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arXiv · 0803.0558

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

Yue-Kin Tsang·William R. Young
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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.

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Yue-Kin Tsang, William R. Young. 2008-03-04. Energy-Enstrophy Stability of beta-plane Kolmogorov Flow with Drag. https://doi.org/10.1063/1.2958321

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