The hyper-CASL algorithm: an accurate, efficient new approach to modelling complex atmospheric and oceanic flows
Seminar Room 1, Newton Institute
We describe a powerful new approach to the simulation of layerwise-2D geophysical flows. Our approach combines the CASL algorithm, a hybrid contour-dynamics method ideally suited for the Lagrangian advection of potential vorticity (PV) contours across an Eulerian fixed grid, with a standard vortex-in-cell method. The latter is here used to compensate for errors arising from contour regularisation or `surgery' appearing at the level of the grid. In this way, (essential) dissipation occurs only at sub-grid scales, and there is no direct impact of surgery on the computed velocity field, which is obtained on the grid by standard spectral or (compact) finite-difference methods. This is particularly important for long-term simulations, where error accumulation needs to be minimised.
This new approach, coined the `hyper-CASL algorithm', also allows for general non-conservative effects, by design. For instance, one may take account of radiative (thermal) effects which attract a given flow to some thermal equilibrium distribution, or one can account for `Ekman pumping' which converts wind stress at the ocean's surface into a vorticity source or sink there. In fact, very general forms of forcing or damping can be accounted for (e.g. stochastic, moisture, small-scale convection, etc.).
Hyper-CASL is not limited to PV, but can be applied to other tracers such as chemical species in the atmosphere, including moisture. In particular, modelling water vapour by contours and subgrid-scale convection by Lagrangian particles may be a timely opportunity to improve the forecasting of precipitation.
Hyper-CASL is illustrated here in long-term simulations of quasi-geostrophic and shallow-water turbulence. These simulations reveal unprecedented detail, in particular vortices spanning a very wide range of scales and significantly affecting flow statistics.