Identification and extraction of vortical structures and of waves in a
disorganised flow is a mayor challenge in the study of turbulence. We present a
study of the spatio-temporal behavior of turbulent flows in the presence of
different restitutive forces. We show how to compute and analyse the
spatio-temporal spectrum from data stemming from numerical simulations and from
laboratory experiments. Four cases are considered: homogeneous and isotropic
turbulence, rotating turbulence, stratified turbulence, and water wave
turbulence. For homogeneous and isotropic turbulence, the spectrum allows
identification of sweeping by the large scale flow. For rotating and for
stratified turbulence, the spectrum 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. Finally, in water wave turbulence the spectrum shows a
transition from gravity-capillary waves to bound waves as the amplitude of the
forcing is increased.Comment: Added new references and analysi
