The upper-branch stability of compressible boundary-layer flows

Gajjar, Jitesh S. B.; Cole, Jim

doi:10.1007/bf00272140

Cited by 9 publications

(1 citation statement)

References 19 publications

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“…Consistent multi-deck asymptotic matching procedures have been employed to determine the non-linear effects on the lower branch solution by Smith (1979c,d ) and subsequently for the upper branch by Smith & Bodonyi (1980, 1982. Multi-deck asymptotic analysis for non-linear development of neutral disturbances in compressible boundary layers have been shown in the works of (Gajjar, 1990(Gajjar, , 1994, and the upper branch scalings in the work by Gajjar & Cole (1989).…”

Section: Introductionmentioning

confidence: 99%

Stability of a high Mach number flow in a channel

Deka¹,

Tomar²,

Kumaran³

2022

Preprint

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Modal instabilities in a flow through a channel at high Reynolds and Mach numbers are studied for three-dimensional perturbations. In addition to the Tollmien-Schlichting modes, there exist higher modes in a channel flow that do not have a counterpart in the incompressible limit. The stability characteristics of these higher modes, obtained through numerical calculations, are compared with boundary layer and Couette flows that have been previously studied. The dominant higher mode instabilities in a channel flow are shown to be viscous in nature, in contrast to compressible boundary layer modes. For general compressible bounded-domain flows, a necessary condition for the existence of neutral modes in the inviscid limit is obtained. This criterion is used to construct a procedure to determine a critical value of Mach number below which the higher modes remain stable. This criterion also delineates a range of angles of inclination of the wave number with respect to the flow direction which could go unstable at a specified Mach number. Asymptotic analysis is carried out for the lower and upper branch of the stability curve in the limit of high Reynolds number. A common set of relations are identified for these exponents for the upper and lower branch for the continuation of the Tollmien-Schlichting modes and the compressible modes. The scalings for the Tollmien-Schlichting modes are identical to those for an incompressible flow. The scalings for the finite wave number modes are different; the wave speed c scales as Re − 1 3 for the lower branch and Re − 1 5 for the upper branch, where Re is the Reynolds number. The asymptotic analysis shows that the stability boundaries for three-dimensional perturbations at high Reynolds numbers can be calculated from the strain rate and the temperature of the base flow at the wall.

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Section: Introductionmentioning

confidence: 99%

Stability of a high Mach number flow in a channel

Deka¹,

Tomar²,

Kumaran³

2022

Preprint

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On the Nonlinear Development of Görtler Vortices in a Compressible Boundary Layer

Wadey

1991

Stud Appl Math

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The nonlinear development of the GortIer instability in compressible boundary layers on curved walls is considered for vortices of asymptotically large wavenumber. The starting point for our calculations lies in the work of , where the incompressible results were formulated. Without neglecting downstream partial derivatives, the initial development of a vortex from the point where it first starts to grow is calculated. It is shown how the same basic structure that occurs in incompressible flow exists, where the disturbance is confined to a core region bounded above and below by thin shear layers, but that the flow in the core region is of more complicated form than that for incompressible flow.

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