For a second order difference equation that arises in the study of stability of unidirectional
(generalized Kolmogorov) flows for the Euler equations of ideal fluids on the two …

Sinusoidal flows are important explicit stationary solutions of the incompressible Euler
equation on a flat two-torus. In this paper, we prove that sinusoidal flows related to least …

We study the point spectrum of a second order difference operator with complex potential on
the half-line via Fredholm determinants of the corresponding Birman-Schwinger operator …

We study instability of unidirectional flows for the linearized 2D Navier–Stokes equations on
the torus. Unidirectional flows are steady states whose vorticity is given by Fourier modes …

We study stability of unidirectional flows for the linearized 2D $\alpha $-Euler equations on
the torus. The unidirectional flows are steady states whose vorticity is given by Fourier …

We study the point spectrum of the linearisation of Euler's equation for the ideal fluid on the
torus about a shear flow. By separation of variables the problem is reduced to the spectral …

We derive a simple Poisson structure in the space of Fourier modes for the vorticity
formulation of the Euler equations on a three-dimensional periodic domain. This allows us to …

The study of shear flow steady states has led to a wealth of research in the field of fluid
dynamics. By studying shear flows, we can understand how a fluid behaves and how …

The Euler equations on a three-dimensional periodic domain have a family of shear flow
steady states. We derive a formulation of the dynamics of the vorticity Fourier modes on a …

We analyze the hydrodynamic stability of force-driven parallel shear flows in nonequilibrium
molecular simulations with three-dimensional periodic boundary conditions. We show that …