Geostrophic Turbulence in the Frequency–Wavenumber Domain: Eddy-Driven Low-Frequency Variability*

Abstract

Motivated by the potential of oceanic mesoscale eddies to drive intrinsic low-frequency variability, this paper examines geostrophic turbulence in the frequency–wavenumber domain. Frequency–wavenumber spectra, spectral fluxes, and spectral transfers are computed from an idealized two-layer quasigeostrophic (QG) turbulence model, a realistic high-resolution global ocean general circulation model, and gridded satellite altimeter products. In the idealized QG model, energy in low wavenumbers, arising from nonlinear interactions via the well-known inverse cascade, is associated with energy in low frequencies and vice versa, although not in a simple way. The range of frequencies that are highly energized and engaged in nonlinear transfer is much greater than the range of highly energized and engaged wavenumbers. Low-frequency, low-wavenumber energy is maintained primarily by nonlinearities in the QG model, with forcing and friction playing important but secondary roles. In the high-resolution ocean model, nonlinearities also generally drive kinetic energy to low frequencies as well as to low wavenumbers. Implications for the maintenance of low-frequency oceanic variability are discussed. The cascade of surface kinetic energy to low frequencies that predominates in idealized and realistic models is seen in some regions of the gridded altimeter product, but not in others. Exercises conducted with the general circulation model suggest that the spatial and temporal filtering inherent in the construction of gridded satellite altimeter maps may contribute to the discrepancies between the direction of the frequency cascade in models versus gridded altimeter maps seen in some regions. Of course, another potential reason for the discrepancy is missing physics in the models utilized here.

Intrinsic Variability of Sea Level from Global Ocean Simulations: Spatiotemporal Scales

“…Regions of strong mesoscale variability closely coincide with regions where LFSS variability is large. This coincidence suggests that mesoscale energy may spontaneously cascade toward longer time scales through nonlinear processes, as recently suggested by Arbic et al (2014).…”

“…The marked coincidence between HFSS and LFSS intrinsic variability maps suggests that the energy of these mesoscale motions may spontaneously cascade toward longer time scales and feed the LFSS spectral component. Such a temporal inverse cascade has indeed been diagnosed recently from idealized and realistic simulations (Arbic et al 2012(Arbic et al , 2014, albeit over a narrower range of time scales. Whether this nonlinear process may actually transfer mesoscale kinetic energy up to interannual and longer time scales remains to be assessed and is currently being investigated.…”

“…Based on 5-yr SLA time series, simulated by a global eddying OGCM driven by a full forcing, Arbic et al (2014) showed that nonlinear eddy-eddy interactions can spontaneously transfer kinetic energy from mesoscale eddies, which are largely chaotic, to longer time scales. In other words, this temporal inverse cascade process might well transfer the mesoscale intrinsic chaotic variability toward lower frequencies.…”

“…intrinsic, eddy-driven inverse cascade processes may be transferring mesoscale (HFSS) kinetic energy toward larger temporal (LFSS) and spatial (LFLS) scales (e.g., Berloff et al 2007;Arbic et al 2014). The contribution of intrinsic processes to the fully forced, low-frequency large-scale SLA variance is therefore substantial in several regions (bottom panel in Fig.…”

Properties and Origins of the Anisotropic Eddy-Induced Transport in the North Atlantic

“…In particular, it is possible that zonal transients are normal modes and exist because of the linear dynamics through their interactions with the mean flow (Berloff and Kamenkovich 2013a,b). Alternatively, the energy at the zonal transient part of the spectrum can exist because of the nonlinear energy transfer due to interactions among transient eddies (Arbic et al 2014). Investigation of the dynamics of zonal transients is left for future studies.…”