84 citations · 107 across the 6 of their papers we have counts for
6 papers
Monge-Ampere Geometry and Vortices
Lewis Napper, Ian Roulstone, Vladimir Rubtsov +1
We introduce a new approach to Monge-Ampere geometry based on techniques from higher symplectic geometry. Our work is motivated by the application of Monge-Ampere geometry to the P…
Solutions and Singularities of the Semigeostrophic Equations via the Geometry of Lagrangian Submanifolds
Roberto D'Onofrio, Giovanni Ortenzi, Ian Roulstone +1
Using Monge-Ampère geometry, we study the singular structure of a class of nonlinear Monge-Ampère equations in three dimensions, arising in geophysical fluid dynamics. We extend se…
A method for generating coherent spatially explicit maps of seasonal palaeoclimates from site-based reconstructions
S. F. Cleator, S. P. Harrison, N. K. Nichols +2
We describe a method for reconstructing spatially explicit maps of seasonal palaeoclimate variables from site-based reconstructions. Using a 3D-Variational technique, the method fi…
Monge-Ampère Structures and the Geometry of Incompressible Flows
Bertrand Banos, Vladimir Roubtsov, Ian Roulstone
We show how a symmetry reduction of the equations for incompressible hydrodynamics in three dimensions leads naturally to a Monge-Ampère structure, and Burgers'-type vortices are a…
Quaternions and particle dynamics in the Euler fluid equations
John D. Gibbon, Darryl D. Holm, Robert M. Kerr +1
Vorticity dynamics of the three-dimensional incompressible Euler equations is cast into a quaternionic representation governed by the Lagrangian evolution of the tetrad consisting…
K"ahler Geometry and the Navier-Stokes Equations
Ian Roulstone, Bertrand Banos, John D. Gibbon +1
We study the Navier-Stokes and Euler equations of incompressible hydrodynamics in two and three spatial dimensions and show how the constraint of incompressiblility leads to equati…