相关论文: A structure preserving stochastic perturbation of …

We devise a stochastic Hamiltonian formulation of the water wave problem. This stochastic representation is built within the framework of the modelling under location uncertainty. Starting from restriction to the free surface of the general…

Many equations that arise in a physical context can be posed in the form of a Hamiltonian system, meaning that there is a symplectic structure on an appropriate phase space, and a Hamiltonian functional with respect to which time evolution…

We review opportunities for stochastic geometric mechanics to incorporate observed data into variational principles, in order to derive data-driven nonlinear dynamical models of effects on the variability of computationally resolvable…

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 preserving the fundamental advective transport properties of ideal…

This paper derives stochastic partial differential equations (SPDEs) for fluid dynamics from a stochastic variational principle (SVP). The Legendre transform of the Lagrangian formulation of these SPDEs yields their Lie-Poisson Hamiltonian…

We describe the Hamiltonian structures, including the Poisson brackets and Hamiltonians, for free boundary problems for incompressible fluid flows with vorticity. The Hamiltonian structure is used to obtain variational principles for…

The spatial Dysthe equations describe the envelope evolution of the free-surface and potential of gravity waves in deep waters. Their Hamiltonian structure and new invariants are unveiled by means of a gauge transformation to a new…

A novel mathematical nonlinear theory of surface gravity waves in deep water is presented, in which analytical analysis of the classical nonlinear equations of fluid dynamics is performed under less restrictive assumptions than those…

Third-order approximate solutions for surface gravity waves in the finite water depth are studied in the context of potential flow theory. This solution provides explicit expressions for the surface elevation, free-surface velocity…

Stochastic processes associated with traveling wave solutions of the sine-Gordon equation are presented. The structure of the forward Kolmogorov equation as a conservation law is essential in the construction and so is the traveling wave…

Considered herein is a particular nonlinear dispersive stochastic equation. It was introduced recently in [3], as a model describing surface water waves under location uncertainty. The corresponding noise term is introduced through a…

Stochastic processes are proposed whose master equations coincide with classical wave, telegraph, and Klein-Gordon equations. Similar to predecessors based on the Goldstein-Kac telegraph process, the model describes the motion of particles…

Holm (Proc. Roy. Soc 2015) introduced a variational framework for stochastically parametrising unresolved scales of hydrodynamic motion. This variational framework preserves fundamental features of fluid dynamics, such as Kelvin's…

A reduced dynamical model is derived which describes the interaction of weak inertia-gravity waves with nonlinear vortical motion in the context of rotating shallow-water flow. The formal scaling assumptions are (i) that there is a…

The present paper introduces stochastic velocity as improvement for moving particle semi-implicit (MPS) method. This improvement is to overcome energy loss caused by numerical dissipation in the basic MPS that brings about rapid decay of…

We show that the governing equations for two-dimensional gravity water waves with constant non-zero vorticity have a nearly-Hamiltonian structure, which becomes Hamiltonian for steady waves.

In this paper, we investigate the wave solutions of a stochastic rotating shallow water model. This approximate model provides an interesting simple description of the interplay between waves and random forcing ensuing either from the wind…

In {\em{Holm}, Proc. Roy. Soc. A 471 (2015)} stochastic fluid equations were derived by employing a variational principle with an assumed stochastic Lagrangian particle dynamics. Here we show that the same stochastic Lagrangian dynamics…

Periodic travelling waves at the free surface of an incompressible inviscid fluid in two dimensions under gravity are numerically computed for an arbitrary vorticity distribution. The fluid domain over one period is conformally mapped from…

We derive a simple algebraic form of the nonlinear wavenumber correction of surface gravity waves in deep water, based on temporal measurements of the water surface and the spatial Zakharov equation. This allows us to formulate an…