  We investigate the fluctuations of thermodynamic state-variables in
compressible aerodynamic wall-turbulence, using results of direct numerical
simulation (DNS) of compressible turbulent plane channel flow. The basic
transport equations governing the behaviour of thermodynamic variables
(density, pressure, temperature and entropy) are reviewed and used to derive
the exact transport equations for the variances and fluxes (transport by the
fluctuating velocity field) of the thermodynamic fluctuations. The scaling with
Reynolds and Mach number of compressible turbulent plane channel flow is
discussed. Correlation coefficients and higher-order statistics of the
thermodynamic fluctuations are examined. Finally, detailed budgets of the
transport equations for the variances and fluxes of the thermodynamic variables
from a well-resolved DNS are analysed. Implications of these results both to
the understanding of the thermodynamic interactions in compressible
wall-turbulence and to possible improvements in statistical modelling are
assessed. Finally, the required extension of existing DNS data to fully
characterise this canonical flow is discussed.
