Nonlinear stability of Euler flows in two-dimensional periodic domains
Wirosoetisno, D. and Shepherd, T. G. (1999) Nonlinear stability of Euler flows in two-dimensional periodic domains. Geophysical & Astrophysical Fluid Dynamics, 90 (3-4). pp. 229-246. ISSN 0309-1929
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To link to this item DOI: 10.1080/03091929908204120
The non-quadratic conservation laws of the two-dimensional Euler equations are used to show that the gravest modes in a doubly-periodic domain with aspect ratio L = 1 are stable up to translations (or structurally stable) for finite-amplitude disturbances. This extends a previous result based on conservation of energy and enstrophy alone. When L 1, a saturation bound is established for the mode with wavenumber |k| = L −1 (the next-gravest mode), which is linearly unstable. The method is applied to prove nonlinear structural stability of planetary wave two on a rotating sphere.