J . Fluid Mech . 1 Direct numerical simulation of a supersonicturbulent boundary layer at Mach 2 . 5 By STEPHEN

A direct numerical simulation of a supersonic turbulent boundary layer has been performed. We take advantage of a technique developed by Spalart for incompressible ow. In this technique, it is assumed that the boundary layer grows so slowly in the stream-wise direction that the turbulence can be treated as approximately homogeneous in this direction. The slow growth is accounted for by a coordinate transformation and a multiple-scale analysis. The result is a modiied system of equations, in which the ow is homogeneous in both the streamwise and spanwise directions, and which represents the state of the boundary layer at a given streamwise location. The equations are solved using a mixed Fourier and B-spline Galerkin method. Results are presented for a case having an adiabatic wall, a Mach number of M = 2:5, and a Reynolds number, based on momentum integral thickness and wall viscosity, of R 0 = 849. The Reynolds number based on momentum integral thickness and freestream viscosity is R = 1577. The results indicate that the Van Driest transformed velocity satisses the incompressible scalings and a small logarithmic region is obtained. Both turbulence intensities and the Reynolds shear stress compare well with the incompressible simulations of Spalart when scaled by mean density. Pressure uctuations are higher than in incompressible ow. Morkovin's prediction that streamwise velocity and temperature uctuations should be anti-correlated, which happens to be supported by compressible experiments, does not hold in the simulation. Instead, a relationship is found between the rates of turbulent heat and momentum transfer. The turbulent kinetic energy budget is computed and compared with the budgets from Spalart's incompressible simulations.