Canonical transfer and mean-eddy-turbulence interaction in geophysical fluid flows

It has long been observed in the atmosphere that the local rate of perturbation growth in a flow does not necessarily correspond in location and strength to the dynamical origin of the perturbation; the source could be from somewhere else. In this study, we show that this internal multiscale subspace interaction, or multiscale window interaction as we will refer to henceforth, can be put on a rigorous footing in terms of energy transfers. For an incompressible geophysical fluid flow, the resulting transfer between two windows bears a form reminiscent of the Poisson bracket in Hamiltonian mechanics; it is accordingly called canonical transfer in distinction from those one may have encountered in the literature. Canonical transfers are invariant with respect to averaging schemes; they merely redistribute energy between the multiscale windows, without generating or destroying energy as a whole. It is shown that the intricate nonlinear multiscale energetic process in geophysical flows can be uniquely decomposed into a transport, which integrates to zero over a closed domain, plus a canonical transfer. This result has been validated with a benchmark hydrodynamic instability model namely the Kuo model for the stability of the zontal atmospheric jet stream. We see a distribution of canonical transfer consistent with the instability structure inferred based on Kuo's theorem, while the traditional diagnostic quantities, such as the widely used ``Reynolds stress extraction'', do not agree with the inference. The theory has been utilized to harness the vortex shedding in the wake of a cylindric bluff body, and applied to the studies of several real ocean and atmosphere problems, such as the Monterey Bay processes, the Mid-Atlantic Bight shelfbreak frontal dynamics, and the generation of the North Atlantic Oscillation.