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Nonlinear analysis of shock–vortex interaction: Mach stem formation

  • Paul Clavin (a1)
Abstract
Abstract

Shock–vortex interaction is analysed for strong gaseous shock waves and a ratio of specific heats close to unity. A nonlinear wave equation for the wrinkles of the shock front is obtained for weak vortices. The solution breaks down after a finite time and the slope of the front develops jump discontinuities, indicating the formation of Mach stems. Shock–turbulence interactions are also briefly discussed.

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Email address for correspondence: clavin@irphe.univ-mrs.fr
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P. Clavin 2002a Instabilities and nonlinear patterns of overdriven detonations in gases. In Nonlinear PDE’s in Condensed Matter and Reactive Flows (ed. H. Berestycki & Y. Pomeau), pp. 4997. Kluwer Academic.

P. Clavin 2002b Self-sustained mean streaming motion in diamond patterns of gaseous detonation. Intl J. Bifurcation Chaos 12 (11), 25352546.

P Clavin & B. Denet 2002 Diamond patterns in the cellular front of an overdriven detonation. Phys. Rev. Lett. 88 (4)044502–1–4.

P. Clavin & F. A. Williams 2012 Analytical studies of the dynamics of gaseous detonations. Phil. Trans. R. Soc A 370, 597624.

J. L. Ellzey , M. R. Henneke , J. M. Picone & E. S. Oran 1995 The interaction of a shock with a vortex: Shock distortion and the production of acoustic waves. Phys. Fluids 7 (1), 172184.

L. Guichard , L. Vervich & P. Domingo 1995 Two-dimensional weak shock–vortex interaction in a mixing zone. AIAA J. 33 (10), 17971802.

O. Inoue 2000 Propagation of sound generated by weak shock–vortex interaction. Phys. Fluids 12 (5), 12581261.

J Larsson & S. K. Lele 2009 Direct numerical simulation of canonical shock/turbulence interaction. Phys. Fluids 21, 126101–1–12.

A. Majda & R. Rosales 1983 A theory for spontaneous mach stem formation in reacting fronts, I The basic perturbation analysis. SIAM J. Appl. Maths 43 (6), 13101334.

S. S. Ribner 1985 Cylindrical sound wave generated by shock–vortex interaction. AIAA J. 23 (11), 17081715.

J. G. Wouchuk & C. Huete Ruiz de Lira 2009 Analytical linear theory of planar shock wave with isotropic turbulent flow field. Phys. Rev. E 79, 06315–1–35.

S. Zhang , Y-T. Zhang & C-W. Shu 2005 Multistage interaction of a shock wave and a strong vortex. Phys. Fluids 17 (116101), 113.

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Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
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