On Eddy Viscosity, Energy Cascades, and the Horizontal Resolution of Gridded Satellite Altimeter Products*

Abstract

Motivated by the recent interest in ocean energetics, the widespread use of horizontal eddy viscosity in models, and the promise of high horizontal resolution data from the planned wide-swath satellite altimeter, this paper explores the impacts of horizontal eddy viscosity and horizontal grid resolution on geostrophic turbulence, with a particular focus on spectral kinetic energy fluxes P(K) computed in the isotropic wavenumber (K) domain. The paper utilizes idealized two-layer quasigeostrophic (QG) models, realistic highresolution ocean general circulation models, and present-generation gridded satellite altimeter data. Adding horizontal eddy viscosity to the QG model results in a forward cascade at smaller scales, in apparent agreement with results from present-generation altimetry. Eddy viscosity is taken to roughly represent coupling of mesoscale eddies to internal waves or to submesoscale eddies. Filtering the output of either the QG or realistic models before computing P(K) also greatly increases the forward cascade. Such filtering mimics the smoothing inherent in the construction of present-generation gridded altimeter data. It is therefore difficult to say whether the forward cascades seen in present-generation altimeter data are due to real physics (represented here by eddy viscosity) or to insufficient horizontal resolution. The inverse cascade at larger scales remains in the models even after filtering, suggesting that its existence in the models and in altimeter data is robust. However, the magnitude of the inverse cascade is affected by filtering, suggesting that the wide-swath altimeter will allow a more accurate determination of the inverse cascade at larger scales as well as providing important constraints on smaller-scale dynamics.

Evidence for Bolgiano-Obukhov scaling in rotating stratified turbulence using high-resolution direct numerical simulations

“…The steep power-law observed at large scale is consistent with many oceanic observations, as analyzed for example in [56,73]. The tendency for energy to pile-up in the large scales, even in the spin-down case, was already noted in [74], where the inverse transfer was attributed to the geostrophic modes, whereas the wave modes undergo a direct energy cascade (for a high-resolution forced case using hyper-viscosity, see [75]).…”

“…Note that spectra with a power-law index close to −2 were found in [55] for N/f varying from 4 to 32, and observations in the ocean also indicate values that are similar and in fact closer to 2.5 [56].…”

Seasonal Mesoscale and Submesoscale Eddy Variability along the North Pacific Subtropical Countercurrent

“…The issue of spurious P(K) . 0 signals in the high-wavenumber range was also raised recently by Arbic et al (2013), and caution is clearly called for in interpreting the forward KE cascade inferred from the gridded AVISO product.…”

“…14a shows that the short-wave cutoff for the inverse KE cascade tends to shift gradually to a smaller wavenumber. Several studies in the past have utilized satellite altimetry data to infer the spectral KE fluxes (e.g., Scott and Wang 2005;Qiu et al 2008;Tulloch et al 2011;Arbic et al 2013). While the AVISO-derived P(K) captures the inverse KE cascade at the mesoscale wavenumber range of K , 4 3 10 23 cpkm (see Fig.…”

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

“…Ocean currents and eddies have systematically less kinetic energy (KE) in low-resolution simulations than high-resolution simulations [1,2]. Less energetic currents and eddies can cause biases in e.g., the strength of overturning circulations [3], oceanic heat uptake [4], and mixed-layer depth [5] as well as model drifts [6].…”