Journal of Fluid Mechanics

Shock wave instability and the carbuncle phenomenon: same intrinsic origin?

a1 Department of Modelling Aerodynamics and Energetics, ONERA-CERT, 2, avenue Edouard Belin, 31055 Toulouse Cedex 4, France
a2 Ecole Nationale Supérieure de l'Aéronautique et de l'Espace, 31400 Toulouse, France


The theoretical linear stability of a shock wave moving in an unlimited homogeneous environment has been widely studied during the last fifty years. Important results have been obtained by Dýakov (1954), Landau & Lifchitz (1959) and then by Swan & Fowles (1975) where the fluctuating quantities are written as normal modes. More recently, numerical studies on upwind finite difference schemes have shown some instabilities in the case of the motion of an inviscid perfect gas in a rectangular channel. The purpose of this paper is first to specify a mathematical formulation for the eigenmodes and to exhibit a new mode which was not found by the previous stability analysis of shock waves. Then, this mode is confirmed by numerical simulations which may lead to a new understanding of the so-called carbuncle phenomenon.

(Received February 24 1999)
(Revised February 29 2000)