11 citations · 33 across the 6 of their papers we have counts for
6 papers
Stability Theory of the 3-Dimensional Euler Equations
Holger R. Dullin, Joachim Worthington
The Euler equations on a three-dimensional periodic domain have a family of shear flow steady states. We show that the linearised system around these steady states decomposes into…
Instability of unidirectional flows for the 2D -Euler equations
Holger Dullin, Yuri Latushkin, Robert Marangell +2
We study stability of unidirectional flows for the linearized 2D -Euler equations on the torus. The unidirectional flows are steady states whose vorticity is given by Fourier mo…
Poisson Structure of the Three-Dimensional Euler Equations in Fourier Space
Holger R. Dullin, James D. Meiss, Joachim Worthington
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 an…
Stability Results for Idealised Shear Flows on a Rectangular Periodic Domain
Holger Dullin, Joachim Worthington
We present a new linearly stable solution of the Euler fluid flow on a torus. On a two-dimensional rectangular periodic domain for , the E…
Instability of Equilibria for the 2D Euler Equations on the torus
Joachim Worthington, Holger R. Dullin, Robert Marangell
We consider the hydrodynamics of an incompressible fluid on a 2D periodic domain. There exists a family of stationary solutions with vorticity given by $Ω^*=α\cos (\mathbf{p} \cdot…
The Vanishing Twist in the Restricted Three Body Problem
Holger R Dullin, Joachim Worthington
This paper demonstrates the existence of twistless tori and the associated reconnection bifurcations and meandering curves in the planar circular restricted three-body problem. Nea…