  In this paper, we present an overview of concepts and data concerning inverse
cascades of excitation towards scales larger than the forcing scale in a
variety of contexts, from two-dimensional fluids and wave turbulence, to
geophysical flows in the presence of rotation and stratification. We briefly
discuss the role of anisotropy in the occurrence and properties of such
cascades. We then show that the cascade of some invariant, for example the
total energy, may be transferred through nonlinear interactions to both the
small scales and the large scales, with in each case a constant flux. This is
in contrast to the classical picture, and we illustrate such a dual cascade in
the context of atmospheric and oceanic observations, direct numerical
simulations and modeling. We also show that this dual cascade of total energy
can in fact be decomposed in some cases into separate cascades of the kinetic
and potential energies, provided the Froude and Rossby numbers are small
enough. In all cases, the potential 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 between potential
and kinetic modes is obtained, leading to an energy ratio close to one, with
strong departure at large scales due to the dominant kinetic energy inverse
cascade and piling-up at the lowest spatial frequency, and at small scales due
to unbalanced dissipation processes, even though the Prandtl number is equal to
one.
