Many flows in the laboratory and in Nature support waves and are also turbulent and thus difficult to characterize, model and predict. Fluids and plasmas for which the dissipative time based on viscosity is much longer than the time-scale of vortices (i.e. at large Reynolds numbers) need a way to dissipate the energy injected in the system, say by the Sun or the wind for the atmosphere and the oceans. Turbulence provides such a mechanism through numerous nonlinear mode coupling and the systematic formation of strong localized (intermittent) small-scale gradients, for instance in the form of current, vorticity and shear structures competing with inertial, gravity or Alfvén waves. It is in these structures that energy dissipation can occur, in a complex interplay between the large scales and the small intense scales at the origin of intermittency (see Figure 1).
Thus, why and how dissipation takes place physically in hydrodynamics, magnetohydrodynamic (MHD) and in other turbulent nonlinear systems as in the solar wind, the sun, the interstellar medium and beyond, is briefly presented, starting from basic considerations relying on simple models. The role of waves – such as those due to gravity, rotation or magnetic fields – is then analyzed in this context in terms of one governing parameter, namely the ratio of the wave period to the turbulent eddy (turn-over) time. It is shown that the spatially localized dissipation in such systems can be, in some cases and by some measure, stronger than for homogeneous isotropic turbulence in the absence of waves. This is associated with the occurrence of non-Gaussian probability distribution functions (PDFs) for various fields. The intermittency of strong localized structures is then analyzed in more detail through the joint behavior of normalized third and fourth-order moments (namely skewness S and kurtosis K) of the PDFs of these fields (see Rosenberg et al., 2023 Atmosphere 15 and references therein), noting that S = 0, K = 3 for a Gaussian. Parabolic K(S) ∼ S2 relations are observed in many instances, possibly justified through a Langevin model with additive and multiplicative noise, as already proposed for the sea-surface temperature of the ocean, the planetary boundary layer, the climate, as well as for fusion plasmas, the magnetosphere, the solar wind and dwarf galaxies. Is this a universal key to characterize turbulence properties?