Nonlinear stability of Euler flows in two-dimensional periodic domainsWirosoetisno, 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 Full text not archived in this repository. It is advisable to refer to the publisher's version if you intend to cite from this work. See Guidance on citing. To link to this item DOI: 10.1080/03091929908204120 Abstract/SummaryThe 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.
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