### 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 language | English |
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Article number | 084106 |

Pages (from-to) | 1-14 |

Number of pages | 14 |

Journal | Physics of Fluids |

Volume | 17 |

Issue number | 8 |

DOIs | |

State | Published - Aug 2005 |

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### Cite this

*Physics of Fluids*,

*17*(8), 1-14. [084106]. https://doi.org/10.1063/1.2013261

}

*Physics of Fluids*, vol. 17, no. 8, 084106, pp. 1-14. https://doi.org/10.1063/1.2013261

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

Research output: Contribution to journal › Article

TY - JOUR

T1 - Initial-value problem for three-dimensional disturbances in a compressible boundary layer

AU - Forgoston, Eric

AU - Tumin, Anatoli

PY - 2005/8

Y1 - 2005/8

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=24144454872&partnerID=8YFLogxK

U2 - 10.1063/1.2013261

DO - 10.1063/1.2013261

M3 - Article

AN - SCOPUS:24144454872

VL - 17

SP - 1

EP - 14

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 8

M1 - 084106

ER -