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The Geometry of Stochastic Fluid Dynamics
Darryl D. Holm
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preser…
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…
Stochastic Geometric Mechanics for Fluid Dynamics
Darryl D. Holm, Erwin Luesink
Stochastic geometric mechanics (SGM) is known for its potential utility in quantifying uncertainty in global climate modelling of the Earth's ocean and atmosphere while also preser…
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…
Deterministic and Stochastic Euler-Boussinesq Convection
Darryl D. Holm, Wei Pan
Stochastic parametrisations of the interactions among disparate scales of motion in fluid convection are often used for estimating prediction uncertainty, which can arise due to in…
Nonlinear dispersion in wave-current interactions
Darryl D. Holm, Ruiao Hu
Via a sequence of approximations of the Lagrangian in Hamilton's principle for dispersive nonlinear gravity waves we derive a hierarchy of Hamiltonian models for describing wave-cu…