mode S with acoustic waves at a streamwise wave number α1;→0 is primarily two-dimensional; (2) at high angles of disturbance 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 is not accompanied by a mode S instability, and at even higher angles of disturbance propagation, mode S and mode F are not synchronized.",
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Initial-value problem for three-dimensional disturbances in a compressible boundary layer. / Forgoston, Eric; Tumin, Anatoli.

In: Physics of Fluids, Vol. 17, No. 8, 084106, 08.2005, p. 1-14.

Research output: Contribution to journalArticle

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