Turbulence is ubiquitous in a large variety of flows, from geophysical and astrophysical to industrial flows. Given their complexity, turbulent flows are often studied by combining numerical, experimental and theoretical approaches. One of the building blocks when describing turbulence is the concept of the eddy, a swirling flow loosely associated with vortical structures. However, in flows in the atmosphere, the oceans, and in the interplanetary medium, restitutive forces (such as the Coriolis force associated with rotation, buoyancy forces associated with stratification, gravity and capillary forces in free surfaces, and the Lorentz force in ionized media) allow the system to also sustain waves, which in turn interact with vortical structures in the flow thus changing the fluid dynamics and the turbulent transport. In numerical simulations, the resulting nonlinear interaction between waves, as well as the interaction between waves and eddies, are hard to measure and quantify. In this talk I will present numerical simulations of turbulent flows, and a method to compute spectra resolved in time and in space to extract the waves from the turbulence, and to precisely quantify their relevance in the overall dynamics of the system. Several examples of turbulent flows will be considered, with an emphasis in rotating and in stratified turbulence, where the method allows identification of the waves, precise quantification of the energy in the waves and in the turbulent eddies, and identification of physical mechanisms such as Doppler shift and wave absorption in critical layers.
