Special Session 108: 

An Evans function for 2D steady flows of the Euler equations on the torus

Robert Marangell
University of Sydney
Australia
Co-Author(s):    H Dullin
Abstract:
This talk will consider the stability of time independent solutions to the incompressible, inviscid Euler equations on the torus whose stream functions have the form $\psi = U(\xi) =U(p_1x + p_2y)$ for fixed integers $p_1$ and $p_2$. By an appropriate change of coordinates and separation of variables, the linearised spectral problem is reduced to the study of a Hill`s equation with a complex potential. By using Hill determinants, an Evans function of the original linearised Euler equation can be constructed. For certain, well-known shear flows, the form of the Hill determinant makes such an Evans function numerically straightforward to compute.