Abstract
We consider the separation of motion related to internal gravity waves and eddy dynamics in stably stratified flows obtained by direct numerical simulations. The waves’ dispersion relation links their angle of propagation to the vertical θ , to their frequency ω , so that two methods are used for characterizing wave-related motion: (a) the concentration of kinetic energy density in the ( θ , ω ) map along the dispersion relation curve; and (b) a direct computation of two-point two-time velocity correlations via a four-dimensional Fourier transform, permitting to extract wave-related space-time coherence. The second method is more computationally demanding than the first. In canonical flows with linear kinematics produced by space-localized harmonic forcing, we observe the pattern of the waves in physical space and the corresponding concentration curve of energy in the ( θ , ω ) plane. We show from a simple laminar flow that the curve characterizing the presence of waves is distorted differently in the presence of a background convective mean velocity, either uniform or varying in space, and also when the forcing source is moving. By generalizing the observation from laminar flow to turbulent flow, this permits categorizing the energy concentration pattern of the waves in complex flows, thus enabling the identification of wave-related motion in a general turbulent flow with stable stratification. The advanced method (b) is finally used to compute the wave-eddy partition in the velocity–buoyancy fields of direct numerical simulations of stably stratified turbulence. In particular, we use this splitting in statistics as varied as horizontal and vertical kinetic energy, as well as two-point velocity and buoyancy spectra.
Highlights
Most geophysical flows on Earth exhibit density variations and are submitted to the effect of rotation, so that their dynamics is the result of several intermingled phenomena of different nature: turbulent transport, waves, thermal diffusion, and convection, to cite but a few
Several articles have been devoted to the determination of the presence of inertial waves in rotating turbulence or of internal gravity waves in stratified turbulent flows. This determination is based on their dispersion relation, whose trace is sought in different forms in velocity–density statistics, from data obtained in experiments [8] or direct numerical simulations [9,10]
We propose numerical simulations of Navier–Stokes–Boussinesq for stably stratified flows generated by specific forcings, in which we use two spatiotemporal techniques for separating the wave motion from the eddy motion
Summary
Most geophysical flows on Earth exhibit density variations and are submitted to the effect of rotation, so that their dynamics is the result of several intermingled phenomena of different nature: turbulent transport, waves, thermal diffusion, and convection, to cite but a few. Several articles have been devoted to the determination of the presence of inertial waves in rotating turbulence or of internal gravity waves in stratified turbulent flows This determination is based on their dispersion relation, whose trace is sought in different forms in velocity–density statistics, from data obtained in experiments [8] or direct numerical simulations [9,10]. A new technique based on spatiotemporal decomposition is implemented that requires a four-dimensional (4D) Fourier transform (3D in space and 1D in time) and permits to filter the waves by using the dispersion relation modified by the sweeping effect due to VSHF With this decomposition, statistics for the separate waves and eddy contents of the flow are obtained, e.g., their energy spectra, as well as maps of the respective flow structures by visualization in physical space.
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