Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-graining Approach
Journal of Physical Oceanography
American Meteorological Society
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A coarse-graining framework is implemented to analyze nonlinear processes, measure energy transfer rates and map out the energy pathways from simulated global ocean data. Traditional tools to measure the energy cascade from turbulence theory, such as spectral flux or spectral transfer rely on the assumption of statistical homogeneity, or at least a large separation between the scales of motion and the scales of statistical inhomogeneity. The coarse-graining framework allows for probing the fully nonlinear dynamics simultaneously in scale and in space, and is not restricted by those assumptions. This paper describes how the framework can be applied to ocean flows. Energy transfer between scales is not unique due to a gauge freedom. Here, it is argued that a Galilean invariant subfilter scale (SFS) flux is a suitable quantity to properly measure energy scale-transfer in the Ocean. It is shown that the SFS definition can yield answers that are qualitatively different from traditional measures that conflate spatial transport with the scale-transfer of energy. The paper presents geographic maps of the energy scale-transfer that are both local in space and allow quasi-spectral, or scale-by-scale, dynamics to be diagnosed. Utilizing a strongly eddying simulation of flow in the North Atlantic Ocean, it is found that an upscale energy transfer does not hold everywhere. Indeed certain regions, near the Gulf Stream and in the Equatorial Counter Current have a marked downscale transfer. Nevertheless, on average an upscale transfer is a reasonable mean description of the extra-tropical energy scale-transfer over regions of O(10^3) kilometers in size.
Financial support was provided by IGPPS at Los Alamos National Laboratory (LANL) and NSF grant OCE-1259794. HA was also supported through DOE grants de-sc0014318, de-na0001944, and the LANL LDRD program through project number 20150568ER. MH was also supported through the HiLAT project of the Regional and Global Climate Modeling program of the DOE’s Office of Science, and GKV was also supported by NERC, the Marie Curie Foundation and the Royal Society (Wolfson Foundation). This research used resources of the National Energy Research Scientific Computing Center, a DOE Office of Science User Facility supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC02-05CH11231.
This is the final version of the article. Available from AMS via the DOI in this record.
Vol. 48 (2), pp. 225-244