TRR 181 Seminar "Subgrid parameterizations of quasi-2d turbulence and implementation in NEMO ocean model" by Pavel Perezhogin

The TRR 181 seminar is held by Pavel Perezhogin (Institute of Numerical Mathematics of RAS) on April 29, 11am.

Abstract

Subgrid parameterizations of quasi-2d turbulence and implementation in NEMO ocean model

P.A. Perezhogin, A.V. Glazunov

Marchuk Institute of Numerical Mathematics of the Russian Academy of Sciences, Moscow

The talk consists of two parts. Shortly, we study complex subgrid closures in simple configuration (decaying 2d turbulence), and simpler closures, but in NEMO ocean model.

First part:

In quasi-2d turbulence both dissipation and backscatter associated to subgrid scales should be parameterized. In contrast to research in 3D turbulence, dissipation in 2D turbulence is usually parameterized by the eddy viscosity with prescribed coefficient or prescribed Smagorinsky constant. We test popular in 3D turbulence approaches to parameterize dissipation (dynamic model, partial reconstruction of subfilter stress (mixed model)) in comparison to conventional parameterization used in ocean models.

Usually there is a little knowledge about how to parameterize kinetic energy backscatter (KEB). There are two main parts of KEB parameterization:

1. An operator returning energy, such as negative viscosity or stochastic tendency.
2. An estimation of amount of backscattered energy. It is either proportional to dissipation, or subgrid kinetic energy equation is introduced.

Free parameters in these parts of KEB are usually chosen by hand, i.e., correlation radius, backscatter rate, and so on.

Based on a priori analysis of subgrid forces we derive both parts of KEB in rigorous large eddy simulation (LES) approach. Particularly, an approximation to Reynolds stress is proposed as an operator returning energy and enstrophy dissipation as an estimation of upscale energy flux.

The possible benefits of LES closures for ocean models are discussed.

Second part:

We study two types of KEB parameterizations (negative viscosity and stochastic tendency) in NEMO ocean model in Double Gyre configuration. They are analogous to Jansen2015 and Berner2009 formulations. Some technical points are discussed: the construction of spatially correlated stochastic tendency, an estimation of energy input for different stochastic processes. We show that KEBs can improve MOC and integrated meridional eddy heat flux, but is unable to correctly reproduce WBC extension at eddy-permitting resolution. Instead of EKE to be elongated in meridional direction, it is distributed along a boundary. This possibly results to overestimated meridional eddy heat flux near the surface. White-noise in time stochastic backscatter is shown to produce spurious generation of inertial waves. This suggests that autoregressive in time stochastic parameterizations should be used.

Based on the analysis of interaction with subgrid scales (a priori analysis), we try to answer the following questions:

1. How spatial scale of backscatter depends on the resolution
2. Can it be associated to some integral length scale of turbulent flow
3. How backscatter rate depends on the resolution

To answer these questions, we apply conventional approach with spatial filtering and nudging technique. The reliability of nudging data to construct subgrid closures is demonstrated by learning an artificial neural network simulating backscatter which is good enough in a posteriori experiment. Spectral characteristics of KEB parameterizations are compared to a priori data. A popular formula for backscatter rate based on the local Rossby number is diagnosed. Preliminary experiments at eddy-resolving resolution are presented.