83 citations · 158 across the 11 of their papers we have counts for
11 papers
A new implementation of the geometric method for solving the Eady slice equations
Charlie P. Egan, David P. Bourne, Colin J. Cotter +4
We present a new implementation of the geometric method of Cullen & Purser (1984) for solving the semi-geostrophic Eady slice equations which model large scale atmospheric flows an…
Cullen's Stability Principle and Weak Solutions of the Free-surface Semi-geostrophic Equations
Mike J. P. Cullen, Tobias Kuna, Beatrice Pelloni +1
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 incompressibl…
Particle relabelling symmetries and Noether's theorem for vertical slice models
Colin J. Cotter, Michael J. P. Cullen
We consider the variational formulation for vertical slice models introduced in Cotter and Holm (Proc Roy Soc, 2013). These models have a Kelvin circulation theorem that holds on a…
Vertical slice modelling of nonlinear Eady waves using a compatible finite element method
Hiroe Yamazaki, Jemma Shipton, Michael J. P. Cullen +2
A vertical slice model is developed for the Euler-Boussinesq equations with a constant temperature gradient in the direction normal to the slice (the Eady-Boussinesq model). The mo…
A rigorous treatment of moist convection in a single column
Bin Cheng, Jingrui Cheng, Michael Cullen +2
We study a single column model of moist convection in the atmosphere. We state the conditions for it to represent a stable steady state. We then evolve the column by subjecting it…
Semi-geostrophic System with Variable Coriolis parameter
Jingrui Cheng, Michael Cullen, Mikhail Feldman
We prove short time existence and uniqueness of smooth solutions ( in with ) to the 2-D semi-geostrophic system and semi-geostrophic shallow water system with…
Convection in a Single Column -- Modelling, Algorithm and Analysis
Onno Bokhove, Bin Cheng, Andreas Dedner +5
The group focused on a model problem of idealised moist air convection in a single column of atmosphere. Height, temperature and moisture variables were chosen to simplify the math…
Recent progress and review of issues related to Physics Dynamics Coupling in geophysical models
Markus Gross, Hui Wan, Philip J. Rasch +19
Geophysical models of the atmosphere and ocean invariably involve parameterizations. These represent two distinct areas: Subgrid processes that the model cannot resolve, and diabat…
Mesh Adaptation on the Sphere using Optimal Transport and the Numerical Solution of a Monge-Ampère type Equation
Hilary Weller, Philip Browne, Chris Budd +1
An equation of Monge-Ampère type has, for the first time, been solved numerically on the surface of the sphere in order to generate optimally transported (OT) meshes, equidistribut…
Free upper boundary value problems for the semi-geostrophic equations
M. J. P. Cullen, D. K. Gilbert, T. Kuna +1
The semi-geostrophic system is widely used in the modelling of large-scale atmospheric flows. In this paper, we prove existence of solutions of the incompressible semi-geostrophic…
On a model of forced axisymmetric flows
Mike Cullen, Marc Sedjro
In this work, we consider a model of forced axisymmetric flows which is derived from the inviscid Boussinesq equations. What makes these equations unusual is the boundary condition…