Related papers: Stochastic Geometric Mechanics for Fluid Dynamics
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…
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. Here, we derive stochastic equations for the behaviour of…
Noether's celebrated theorem associating symmetry and conservation laws in classical field theory is adapted to allow for broken symmetry in geometric mechanics and is shown to play a central role in deriving and understanding the…
Inspired by spatiotemporal observations from satellites of the trajectories of objects drifting near the surface of the ocean in the National Oceanic and Atmospheric Administration's `Global Drifter Program', this paper develops data-driven…
The General Lagrangian Mean (GLM) theory uses a set of averaged equations of fluid dynamics to describe interactions between mean flows and waves. These equations are formulated in coordinates that follow the fluid's average velocity and…
In the paper, some concepts of modern differential geometry are used as a basis to develop an invariant theory of mechanical systems, including systems with gyroscopic forces. An interpretation of systems with gyroscopic forces in the form…
A systematic Bayesian framework is developed for physics constrained parameter inference ofstochastic differential equations (SDE) from partial observations. The physical constraints arederived for stochastic climate models but are…
A stochastic deformation of a thermodynamic symplectic structure is studied. The stochastic deformation procedure is analogous to the deformation of an algebra of observables like deformation quantization, but for an imaginary deformation…
We introduce a physically relevant stochastic representation of the rotating shallow water equations. The derivation relies mainly on a stochastic transport principle and on a decomposition of the fluid flow into a large-scale component and…
Many fluctuation-driven phenomena in fluids can be analysed effectively using the generalised Lagrangian mean (GLM) theory of Andrews & McIntyre (1978). This theory relies on particle-following averaging to incorporate the constraints…
The understanding of fluid turbulence has considerably progressed in recent years. The application of the methods of statistical mechanics to the description of the motion of fluid particles, i.e. to the Lagrangian dynamics, has led to a…
A stochastic flow representation is considered with the Eulerian velocity decomposed between a smooth large scale component and a rough small-scale turbulent component. The latter is specified as a random field uncorrelated in time.…
A set of exact integrals of motion is found for systems driven by homogenous isotropic stochastic flow. The integrals of motion describe the evolution of (hyper-)surfaces of different dimensions transported by the flow, and can be expressed…
The Hamiltonian dynamics of a compressible inviscid fluid is formulated as a gauge theory. The idea of gauge equivalence is exploited to unify the study of apparantly distinct physical problems and solutions of new models can be generated…
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…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
A method is developed to estimate the properties of a global hydrodynamic instability in turbulent flows from measurement data of the limit-cycle oscillations. For this purpose, the flow dynamics are separated in deterministic contributions…
The last decade has seen the success of stochastic parameterizations in short-term, medium-range and seasonal forecasts: operational weather centers now routinely use stochastic parameterization schemes to better represent model inadequacy…
The statistical nature of discrete fluid molecules with random thermal motion so far has not been considered in mainstream fluid mechanics based on Navier-Stokes equations, wherein fluids have been treated as a continuum breaking into many…
In the study of gas dynamics, theoretical modeling and numerical simulation are mostly set up with deterministic settings. Given the coarse-grained modeling in theories of fluids, considerable uncertainties may exist between flow-field…