CAS Seminar

Gökce Tuba Masur

(Jacobs University)

"Optimal balance for the rotating shallow water model in primitive variables"

Date: Mon, October 21, 2019
Time: 11:15
Place: Research I Seminar Room

Abstract: Spontaneously generated gravity waves and their subsequent capture are assumed to provide a significant contribution to a dissipation route of energy in the ocean. To understand this dissipation route properly, it is required to decompose gravity waves from geophysical flows. This flow decomposition can be achieved by the method of optimal balance, which is introduced by Viúdez and Dritschel (2004) in the context of rapidly rotating fluid flow with Lagrangian view to provide balanced initializations for geophysical flows. We, however, still do not know about quantification of gravity-waves excitation starting with a balanced initialization and the importance of these flows in the dissipation route. To analyse them, it is necessary to perform diagnostic derivation of balanced flows from geophysical ocean models in primitive variables. We, therefore, apply the method of optimal balance to the \(f\)-plane shallow water model. The method is carried out as a boundary value problem in time through adiabatically deforming the nonlinear model into its linear form, where wave-splitting is exact and this problem is solved iteratively until converging a balanced flow. We explain the formulation of the method in an algorithm where whole dynamics are in the primitive variables while kinematic potential vorticity inversion formulas appears if potential vorticity is set as "base-point" field. The implementation of the algorithm demonstrated that it is also possible to balance a flow by setting height field as a "base-point", which led the whole algorithm to be in the primitive variables. Optimal balance, hence, has the promise to produce accurate imbalance decomposition without the need of any asymptotic analysis and it can minimize generation of unrealistic waves, detected as gravity waves, so that, more accurate the route to dissipation can be visible.