We study the linear stability problem of the stationary solution psi* = -cos y for the Euler equation on a 2-dimensional flat torus of sides 2 pi L and 2 pi. We show that psi* is stable if L is an element of (0, 1) and that exponentially unstable modes occur in a right neighborhood of L = n for any integer n. As a corollary, we gain exponentially instability for any L large enough and an unbounded growth of the number of unstable modes as L diverges.
On the Stability Problem of Stationary Solutions for the Euler Equation on a 2-Dimensional Torus / Butta', Paolo; Negrini, Piero. - In: REGULAR & CHAOTIC DYNAMICS. - ISSN 1560-3547. - STAMPA. - 15:6(2010), pp. 637-645. [10.1134/s1560354710510143]
On the Stability Problem of Stationary Solutions for the Euler Equation on a 2-Dimensional Torus
BUTTA', Paolo;NEGRINI, Piero
2010
Abstract
We study the linear stability problem of the stationary solution psi* = -cos y for the Euler equation on a 2-dimensional flat torus of sides 2 pi L and 2 pi. We show that psi* is stable if L is an element of (0, 1) and that exponentially unstable modes occur in a right neighborhood of L = n for any integer n. As a corollary, we gain exponentially instability for any L large enough and an unbounded growth of the number of unstable modes as L diverges.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
