Dynamical Systems Seminar: Joachim Worthington
Instability of Certain Equilibrium Solutions of the Euler Equations on a Toroidal Domain
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Date and time:听
Thursday, May 14, 2015 - 2:00pm
尝辞肠补迟颈辞苍:听
ECCR 257
础产蝉迟谤补肠迟:听
The 2D Euler Equations can be written on a toroidal domain as an infinite dimensional Hamiltonian system. We have studied the stability of the family of stationary solutions cos(mx+ny). We use a Poisson structure-preserving truncation described by Zeitlin (1991) to reduce the full problem into a finite-mode system in Fourier Space, and consider the limit as the truncation goes to infinity. We replicate some results by Li (2000) in this new finite-mode setting, namely the splitting of the linearised problem into 鈥漜lasses鈥, most of which are stable. We also show that nearly all the stationary solutions described are unstable. The usefulness of Zeitlin鈥檚 truncation, both numerically and analytically, is also demonstrated.