Related Experiment Video
Updated: Jan 5, 2026

Magnetically Induced Rotating Rayleigh-Taylor Instability
Published on: March 3, 2017
The Stability Principle and global weak solutions of the free surface semi-geostrophic equations in geostrophic
M J P Cullen1, T Kuna2, B Pelloni3
1Met Office, Exeter, UK.
Abstract:
The semi-geostrophic equations are used widely in the modelling of large-scale atmospheric flows. In this note, we prove the global existence of weak solutions of the incompressible semi-geostrophic equations, in geostrophic coordinates, in a three-dimensional domain with a free upper boundary. The proof, based on an energy minimization argument originally inspired by the Stability Principle as studied by Cullen, Purser and others, uses optimal transport techniques as well as the analysis of Hamiltonian ODEs in spaces of probability measures as studied by Ambrosio and Gangbo. We also give a general formulation of the Stability Principle in a rigorous mathematical framework.
Related Concept Videos
Navier–Stokes Equations
Stability of Equilibrium Configuration: Problem Solving
Problem-solving in the context of the stability of equilibrium configuration...
Buoyancy and Stability for Submerged and Floating Bodies
Stability of Equilibrium Configuration
A stable equilibrium occurs when a system tends to return to its original position when given a small displacement, and the potential energy is at its minimum. An example of a stable equilibrium is when a cantilever beam is fixed at one end and a weight is attached to the other end. If the weight...
Oscillations about an Equilibrium Position
Euler's Equations of Motion

