An asymptotic analysis of the equations describing supersonic turbulen
t flow over an adiabatic wall is carried out for high Reynolds numbers
, Re, and mainstream Mach numbers, M(e) = O(1). A general expression f
or the adiabatic-wall temperature is derived. The asymptotic theory co
nstrains the types of turbulence models that are suitable to represent
the effects of viscous dissipation. A simple algebraic turbulence mod
el is proposed and comparisons with measured total enthalpy profile da
ta show good agreement, capturing the overshoot observed in total enth
alpy near the boundary-layer edge.