Nonlinear stability of Euler flows in two-dimensional periodic domains

Wirosoetisno, D. and Shepherd, T. G. ORCID: https://orcid.org/0000-0002-6631-9968 (1999) Nonlinear stability of Euler flows in two-dimensional periodic domains. Geophysical and Astrophysical Fluid Dynamics, 90 (3-4). pp. 229-246. ISSN 0309-1929 doi: 10.1080/03091929908204120

Abstract/Summary

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.