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

MININNI, P. D.; MARINO, R.; POUQUET, A.; ROSENBERG, D.

PHYSICS OF FLUIDS

AMER INST PHYSICS

Lugar: New York; Año: 2017 vol. 29

1070-6631

In this paper, we present an overview of concepts and data concerning inverse cascades of excitationtowards scales larger than the forcing scale in a variety of contexts, from two-dimensional fluidsand wave turbulence to geophysical flows in the presence of rotation and stratification. We brieflydiscuss the role of anisotropy in the occurrence and properties of such cascades. We then show thatthe cascade of some invariant, for example, the total energy, may be transferred through nonlinearinteractions to both the small scales and the large scales, with in each case a constant flux. This is incontrast to the classical picture, and we illustrate such a dual cascade in the context of atmosphericand oceanic observations, direct numerical simulations, and modeling. We also show that this dualcascade of total energy can in fact be decomposed in some cases into separate cascades of the kineticand potential energies, provided the Froude and Rossby numbers are small enough. In all cases, thepotential energy flux remains small, of the order of 10% or less relative to the kinetic energy flux.Finally, we demonstrate that, in the small-scale inertial range, approximate equipartition betweenpotential and kinetic modes is obtained, leading to an energy ratio close to one, with strong departureat large scales due to the dominant kinetic energy inverse cascade and piling-up at the lowest spatialfrequency and at small scales due to unbalanced dissipation processes, even though the Prandtl numberis equal to one.