8 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…
Numerical comparison of energy- versus circulation-preserving stochastic vortex dynamics
Sagy Ephrati, Darryl D. Holm
We compare two geometric stochastic frameworks for the two-dimensional Euler equations, being the circulation-preserving stochastic advection by Lie transport (SALT) and the energy…
Surface Wave Solutions in 1D and 2D for the Broer-Kaup-Boussinesq-Kupershmidt (BKBK) System
Darryl D. Holm, Ruiao Hu, Hanchun Wang
The BKBK system is a singular perturbation of the classical shallow water equations which modifies their transport velocity to depend on wave elevation slope. This modification int…
A Multiscale Camassa--Holm Equation
Darryl D Holm, Maneesh Kumar Singh
A system of equations for Multiscale Geodesic Flow (MGF) is introduced whose solutions illustrate the paradigm of whorls within whorls within whorls, introduced by L. F. Richardson…
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.…