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#### Comparing isopycnal eddy diffusivities in the Southern Ocean with predictions from linear theory

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##### Citation

Griesel, A., Eden, C., Koopmann, N., & Yulaeva, E. (2015). Comparing isopycnal
eddy diffusivities in the Southern Ocean with predictions from linear theory.* Ocean Modelling,*
*94*, 33-45. doi:10.1016/j.ocemod.2015.08.001.

Cite as: https://hdl.handle.net/11858/00-001M-0000-002D-CF15-3

##### Abstract

We show that the potential vorticity diffusivity predicted by linear stability analysis (LSA), is the same as a linearized version of Lagrangian cross stream isopycnal diffusivity. Both can be written in terms of the same expression the product of the eddy kinetic energy (EKE) and the integral time scale that involves the Lagrangian decay scale gamma or the growth rate omega(i) of the most unstable wave, and a frequency that is related to the difference of the mean flow speed and real part of the phase speed of the unstable waves.
Diffusivities from LSA are compared to Lagrangian isopycnal eddy diffusivities estimated from more than 700,000 numerical particles in the Southern Ocean of an eddying model. They show different spatial dependency. LSA predicts eddy diffusivities that are enhanced at the steering level where the mean flow speed equals the phase speed of the unstable waves. In contrast, Lagrangian diffusivities exhibit no clear steering level maxima, but are instead surface intensified in many places. The differences between the Lagrangian and diffusivities from LSA can be understood because EKE predicted from LSA differs from the simulated one, and because the estimated decay scale gamma is On average about 4 times larger than the largest linear growth rate. The diagnosed Lagrangian integral time scale has maxima at the depth where the mean flow speed equals the phase speed of the most unstable wave, but the diffusivity maxima are shifted towards the surface because the simulated EKE decreases rapidly with depth. Possibilities for a simple parameterization for the diffusivity are discussed. (C) 2015 Elsevier Ltd. All rights reserved.