  We develop a tractable interaction model for a polyatomic gas, whose kinetic
equation combines a Vlasov-type mean field forcing due to an intermolecular
potential, and a Boltzmann-type collision integral due to rotational
interactions. We construct a velocity moment hierarchy for the new kinetic
equation, and find that, under the high Reynolds number condition, the pressure
equation becomes decoupled from the angular momentum and stress. For the heat
flux, we propose a novel closure by prescribing the specific heat capacity of
the gas flow. Setting the specific heat capacity to that of a constant-pressure
process leads to the system of equations for a balanced flow, where the
momentum transport equation contains the mean field forcing, which is an
averaged effect of the intermolecular potential. Remarkably, the balanced flow
equations do not contain any information about internal thermodynamic
properties of the gas, and are thereby applicable to a broad range of different
gases. We conduct numerical simulations for an air-like gas at normal
conditions in the inertial flow regime, where the pressure is constant
throughout the domain. We find that the presence of the intermolecular
potential produces a distinctly turbulent flow, whose time-averaged Fourier
spectra of the kinetic energy and temperature exhibit Kolmogorov's power decay.
