**Principal Investigator**
Joerg-Olaf Wolff **Project** g28

Antarctic CRC, **Machine** VP

University of Tasmania

**Parameterization of Potential Vorticity Fluxes**

Oceanic eddies are the main carrier of meridional transports of heat, salt and other tracers all along the path of the ACC and play a vital role in the overall dynamical balance of this current system. It is therefore important to find the best parameterization of the effect of the eddy field in coarse (non-eddy resolving) global climate models. Classical parameterization of eddies in ocean models, turbulent eddy viscosities and diffusivities with constant "Austausch"-coefficients, in analogy to Fickian diffusion, have been shown to be inappropriate in the ACC/SO. Results from quasigeostrophic eddy resolving models and analytical arguments indicate, that a parameterization of eddy potential vorticity fluxes may give a more realistic dynamical balance and may lead to improved simulations. The advantage of parameterizing potential vorticity fluxes is that only one parameterization is needed to combine the two different fluxes of momentum and heat. In the special case of a jetstream in a zonal channel over flat topography the classical momentum parameterization would need negative diffusion coefficients. This is numerically unstable. In contrast model results show that eddy potential vorticity is transported down the mean gradient of potential vorticity in this case, which translates into positive diffusion coefficients. Preliminary experiments with underlying bottom relief have shown a more complex structure of the transfer coefficients. The balance equation of eddy potential enstrophy (= squared vorticity) gives a direct expression of the perturbation potential vorticity fluxes down the mean gradient of potential vorticity. This expression is mathematically simple, especially in flat bottom simulations. In simulations with bottom relief an additional term appears which has a large rotational component without dynamical significance. It is the nonrotational component which is the key to this parameterization problem.

This project is aimed at diagnosing higher order statistics (eddy potential enstrophy) in a quasigeostrophic eddy resolving channel model (QG-CHANNEL). The model was developed by the PI at the Max-Planck-Institute for Meteorology in Hamburg, FRG, and was used in a variety of experiments to investigate the momentum balance of the ACC.

**What are the basic questions addressed?**

The first aim of this project is to diagnose the eddy enstrophy balance in a fully developed geostrophic turbulent flow in experiments with and without bottom relief. The second aim is to define a functional relationship between the eddy transports of potential vorticity and the gradient of the mean field of potential vorticity.

**What are the results to date and future of the
work?**

The first attempt to compute the higher order statistics of the eddy potential enstrophy balance with accumulation of the correlations during the run gave only unsatisfactorily results. Although this method seems to be a quite elegant solution it unfortunately converges only very slowly. We have therefore repeated the flat bottom experiments with the direct perturbation method and the imbalance in the eddy potential enstrophy balance is now less than 1 % for a 90 year average. The experiments have been extended to a case with an analytitical obstacle (a Gaussian mount) and to a run with half the grid point distance. The latter run became necessary after comments by a Dutch colleague, Mr Fred Walsteyn, working on related problems, indicating that the higher-order numerical stencil used in computing the Jacobian term might not be necessary if the grid resolution was improved. Halving the grid resolution, now a very conservative resolution in terms of resolving the baroclinic Rossby radius, has shown that the lower-order Jacobian stencil still shows the old erroneous solution in the enstrophy balance. The project will be completed with an integration of the model over complex realistic topography at the Antarctic CRC on its new CRAY J90. I would like to take the opportunity to thank the ANU, STAC and the staff for continuing high-level support of this project in times when there were no supercomputer resources available in Tasmania.

**What computational techniques are used and why
is a supercomputer required?**

The model is compared to primitive equation models
very efficient in CPU time and uses multiple fast Fourier transforms
(FFTs) for the direct solution of the model equations. Each experiment
needs about 500,000 timesteps for stable higher order statistics,
which translates into approximately 13 hours of CPU time on the
VP2200 at about 94 % vectorization.

Fig. 1: Instantaneous streamfunction (top) and 90-year
time mean streamfunction (bottom) in the upper layer for a model
run with eastward windstress over flat bottom topography. Note
the the jet intensification in the time mean velocity field at
the center of the channel.