Seasonality in Transition Scale from Balanced to Unbalanced Motions in the World Ocean

Abstract

The transition scale Lt from balanced geostrophic motions to unbalanced wave motions, including near-inertial flows, internal tides, and inertia–gravity wave continuum, is explored using the output from a global 1/48° horizontal resolution Massachusetts Institute of Technology general circulation model (MITgcm) simulation. Defined as the wavelength with equal balanced and unbalanced motion kinetic energy (KE) spectral density, Lt is detected to be geographically highly inhomogeneous: it falls below 40 km in the western boundary current and Antarctic Circumpolar Current regions, increases to 40–100 km in the interior subtropical and subpolar gyres, and exceeds, in general, 200 km in the tropical oceans. With the exception of the Pacific and Indian sectors of the Southern Ocean, the seasonal KE fluctuations of the surface balanced and unbalanced motions are out of phase because of the occurrence of mixed layer instability in winter and trapping of unbalanced motion KE in shallow mixed layer in summer. The combined effect of these seasonal changes renders Lt to be 20 km during winter in 80% of the Northern Hemisphere oceans between 25° and 45°N and all of the Southern Hemisphere oceans south of 25°S. The transition scale’s geographical and seasonal changes are highly relevant to the forthcoming Surface Water and Ocean Topography (SWOT) mission. To improve the detection of balanced submesoscale signals from SWOT, especially in the tropical oceans, efforts to remove stationary internal tidal signals are called for.

Partitioning Ocean Motions Into Balanced Motions and Internal Gravity Waves: A Modeling Study in Anticipation of Future Space Missions

“…Such slope discontinuity is not observed on the KE spectrum from surface motions (gray curve on Figure b). These results, similar to those reported in Rocha, Gille, et al () and Qiu et al (), are consistent with the ω ‐k spectra on Figures c and f, indicating that in summer, IGWs much more dominate the SSH field than the KE field for scales <50 km. Considering SSH as a proxy for potential energy (PE), this suggests these conspicuous differences between KE and SSH spectra in summer should be explained in terms of the relationship between PE and KE that differs for BMs and IGWs (as detailed in Gill, ; see also Qiu et al, ).…”

“…These results, similar to those reported in Rocha, Gille, et al () and Qiu et al (), are consistent with the ω ‐k spectra on Figures c and f, indicating that in summer, IGWs much more dominate the SSH field than the KE field for scales <50 km. Considering SSH as a proxy for potential energy (PE), this suggests these conspicuous differences between KE and SSH spectra in summer should be explained in terms of the relationship between PE and KE that differs for BMs and IGWs (as detailed in Gill, ; see also Qiu et al, ). Indeed, using a shallow water model associated with a given vertical normal mode (in that case, PE is directly related to SSH), it can be shown that on one hand, the relationship between KE and PE for BMs in the spectral space (using the geostrophic approximation) is simply given by: …”

“…This represents a total of 12,000 ω ‐k spectra! Before computing the ω ‐ k spectrum for a given variable in each box, the linear trend in space and time was removed and the three‐dimensional dataset (three‐month blocks, ϕ ( x , y , t ), where ϕ is an arbitrary variable) was multiplied by a three‐dimensional ( x , y , and t ) Hanning window (Qiu et al, ). Afterward, a discrete three‐dimensional Fourier transform was computed ( , where k is the zonal wave number, l is the meridional wave number, and ω denotes frequency).…”

“…Using the dispersion relation curve for IGWs corresponding to the tenth baroclinic mode, highlights two distinct regions in the ω ‐ k spectra (see Figure : schematic of the frequency‐wave number spectrum of KE with, both, the frequency [left] and wave number [top] spectra). This methodology is used in Savage, Savage, Arbic, Alford, et al () and Qiu et al (). As already mentioned, the region above this curve (that includes mostly frequencies equal to or higher than f ) exhibits discrete beams aligned with the dispersion relation curves of the different baroclinic modes.…”

“…We first focus on the KE and SSH spectra to better understand the different IGW impacts on these fields, after the results from Rocha, Gille¸ et al () and Qiu et al (). Whereas KE wave number spectrum estimated from SSH, using the geostrophic approximation, (red curve on Figure a) and the KE spectrum estimated from surface motions (gray curve on Figures a) do not display any spectral slope discontinuity in winter, the same spectra in summer (Figure b) reveal conspicuous differences.…”