Mapping the Energy Cascade in the North Atlantic Ocean: The Coarse-Graining Approach

Abstract

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 quasispectral, 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.

The Impact of Horizontal Resolution on Energy Transfers in Global Ocean Models

“…This is different from e.g., [10], where gradients are evaluated in spectral space from the Fourier transformed velocities. Our method also differs from Aluie, et al [32], which may be more accurate.…”

Surface Ocean Enstrophy, Kinetic Energy Fluxes, and Spectra From Satellite Altimetry

“…However, a careful examination of the energy budget in numerical simulations reveals that, while KE cascades to larger scales, the total energy in the first baroclinic mode does indeed flow downscale (Scott & Arbic, 2007); a feature that is comforting in the context of the traditional theory. In fact, along with the two-layer QG study of Scott and Arbic (2007), inverse transfer of KE has also been documented in more comprehensive ocean models (Aluie et al, 2017;Arbic et al, 2014;Schl€ osser & Eden, 2007;Venaille et al, 2011). However, the relatively smaller forward flux of KE at small scales is more delicate, and is possibly a result of the limited resolution of the altimetry data (Arbic et al, 2013).…”

Modulation of Lateral Transport by Submesoscale Flows and Inertia‐Gravity Waves

“…Specifically, we take the raw velocity fields (sampled at hourly resolution) and average them over intervals of 1 day and 1 week. We do not explicitly apply any spatial filtering (e.g., Aluie et al, ), although the time averaging does result in smoother velocity fields (see section for more details). Below are some of the reasons why we choose to examine time‐averaged velocities: Since different dynamical regimes (e.g., waves vs. balanced motions) are most reliably separated in time rather than in space (Wagner & Young, ), temporal filtering is a straightforward way to remove different processes from a given data set. The SWOT science team has effectively adopted the daily averaged or 3‐day‐averaged flow as the “truth” signal for evaluating methods to separate balanced and unbalanced motions (Qiu et al, , ; Wang et al, ). Ocean model simulations commonly output time‐averaged velocity fields such as daily, 5‐day, or monthly averages. The processing algorithms used to map along‐track SSH observations to gridded maps (e.g., AVISO Ducet et al, ) involve some temporal smoothing. Time averaging is computationally tractable even with very large data sets. …”

“…Specifically, we take the raw velocity fields (sampled at hourly resolution) and average them over intervals of 1 day and 1 week. We do not explicitly apply any spatial filtering (e.g., Aluie et al, 2018), although the time averaging does result in smoother velocity fields (see section 3 for more details). Below are some of the reasons why we choose to examine time-averaged velocities:…”