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 Fourier 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$^\circ$) 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.