An ensemble-based eddy and spectral analysis, with application to the
Gulf Stream
Abstract
The ‘eddying’ ocean,
recognized for several decades, has been the focus of much observational
and theoretical research.
We here describe a generalization for the analysis of eddy energy, based
on the use of ensembles, that addresses two key related issues: the
definition of an ‘eddy’ and the general computation of energy spectra.
An ensemble identifies eddies as the unpredictable component of the
flow, and permits the scale decomposition of their energy in
inhomogeneous and non-stationary settings. We present two distinct, but
equally valid, spectral estimates: one is similar to classical spectra,
the other reminiscent of classical EOF analysis. Both satisfy Parseval’s
equality and thus can be interpreted as length-scale dependent energy
decompositions.
The issue of ‘tapering’ or ‘windowing’ of the data, used in traditional
approaches, is also discussed.
We apply the analyses to a mesoscale ‘resolving’ (1/12) ensemble of the
separated North Atlantic Gulf Stream.
Our results reveal highly anisotropic spectra in the Gulf Stream and
zones of both agreement and disagreement with theoretically expected
spectral shapes. In general, we find spectral slopes that fall off
faster than the steepest slope expected from quasi-geostrophic theory.