7 papers
Variational derivation of a moist thermal rotating shallow water model
Colin J. Cotter, Darryl D. Holm, Oliver D. Street
We introduce a new energy-conserving, moist shallow water model with thermal stratification and rotation. The model is derived from a variational principle, using a Lagrangian expr…
Symplectic techniques for stochastic differential equations on reductive Lie groups with applications to Langevin diffusions
Erwin Luesink, Oliver D. Street
We show how Langevin diffusions can be interpreted in the context of stochastic Hamiltonian systems with structure-preserving noise and dissipation on reductive Lie groups. Reducti…
A comparative numerical study of stochastic Hamiltonian Camassa-Holm equations
Darryl D. Holm, Maneesh Kumar Singh, Oliver D. Street
We introduce a stochastic perturbation of the Camassa-Holm equation such that, unlike previous formulations, energy is conserved by the stochastic flow. We compare this to a comple…
Compound Burgers-KdV Soliton Behaviour: Refraction, Reflection and Fusion
Darryl D. Holm, Ruiao Hu, Oliver D. Street +1
We consider a coupled PDE system between the Burgers equation and the KdV equation to model the interactions between `bore'-like structures and wave-like solitons in shallow water.…
A thermal Green-Naghdi model with time dependent bathymetry and complete Coriolis force
Darryl D. Holm, Oliver D. Street
This paper extends the theoretical Euler-Poincaré framework for modelling ocean mixed layer dynamics. Through a symmetry-broken Lie group invariant variational principle, we deriv…
Plasma dynamics in thin domains
Darryl D. Holm, Ruiao Hu, Oliver D. Street
In the present work, we study the geometric structures of the Rotating Shallow Water Magnetohydrodynamics (RSW-MHD) equations through a Lie group invariant Euler-Poincaré variatio…