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Compressible laminar streaks with wall suction

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10.1063/1.4807066

### Abstract

The response of a compressible laminar boundary layer subject to free-stream vortical disturbances and steady mean-flow wall suction is studied. The theoretical frameworks of Leib et al. [J. Fluid Mech.380, 169–203 (Year: 1999)10.1017/S0022112098003504] and Ricco and Wu [J. Fluid Mech.587, 97–138 (Year: 2007)10.1017/S0022112007007070], based on the linearized unsteady boundary-region equations, are adopted to study the influence of suction on the kinematic and thermal streaks arising through the interaction between the free-stream vortical perturbations and the boundary layer. In the asymptotic limit of small spanwise wavelength compared with the boundary layer thickness, i.e., when the disturbance flow is conveniently described by the steady compressible boundary region equations, the effect of suction is mild on the velocity fluctuations and negligible on the temperature fluctuations. When the spanwise wavelength is comparable with the boundary layer thickness, small suction values intensify the supersonic streaks, while higher transpiration levels always stabilize the disturbances at all Mach numbers. At larger spanwise wavelengths, very small amplitudes of wall transpiration have a dramatic stabilizing effect on all boundary layer fluctuations, which can take the form of transiently growing thermal streaks, large amplitude streamwise oscillations, or oblique exponentially growing Tollmien-Schlichting waves, depending on the Mach number and the wavelengths. The range of wavenumbers for which the exponential growth occurs becomes narrower and the location of instability is significantly shifted downstream by mild suction, indicating that wall transpiration can be a suitable vehicle for delaying transition when the laminar breakdown is promoted by these unstable disturbances. The typical streamwise wavelength of these disturbances is instead not influenced by suction, and asymptotic triple deck theory predicts the strong changes in growth rate and the very mild modifications in streamwise wavenumber in the limit of larger downstream distance and small spanwise wavenumber.

© 2013 AIP Publishing LLC

Received 22 October 2012
Accepted 22 April 2013
Published online 29 May 2013

Acknowledgments: EPSRC First Grant EP/I033173/1 partly supported P.R. and fully supported P.D.H.

Article outline:

I. INTRODUCTION

II. MATHEMATICAL FORMULATION

A. The boundary-layer mean flow

1. Limit of large mean-flow suction

B. The boundary-layer disturbance flow

III. RESULTS

A. Klebanoff modes for κ ≫ 1

B. Klebanoff modes for κ =

C. Klebanoff modes and large-scale streamwise oscillations for κ ⪅ 4κ_{ c }

D. Klebanoff modes and TS waves for κ **⪅** κ_{ c }

E. Klebanoff modes and TS waves for κ ≪ 1

IV. SUMMARY

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/content/aip/journal/pof2/25/5/10.1063/1.4807066

2013-05-29

2014-04-18

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