Nonlinear Processes in Oceanic and Atmospheric Flows

Presentation

Energy-Enstrophy Stability of beta-plane Kolmogorov Flow with Drag

Author: Yue-Kin Tsang, Scripps Institution of Oceanography.

Names and affiliation of other authors:
William R. Young
Scripps Institution of Oceanography

Oral or poster: Oral presentation

Downloadable talk file:

Energy-Enstrophy Stability of beta-plane Kolmogorov Flow with Drag

(nloa08.pdf, 8114273 bytes)

Abstract:
We develop a new nonlinear stability method, the Energy-Enstrophy (EZ) method, that is specialized to two-dimensional hydrodynamics; the method is applied to a beta-plane flow driven by a sinusoidal body force, and retarded by drag with damping time-scale mu^{-1}. The standard energy method (Fukuta and Murakami, J. Phys. Soc. Japan, 64, 1995, pp 3725) shows that the laminar solution is monotonically and globally stable in a certain portion of the (mu,beta)-parameter space. The EZ method proves nonlinear stability in a larger portion of the (mu,beta)-parameter space. And by penalizing high wavenumbers, the EZ method identifies a most strongly amplifying disturbance that is more physically realistic than that delivered by the energy method. Linear instability calculations are used to determine the region of the (mu,beta)-parameter space where the flow is unstable to infinitesimal perturbations. There is only a small gap between the linearly unstable region and the nonlinearly stable region, and full numerical solutions show only small transient amplification in that gap.

*Satellite images from NASA and ESA

Nonlinear Processes in Oceanic and Atmospheric Flows. July 2-4, 2008. Castro Urdiales, Cantabria, Spain.