An asymptotic analysis of the compressible turbulent boundary-layer eq
uations is carried out for large Reynolds numbers and mainstream Mach
numbers of O(1). A self-consistent two-layer asymptotic structure is d
escribed wherein the time-mean velocity and total enthalpy are logarit
hmic within the overlap zone but in terms of the Howarth-Dorodnitsyn v
ariable; the proposed structure leads to a compressible law of the wal
l for high-speed turbulent flows with surface heat transfer. Simple ou
ter-region algebraic turbulence models are formulated to reflect the e
ffects of compressibility. To test the proposed asymptotic structure a
nd turbulence models, a set of self-similar outer-region profiles for
velocity and total enthalpy is obtained for constant-pressure flow and
for constant wall temperature; these are combined with wall-layer pro
files to form a set of composite profiles valid across the entire boun
dary layer. A direct comparison with experimental data shows good agre
ement over a wide range of conditions for flows with and without surfa
ce heat transfer.