Small perturbations in hydromechanics with dissipation

We study the effect of dissipative factors, such as viscosity and thermal conductivity, on the propagation and damping of small perturbations in a one-dimensional hydrodynamics. It is shown that the basic thermodynamic inequalities are just the conditions of linear stability. We analyzed the effect of the degeneracy of the sound waves when they become non-propagating types of disturbances. This effect occurs at very short wavelengths of the order of the mean free path. It is exciting to interpret this fact as a manifestation of atomisticity remaining within the strict limits of approximation of a continuous medium. It is shown that viscosity can have a destabilizing effect. This is associated with a typical “degeneracy” of the hydrodynamic equations, that is, the absence of dissipative terms in the continuity equation.