[en] The fundamental issues involved in compressible turbulence are of great technological importance and present severe challenges for analytical, numerical, and empirical predictive methodologies. One pressing application is to hypersonic flight, especially for the internal flow in combustors. A principal objective is to optimize the efficiency of the fuel-air mixing occurring in the engine. In the very high speed vehicle configurations currently being considered, achieving a high combustor efficiency is particularly difficult. This is a consequence of the fact that with increasing vehicle Mach number, the average Mach number in the combustor also increases. As the combustor Mach number increases the degree of fuel-air mixing that can be achieved through natural convective and diffusive processes is reduced, leading to an overall decrease in combustion efficiency and thrust. Numerical methods for supersonic (and reacting) flow have matured to the point at which they are playing a key role in exploring mechanisms for enhancing mixing and turbulence in compressible flow. In this paper some representative illustrations of recent work directed towards mixing enhancement in supersonic combustors will be presented