Extracting internal gravity waves from simulations of stratified turbulence

In stratified turbulence internal gravity waves and advective motions coexist. A central discussion in the field has been what is the importance of one or the other motion in the dynamics. The main difficulty in answering this question has been the fact that these motions interact within stratified turbulence, which means that it is not straightforward to decompose a turbulent field from an experiment or simulation into waves and material motions. With the advent of modern computing, it has recently become possible to perform Direct Numerical Simulations (DNS) of the problem and to transform a time series of the velocity field into frequency and wavenumber space in a 4D Fourier transform. Since waves should exist only in a specific part of this 4D space which is described by the dispersion relation, this process allows to quantify the amount of energy in the waves. We present results from DNS with isotropic forcing, obtained using such spatio-temporal analysis. It is found that in DNS with buoyancy Reynolds number Re_b ∼ 1, the waves dominate the overall energy in the flow. This result however is dependent on the forcing not exciting the box-filling shear modes directly. In DNS with higher Re_b this picture changes significantly.