A direct numerical simulation of a supersonic turbulent boundary layer has been
performed. We take advantage of a technique developed by Spalart for incompressible
flow. In this technique, it is assumed that the boundary layer grows so slowly
in the streamwise 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 modified system of
equations, in which the flow 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
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 Reθ′ = 849. The Reynolds number based on momentum integral thickness
and free-stream viscosity is Reθ = 1577. The results indicate that the Van Driest
transformed velocity satisfies 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 fluctuations are higher than in incompressible flow. Morkovin's prediction
that streamwise velocity and temperature fluctuations 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.