Hostname: page-component-745bb68f8f-lrblm Total loading time: 0 Render date: 2025-01-09T21:54:03.872Z Has data issue: false hasContentIssue false
  • English
  • Français

Numerical simulation of nonlinear kink instabilities on supersonic shear layers

Published online by Cambridge University Press:  26 April 2006

Gene M. Bassett  and
Paul R. Woodward
Gene M. Bassett
Affiliation:
Department of Astronomy, Army High Performance Computing Research Center, and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, USA Current address: School of Meteorology, 100 E. Boyd, Norman, OK 73019, USA.
Paul R. Woodward
Affiliation:
Department of Astronomy, Army High Performance Computing Research Center, and Minnesota Supercomputer Institute, University of Minnesota, Minneapolis, MN 55455, USA
Get access Rights & Permissions [Opens in a new window]

Abstract

Nonlinear kink instabilities of high-Reynolds-number supersonic shear layers have been studied using high-resolution computer simulations with the piecewise-parabolic-method (PPM). The transition region between the two fluids of the shear layer is spread out over many computational zones to avoid numerical effects introduced on the smallest lengthscales. Mach number, density contrast, and perturbation speed and amplitude were varied to study their effects on the growth of the kink instabilities. In response to a perturbing sound wave, a travelling kink mode grows in amplitude until enough of a disturbance on the shear layer has been created for it to roll up and rapidly grow in thickness. The time it takes for this rapid growth to be initiated is proportional to the initial shear-layer thickness and increases for increasing Mach number or decreasing perturbation amplitude. For equal density, Mach 4 shear layers, perturbed by a sound wave with a 2% amplitude at the travelling mode velocity, the growth time is τg = (546 ± 24) δ/c, where c is the sound speed and δ the half-width of the shear layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 284 , 10 February 1995 , pp. 323 - 340
Copyright
© 1995 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.)

References

Artola, M. & Majda, A. J. 1987 Physica D 28, 253.
Artola, M. & Majda, A. J. 198a Phys. Fluids A 1, 583.
Artola, M. & Majda, A. J. 1989b SIAM J Appl. Maths 49, 1310.
Bassett, G. M. & Woodward, P. R. 1995 Astrophys. J. 441 (in press).
Colella, P. & Woodward, P. R. 1984 J. Comput. Phys. 54, 174.
Miles, J. W. 1957 J. Acoust. Soc. Am. 29, 226.
Payne, D. G. & Cohn, H. 1985 Astrophys. J. 291, 655.
Pedelty, J. A. & Woodward, P. R. 1991 J. Fluid Mech. 225, 101.
Porter, D. H., Pouquet, A. & Woodward, P. R. 1992 Theoret. Comput. Fluid Dyn. 4, 13.
Porter, D. H., Woodward, P. R., Yang, W. & Mei, Q. 1990 In Annals of the New York Academy of Sciences vol. 617 (ed. R. Buchler), p. 234.
Woodward, P. R. 1985 In Numerical Methods for the Euler Equations of Fluid Dynamics (ed. F. Angrand, A. Dervieux, J. Desideri & R. Glowinski), p. 493. SIAM.
Woodward, P. R. 1986 In Astrophysical Radiation Hydrodynamics (ed. K.-H. Winkler & M. L. Norman), p. 245. Reidel.
Woodward, P. R. 1988 In High Speed Computing, Scientific Applications and Algorithm Design (ed. R. B. Wilhelmson), p. 81. University of Illinois Press.
Woodward, P. R. & Colella, P. 1984 J. Comput. Phys. 54, 115.
Woodward, P. R., Porter, D. H., Ondrechen, M., Pedelty, J., Winkler, K.-H., Chalmers, J., Hodson, W. & Zabusky, N. J. 1987 In Science and Engineering on Cray Supercomputers (ed. J. E. Aldag), p. 557. Cray Research, Minneapolis.