  The letter considers non-isothermal fluid flows and revises simplifications
of basic hydrodynamic equations for such flows arriving eventually to a
generalization of the Oberbeck-Boussinesq approximation valid for arbitrary
equation of state including both non-ideal gases as well as liquids. The
proposed approach is based on a suggested general definition of potential
temperature. Special attention is put on the energy conservation principle, and
it is shown that the proposed approximation exactly preserves the total
mechanical energy by approximate equations of motion. The principal importance
for any turbulent boundary layer model to respect the conservation laws is
emphasized explicitly.
