The Contribution of Striations to the Eddy Energy Budget and Mixing: Diagnostic Frameworks and Results in a Quasigeostrophic Barotropic System with Mean Flow

Abstract

Low-frequency oceanic motions have banded structures termed ''striations.'' Since these striations embedded in large-scale gyre flows can have large amplitudes, the authors investigated the effect of mean flow on their directions as well as their contribution to energetics and mixing using a b-plane, barotropic, quasigeostrophic ocean model. In spite of the model simplicity, striations are always found to exist regardless of the imposed barotropic mean flow. However, their properties are sensitive to the mean flow. Rhines jets move with the mean flow and are not necessarily striations. If the meridional component of the mean flow is large, Rhines jets become high-frequency motions; low-frequency striations still exist, but they are nonzonal, have small magnitudes, and contribute little to energetics and mixing. Otherwise, striations are zonal, dominated by Rhines jets, and contribute significantly to energetics and mixing. This study extends the theory of b-plane, barotropic turbulence, driven by white noise forcing at small scales, to include the effect of a constant mean flow. Theories developed in this study, based upon the Galilean invariance property, illustrate that the barotropic mean flow has no effect on total mixing rates, but does affect the energy cascades in the frequency domain. Diagnostic frameworks developed here can be useful to quantify the striations' contribution to energetics and mixing in the ocean and more realistic models. A novel diagnostic formula is applied to estimating eddy diffusivities.

A Multiwavenumber Theory for Eddy Diffusivities and Its Application to the Southeast Pacific (DIMES) Region

“…Surface eddy diffusivities from the F-N theory agree with those from altimetry (e.g., Ferrari and Nikurashin 2010;Klocker and Abernathey 2014;Bates et al 2014). The F-N theory also captures the three-dimensional structure of float-based eddy diffusivities in the intense Kuroshio Extension jet area (Chen et al 2014). On the other hand, the theory appears to break down in regions where large topographic gradients occur (e.g., Griesel et al 2010;Naveira-Garabato et al 2011;Chen et al 2014).…”

“…The F-N theory also captures the three-dimensional structure of float-based eddy diffusivities in the intense Kuroshio Extension jet area (Chen et al 2014). On the other hand, the theory appears to break down in regions where large topographic gradients occur (e.g., Griesel et al 2010;Naveira-Garabato et al 2011;Chen et al 2014). Bates et al (2014) found that the F-N theory is also not effective in capturing the observed vertical structures of eddy diffusivities from the U.S./U.K.…”

“…Note that although some previous studies (e.g., Klocker and Abernathey 2014) assume that the mean flow is zonal, this theory applies to the case with the mean flow in any arbitrary direction (Chen et al 2014). Here, C w denotes the phase speed along the mean flow direction; positive C w corresponds to downstream propagation, and negative C w corresponds to upstream propagation (Chen et al 2014).…”

“…This sensitivity has motivated efforts to estimate eddy mixing rates in the ocean that aim to reveal mixing processes leading to improved eddy parameterizations (e.g., Gille et al 2012). Both float-based and tracer-based diagnostic approaches have been employed to estimate diffusivities in the tropical North Atlantic (e.g., Banyte et al 2013), western boundary currents (e.g., Chen et al 2014), the Southern Ocean (e.g., LaCasce et al 2014;Tulloch et al 2014), and the global surface (e.g., Abernathey and Marshall 2013).…”

“…In fact, the frequency-wavenumber spectra of sea surface height is a broad continuum with no robust peaks, indicating that the oceanic eddy field includes motions over a broad range of wavenumbers and frequencies (e.g., Wunsch 2010;Wortham 2013;Wortham and Wunsch 2014). Even a single Gaussian vortex can be decomposed into wave motions with a range of wavenumbers and frequencies (Chen et al 2015). In the midlatitude ocean interior away from western boundary currents, the phase speeds for all the dominant wavenumbers are roughly the same; however, in the Gulf Stream, the Kuroshio Extension, and the ACC, the dominant waves are dispersive, and both eastward-and westward-propagating waves are nonnegligible [see Figs.…”