Non-local Eddy-Mean Kinetic Energy Transfers in Submesoscale-Permitting
Ensemble Simulations
Abstract
Understanding processes associated with eddy-mean flow interactions
helps our interpretation of ocean energetics, and guides the development
of parameterizations. Here, we focus on the non-local nature of Kinetic
Energy (KE) transfers between mean and turbulent reservoirs. Transfers
are interpreted as non-local when the energy extraction from the mean
flow does not locally sustain energy production of the turbulent flow,
or vice versa. The novelty of our approach is to use ensemble statistics
to define the mean and the turbulent flow. Based on KE budget
considerations, we first rationalize the eddy-mean separation in the
ensemble framework, and discuss the interpretation of a mean flow driven
by the prescribed (surface and boundary) forcing and a turbulent flow u’
driven by non-linear dynamics sensitive to initial conditions. We then
analyze 120-day long, 20-member ensemble simulations of the Western
Mediterranean basin run at 1/60 resolution. Our main contribution is to
recognize the prominent contribution of the cross energy term .u_h’ to
explain non-local energy transfers. This provides a strong constraint on
the horizontal organization of eddy-mean flow KE transfers since this
term vanishes identically for perturbations (u_h’) orthogonal to the
mean flow (). We also highlight the prominent contribution of vertical
turbulent fluxes for energy transfers within the surface mixed layer.
Analyzing the scale dependence of these non-local energy transfers
supports the local approximation usually made in the development of
meso-scale, energy-aware parameterizations for non-eddying models, but
points out to the necessity of accounting for these non-local effects in
the meso-to-submeso scale range.