Study of discrete modes branching in high-speed boundary layers

Yuli Lifshitz; David Degani; Anatoli Tumin

doi:10.2514/1.J051547

Study of discrete modes branching in high-speed boundary layers

Yuli Lifshitz, David Degani, Anatoli Tumin

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Abstract

The branching of discrete modes in high-speed boundary layers is investigated using parabolized stability equations. The fast and slow discrete modes associated with the fast and slow acoustic modes, respectively, are considered in high-speed boundary layers over adiabatic and cooled walls. Whereas the conventional linear stability theory approach leads to singular behavior in the vicinity of the fast-mode synchronization with the entropy and vorticity modes, the parabolized stability equation results do not reveal singular behavior of the solution and are consistent with the available direct numerical simulations of perturbations in high-speed boundary layers. Also, the parabolized stability equation results do not reveal a singular behavior in the vicinity of the point of synchronism of the slow and fast discrete modes.

Original language	English (US)
Pages (from-to)	2202-2210
Number of pages	9
Journal	AIAA journal
Volume	50
Issue number	10
DOIs	https://doi.org/10.2514/1.J051547
State	Published - Oct 2012

ASJC Scopus subject areas

Aerospace Engineering

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10.2514/1.J051547

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title = "Study of discrete modes branching in high-speed boundary layers",

abstract = "The branching of discrete modes in high-speed boundary layers is investigated using parabolized stability equations. The fast and slow discrete modes associated with the fast and slow acoustic modes, respectively, are considered in high-speed boundary layers over adiabatic and cooled walls. Whereas the conventional linear stability theory approach leads to singular behavior in the vicinity of the fast-mode synchronization with the entropy and vorticity modes, the parabolized stability equation results do not reveal singular behavior of the solution and are consistent with the available direct numerical simulations of perturbations in high-speed boundary layers. Also, the parabolized stability equation results do not reveal a singular behavior in the vicinity of the point of synchronism of the slow and fast discrete modes.",

author = "Yuli Lifshitz and David Degani and Anatoli Tumin",

note = "Funding Information: The authors thank A. Fedorov for valuable discussions and comments that have been incorporated into the present manuscript. The authors acknowledge helpful comments of X. Zhong and X. Wang. A. Tumin acknowledges support from the U.S. Air Force Office of Scientific Research/NASA/National Center for Hypersonic Research in Laminar-Turbulent Transition and by the U.S. Air Force Office of Scientific Research, under grant FA9550-08-1-0322, monitored by J. D. Schmisseur.",

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AU - Lifshitz, Yuli

AU - Degani, David

AU - Tumin, Anatoli

N1 - Funding Information: The authors thank A. Fedorov for valuable discussions and comments that have been incorporated into the present manuscript. The authors acknowledge helpful comments of X. Zhong and X. Wang. A. Tumin acknowledges support from the U.S. Air Force Office of Scientific Research/NASA/National Center for Hypersonic Research in Laminar-Turbulent Transition and by the U.S. Air Force Office of Scientific Research, under grant FA9550-08-1-0322, monitored by J. D. Schmisseur.

PY - 2012/10

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N2 - The branching of discrete modes in high-speed boundary layers is investigated using parabolized stability equations. The fast and slow discrete modes associated with the fast and slow acoustic modes, respectively, are considered in high-speed boundary layers over adiabatic and cooled walls. Whereas the conventional linear stability theory approach leads to singular behavior in the vicinity of the fast-mode synchronization with the entropy and vorticity modes, the parabolized stability equation results do not reveal singular behavior of the solution and are consistent with the available direct numerical simulations of perturbations in high-speed boundary layers. Also, the parabolized stability equation results do not reveal a singular behavior in the vicinity of the point of synchronism of the slow and fast discrete modes.

AB - The branching of discrete modes in high-speed boundary layers is investigated using parabolized stability equations. The fast and slow discrete modes associated with the fast and slow acoustic modes, respectively, are considered in high-speed boundary layers over adiabatic and cooled walls. Whereas the conventional linear stability theory approach leads to singular behavior in the vicinity of the fast-mode synchronization with the entropy and vorticity modes, the parabolized stability equation results do not reveal singular behavior of the solution and are consistent with the available direct numerical simulations of perturbations in high-speed boundary layers. Also, the parabolized stability equation results do not reveal a singular behavior in the vicinity of the point of synchronism of the slow and fast discrete modes.

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Study of discrete modes branching in high-speed boundary layers

Abstract

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