# Publications by Tomos David

## Eddy-mixing entropy and its maximization in forced-dissipative geostrophic turbulence

Journal of Statistical Mechanics: Theory and Experiment
IOP Publishing **2018** (2018) 073206

An equilibrium, or maximum entropy, statistical mechanics theory can be derived for ideal, unforced and inviscid, geophysical flows. However, for all geophysical flows which occur in nature,forcing and dissipation play a major role. Here, a study of eddy-mixing entropy in a forced dissipative barotropic ocean model is presented. We heuristically investigate the temporal evolution of eddy-mixing entropy, as defined for the equilibrium theory, in a strongly forced and dissipative system. It is shown that the eddy-mixing entropy provides a descriptive tool for understanding three stages of the turbulence life cycle: growth of instability; formation of large scale structures; and steady state fluctuations. The fact that the eddy-mixing entropy behaves in a dynamically balanced way is not a priori clear and provides a novel means of quantifying turbulent disorder in geophysical flows. Further, by determining the relationship between the time evolution of entropy and the maximum entropy principle, evidence is found for the action of this principle in a forced dissipative flow. The maximum entropy potential vorticity statistics are calculated for the flow and are compared with numerical simulations. Deficiencies of the maximum entropy statistics are discussed in the context of the mean-field approximation for energy. This study highlights the importance of entropy and statistical mechanics in the study of geostrophic turbulence.

## The statistical nature of turbulent barotropic ocean jets

Ocean Modelling Elsevier **113** (2017) 34-49

Jets are an important element of the global ocean circulation. Since these jets are turbulent, it is important that they are characterized using a statistical framework. A high resolution barotropic channel ocean model is used to study jet statistics over a wide range of forcing and dissipation parameters. The first four moments of the potential vorticity distribution on contours of time-averaged streamfunction are considered: mean, standard deviation, skewness and kurtosis. A self-similar response to forcing is found in the mean and standard deviation for eastward barotropic jets which exhibit strong mixing barriers; this self-similarity is related to the global potential enstrophy of the flow. The skewness and kurtosis give a behaviour which is characteristic of mixing barriers, revealing a bi/trimodal statistical distribution of potential vorticity with homogenized potential vorticity on each side of the barrier. The mixing barrier can be described by a simple statistical model. This behaviour is shown to be lost in westward jets due to an asymmetry in the formation of zonal mixing barriers. Moreover, when the statistical analysis is performed on eastward jets in a streamfunction following frame of reference, the distribution becomes monomodal. In this way we can distinguish between the statistics due to wave-like meandering of the jet and the statistics due to the more diffusive eddies. The statistical signature of mixing barriers can be seen in more realistic representations of the Southern Ocean and is shown to be an useful diagnostic tool for identifying strong jets on isopycnal surfaces. The statistical consequences of the presence, and absence, of mixing barriers are likely to be valuable for the development of stochastic representations of eddies and their dynamics in ocean models.

## Scale-Aware Deterministic and Stochastic Parametrizations of Eddy-Mean Flow Interaction

Ocean Modelling Elsevier **111** (2017) 66–80-

The role of mesoscale eddies is crucial for the ocean circulation and its energy budget. The sub-grid scale eddy variability needs to be parametrized in ocean models, even at so-called eddy permitting resolutions. Porta Mana and Zanna (2014) propose an eddy parametrization based on a non-Newtonian stress which depends on the partially resolved scales and their variability. In the present study, we test two versions of the parametrization, one deterministic and one stochastic, at coarse and eddy-permitting resolutions in a double gyre quasi-geostrophic model. The parametrization leads to drastic improvements in the mean state and variability of the ocean state, namely in the jet rectification and the kinetic-energy spectra as a function of wavenumber and frequency for eddy permitting models. The parametrization also appears to have a stabilizing effect on the model, especially the stochastic version. The parametrization possesses attractive features for implementation in global models: very little computational cost, it is flow aware and uses the properties of the underlying flow. The deterministic coefficient is scale-aware, while the stochastic parameter is scale- and flow-aware with dependence on resolution, stratification and wind forcing.

## Non-assimilated tidal modeling of the South China Sea

DEEP-SEA RESEARCH PART I-OCEANOGRAPHIC RESEARCH PAPERS **78** (2013) 42-48