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Waves in stably stratified turbulent flow

Two approaches for the identification of internal gravity waves in sheared and unsheared homogeneous stably stratified turbulence are investigated. First, the phase angle between the vertical velocity and density fluctuations is considered. It is found, however, that a continuous distribution of the phase angle is present in both weakly and strongly stratified flows. Second, a projection onto the solution of the linearized inviscid equations of motion of unsheared stratified flow is investigated. Solutions of the fully nonlinear viscous Navier–Stokes equations are thus decomposed into vertical wave modes and horizontal vortical modes. However, this decomposition includes some ‘turbulent’ motions in the ‘wave’ field when the Froude number is non-zero. In fact, for Fr > 5 the flow kinetic energy is nearly equally split between the turbulent and wave fields for all wave numbers, as for unstratified flows. This calls into question the adequacy of this decomposition, at least for weak or moderate stratification.