Hostname: page-component-7dd5485656-bt4hw Total loading time: 0 Render date: 2025-10-31T09:38:53.281Z Has data issue: false hasContentIssue false
  • English
  • Français

The viscous-diffusion nonlinear critical layer in a stratified shear flow

Published online by Cambridge University Press:  26 April 2006

Yu. I. Troitskaya
Yu. I. Troitskaya
Affiliation:
Institute of Applied Physics, Academy of Sciences of the USSR, Nizhny Novgorod (Gorky), USSR
Get access Rights & Permissions [Opens in a new window]

Abstract

Stationary finite-amplitude wave disturbances in a stratified shear flow with Richardson number larger than ¼ are investigated for large Reynolds numbers when viscosity and thermal conductivity, as well as nonlinearity, are essential factors in the critical layer. The jumps across the critical layer in average vorticity, reflection and transmission coefficients are calculated as functions of the local Reynolds number determined by the amplitude of the incident wave. With the increase of the incident wave amplitude the asymptotic value of the Richardson number on the same side of critical layer as the incident wave tends to 1/4 the reflection coefficient tends to unity and the transmission coefficient to zero.

Information

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 233 , December 1991 , pp. 25 - 48
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Article purchase

Temporarily unavailable

References

Baldwin, P. & Roberts, P. H. 1970 The critical layer in a stratified shear flow. Mathematica 17, 102–119.Google Scholar
Booker, J. R. & Bretherton, F. P. 1967 The critical layer for internal gravity waves in a shear flow. J. Fluid Mech. 27, 513–539.Google Scholar
Bowman, M. R., Thomas, L. & Thomas, R. H. 1980 The propagation of gravity waves through the critical layer for conditions of moderate wind shear. Planet. Space Sci. 28, 119–133.Google Scholar
Brown, S. N., Rosen, A. S. & Maslowe, S. A. 1981 The evolution of a quasi-steady critical layer in a stratified shear layer.. Proc. R. Soc. Lond. A 375, 271–293.Google Scholar
Brown, S. N. & Stewartson, K. 1978 The evolution of a small inviscid disturbance to a marginally unstable stratified shear flow; stage two.. Proc. R. Soc. Lond. A 363, 175–194.Google Scholar
Brown, S. N. & Stewartson, K. 1980 On the nonlinear reflection of a gravity wave at a critical layer. Part 1. J. Fluid Mech. 100, 577–595.Google Scholar
Brown, S. N. & Stewartson, K. 1982a On the nonlinear reflection of a gravity wave at a critical layer. Part 2. J. Fluid Mech. 115, 217–230.Google Scholar
Brown, S. N. & Stewartson, K. 1982b On the nonlinear reflection of a gravity wave at a critical layer. Part 3. J. Fluid Mech. 115, 231–250.Google Scholar
Churilov, S. M. & Shukhman, I. G. 1987 Nonlinear stability of a stratified shear flow: a viscous critical layer. J. Fluid Mech. 180, 1–20.Google Scholar
Churilov, S. M. & Shukhman, I. G. 1988 Nonlinear stability of a stratified shear flow in a regime with an unsteady critical layer. J. Fluid Mech. 194, 187–217.Google Scholar
Collins, D. A. & Maslowe, S. A. 1988 Vortex pairing and resonant wave interactions in a stratified free shear layer. J. Fluid Mech. 191, 465–480.Google Scholar
Duin, C. A. Van & Kelder, H. 1986 Internal gravity waves in shear flows at large Reynolds number. J. Fluid Mech. 169, 293–306.Google Scholar
Forsythe, G. E. & Moler, C. B. 1967 Computer Solution of Linear Algebraic Systems. Prentice-Hall.
Haberman, R. 1972 Critical layer in parallel flows. Stud. Appl. Maths 51, 139–161.Google Scholar
Haberman, R. 1973 Wave-induced distortions of slightly stratified shear flow: a nonlinear critical-layer effect. J. Fluid Mech. 58, 727–735.Google Scholar
Hazel, P. 1967 The effect of viscosity and heat conductivity on internal gravity waves at a critical level. J. Fluid Mech. 30, 775–783.Google Scholar
Howard, L. N. 1961 Note on a paper of John Miles. J. Fluid Mech. 10, 509–512.Google Scholar
Kelly, R. E. & Maslowe, S. A. 1970 The nonlinear critical layer in slightly stratified shear flows. Stud. Appl. Maths 49, 302–326.Google Scholar
Koppel, D. 1964 On the stability of flow of thermally stratified fluid under the action of gravity. J. Math. Phys. 5, 963.Google Scholar
Maslowe, S. A. 1972 The generation of clear air turbulence by nonlinear wave. Stud. Appl. Maths 51, 1–16.Google Scholar
Maslowe, S. A. 1973 Finite-amplitude Kelvin–Helmholtz billows. Boundary-Layer Met. 5, 45–52.Google Scholar
Maslowe, S. A. 1986 Critical layers in shear flows. Ann. Rev. Fluid Mech. 18, 405–432.Google Scholar
Miles, J. W. 1961 On the stability of heterogeneous shear flow. J. Fluid Mech. 10, 496–509.Google Scholar
Stewartson, K. 1981 Marginally stable inviscid flows with critical layers. J. Appl. Maths 27, 133–175.Google Scholar
Tung, K. K., Ko, D. R. S. & Chang, J. J. 1981 Weakly nonlinear internal waves in shear. Stud. Appl. Maths 65, 189–221.Google Scholar