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In this paper, we present an overview of concepts and data concerning inversecascades of excitation towards scales larger than the forcing scale in avariety of contexts, from two-dimensional fluids and wave turbulence, togeophysical flows in the presence of rotation and stratification. We brieflydiscuss the role of anisotropy in the occurrence and properties of suchcascades. We then show that the cascade of some invariant, for example thetotal energy, may be transferred through nonlinear interactions to both thesmall scales and the large scales, with in each case a constant flux. This isin contrast to the classical picture, and we illustrate such a dual cascade inthe context of atmospheric and oceanic observations, direct numericalsimulations and modeling. We also show that this dual cascade of total energycan in fact be decomposed in some cases into separate cascades of the kineticand potential energies, provided the Froude and Rossby numbers are smallenough. In all cases, the potential energy flux remains small, of the order of10% or less relative to the kinetic energy flux. Finally, we demonstrate that,in the small-scale inertial range, approximate equipartition between potentialand kinetic modes is obtained, leading to an energy ratio close to one, withstrong departure at large scales due to the dominant kinetic energy inversecascade and piling-up at the lowest spatial frequency, and at small scales dueto unbalanced dissipation processes, even though the Prandtl number is equal toone.

Dual constant-flux energy cascades to both large scales and small scales