Diagnostics of isopycnal mixing in a circumpolar channel

Abstract

Mesoscale eddies mix tracers along isopycnals and horizontally at the sea surface. This paper compares different methods of diagnosing eddy mixing rates in an idealized, eddy-resolving model of a channel flow meant to resemble the Antarctic Circumpolar Current. The first set of methods, the ''perfect'' diagnostics, are techniques suitable only to numerical models, in which detailed synoptic data is available. The perfect diagnostic include flux-gradient diffusivities of buoyancy, QGPV, and Ertel PV; Nakamura effective diffusivity; and the four-element diffusivity tensor calculated from an ensemble of passive tracers. These diagnostics reveal a consistent picture of isopycnal mixing by eddies, with a pronounced maximum near 1000 m depth. The isopycnal diffusivity differs from the buoyancy diffusivity, a.k.a. the Gent-McWilliams transfer coefficient, which is weaker and peaks near the surface and bottom. The second set of methods are observationally ''practical'' diagnostics. They involve monitoring the spreading of tracers or Lagrangian particles in ways that are plausible in the field. We show how, with sufficient ensemble size, the practical diagnostics agree with the perfect diagnostics in an average sense. Some implications for eddy parameterization are discussed.

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

“…Mixing rates of passive tracers induced by eddies are often quantified using the eddy mixing tensor D ij , (Plumb and Mahlman 1987;Bachman 2012;Bachman and Fox-Kemper 2013;Abernathey et al 2013), which is defined as…”

“…Equation (27) is an underdetermined system for one tracer, and therefore, previous studies solve for D ij by using the pseudoinversion method, which involves initializing multiple tracers with different initial tracer gradients and then calculating D ij through the least squares approach (Plumb and Mahlman 1987;Bachman 2012;Abernathey et al 2013). However, we chose to use a novel approach from G. Flierl (2014, unpublished manuscript).…”

“…(29)- (31)] has several advantages. First, the pseudoinversion approach can be computationally expensive; for example, six tracers are used in Abernathey et al (2013) to infer the eddy mixing tensor in an idealized channel model. However, to diagnose D ij using the new formula, we only need N special tracers in an N-dimensional flow.…”

“…As a key component of the oceanic circulation, they stir and mix tracers (e.g., heat and potential vorticity) and therefore greatly influence the oceanic circulation and climate variability. Given their importance, much effort has been made recently toward estimating and interpreting eddy energy budgets (e.g., Ferrari and Wunsch 2009;Xu et al 2011;Chen et al 2014a) and eddy mixing rates (e.g., Gille et al 2007;Griesel et al 2010;Rypina et al 2012;Klocker et al 2012a,b;Abernathey et al 2013;Chen et al 2014b;Chen et al 2015b) in the global ocean.…”

“…It is important to reveal the eddy dynamics and thereby allow for the improvement of eddy parameterization schemes. As summarized by Abernathey et al (2013), many methods have been used to diagnose eddy mixing rates, such as flux-gradient diffusivities, Nakamura effective diffusivities, and Lagrangian diffusivities. These methods essentially estimate mixing rate contributions from all of the eddies.…”