32 citations · 55 across the 16 of their papers we have counts for
18 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…
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.…
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 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 derive…
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 variation…
Collisions of Burgers Bores with Nonlinear Waves
Albert. Dombret, Darryl D. Holm, Ruiao Hu +2
This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction…
Deterministic and Stochastic Geometric Mechanics for Hall MHD
Darryl D. Holm, Ruiao Hu, Oliver D. Street
We derive new models of stochastic Hall magnetohydrodynamics (MHD) by using a symmetry-reduced stochastic Euler-Poincaré variational principle. The new stochastic Hall MHD theory h…
Geometric theory of perturbation dynamics around non-equilibrium fluid flows
Darryl D. Holm, Ruiao Hu, Oliver D. Street
The present work investigates the evolution of linear perturbations of time-dependent ideal fluid flows with advected quantities, expressed in terms of the second order variations…
Semimartingale driven mechanics and reduction by symmetry for stochastic and dissipative dynamical systems
Oliver D. Street, So Takao
The recent interest in structure preserving stochastic Lagrangian and Hamiltonian systems raises questions regarding how such models are to be understood and the principles through…
Geometric Mechanics of the Vertical Slice Model
Darryl D. Holm, Ruiao Hu, Oliver D. Street
The goals of the present work are to: (i) investigate the dynamics of oceanic frontogenesis by taking advantage of the geometric mechanics underlying the class of Vertical Slice Mo…
On the interactions between mean flows and inertial gravity waves in the WKB approximation
Darryl D. Holm, Ruiao Hu, Oliver D. Street
We derive a Wentzel-Kramers-Brillouin (WKB) closure of the generalised Lagrangian mean (GLM) theory by using a phase-averaged Hamilton variational principle for the Euler--Boussine…
Lagrangian reduction and wave mean flow interaction
Darryl D. Holm, Ruiao Hu, Oliver D. Street
How does one derive models of dynamical feedback effects in multiscale, multiphysics systems such as wave mean flow interaction (WMFI)? We shall address this question for hybrid dy…
A structure preserving stochastic perturbation of classical water wave theory
Oliver D. Street
The inclusion of stochastic terms in equations of motion for fluid problems enables a statistical representation of processes which are left unresolved by numerical computation. He…
Coupling of waves to sea surface currents via horizontal density gradients
Darryl D. Holm, Ruiao Hu, Oliver D. Street
The mathematical models and numerical simulations reported here are motivated by satellite observations of horizontal gradients of sea surface temperature and salinity that are clo…
On the analytical aspects of inertial particle motion
Dan Crisan, Oliver D. Street
In their seminal 1983 paper, M. Maxey and J. Riley introduced an equation for the motion of a sphere through a fluid. Since this equation features the Basset history integral, the…
Wave-current interaction on a free surface
Dan Crisan, Darryl D. Holm, Oliver D. Street
The classic evolution equations for potential flow on the free surface of a fluid flow are not closed because the pressure and the vertical velocity dynamics are not specified on t…
Semi-martingale driven variational principles
Oliver D. Street, Dan Crisan
Spearheaded by the recent efforts to derive stochastic geophysical fluid dynamics models, we present a generic framework for introducing stochasticity into variational principles t…