John Yawny, Department of Applied Mathematics, University of Waterloo
Numerical Methods to Simulate a Hierarchy of Ocean Models
The intermediate scales, O(10-100) km mesoscale and O(1-10) km submesoscale, play an important role in the cascade of energy in the ocean. When studying these smaller scale processes global circulation models (GCMs) tend to be very dissipative due, at least in part, to the low-order methods that they use for discretizing the derivatives. Thus, to study the physical processes in the ocean in an idealized setting, higher-order accurate methods will help to resolve the smaller length scales inherent in submesoscale dynamics. A number of high-order numerical schemes have been compared and an outline of modifications to a current oceanic model, Tempest, has been devised. In addition, methods will be implemented that conserve high order accuracy of the numerical methods and positivity of tracers quantities, such as biological and chemical data. The future intent is to try and adapt this model to a hierarchy of oceanic regimes, which are briefly discussed in the proposal.