The Theory of Turbulence in Supersonic Combustion in the Absence of Solid Walls

It is commonly believed that the higher the Reynolds number of a flow, the larger the separation between the large (integral) and the small (Kolmogorov) scales, and consequently, the stronger the turbulence intensity. What is not commonly appreciated, however, is that flows in the high-speed regime, where the Reynolds number is practically infinite, is more likely going to be laminar! The implication for supersonic combustion problems is that the large velocities in the flow do not imply large turbulence intensities. The disconnect apparently has its origin from the fact that classical turbulence theories are based on low-speed flows. In a supersonic combustion model without solid walls and with negligible buoyancy production of turbulence, we investigate shear production. The shock waves in such a system play the role of a solid wall as far as shear generation of turbulence is concerned. But then, this is a porous wall as per the Rankine-Hugoniot relations, so that the efficiency of turbulence generation will be relatively poor, and the turbulence will be mostly transitional and highly localized. A few results that demonstrate the phenomenon will be discussed.