On energy propagation for internal waves in dissipative fluids

Abstract

In the present note we investigate the classical concept of energy velocity for internal gravity waves in fluids taking into account the effect of dissipation. Assuming the linear Boussinesq approximation in a fluid characterized by a constant Brunt-Vaisala frequency, we introduce the dissipative parameters (viscosity and thermal conductivity), and we compare the energy velocity with the kinematic velocities (group and phase velocity). The effect of dissipation turns out to be overwhelming in a narrow wavelength band around the short wave cut-off, where the group velocity exhibits an anomalous behaviour and cannot be identified with the energy velocity.