Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows

DOI10.1007/s00332-017-9431-0zbMath1431.37068arXiv1703.06774OpenAlexW3102192856WikidataQ55082365 ScholiaQ55082365MaRDI QIDQ722001

François Gay-Balmaz, Darryl D. Holm

Publication date: 20 July 2018

Published in: Journal of Nonlinear Science (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1703.06774

zbMATH Keywords

coadjoint orbitsEuler-Poincaré equationsgeophysical fluid dynamicsstochastic geometric mechanics

Mathematics Subject Classification ID

Hydrology, hydrography, oceanography (86A05) Dynamical systems in fluid mechanics, oceanography and meteorology (37N10) Stochastic partial differential equations (aspects of stochastic analysis) (60H15) Relations of infinite-dimensional Hamiltonian and Lagrangian dynamical systems with topology, geometry and differential geometry (37K25) Generation, random and stochastic difference and differential equations (37H10) Differential geometric methods (tensors, connections, symplectic, Poisson, contact, Riemannian, nonholonomic, etc.) for problems in mechanics (70G45)

Related Items (20)

Stochastic parametrization of the Richardson triple ⋮ Solution properties of the incompressible Euler system with rough path advection ⋮ Testing stationarity of the detrended price return in stock markets ⋮ Predicting uncertainty in geometric fluid mechanics ⋮ Variational principles for fluid dynamics on rough paths ⋮ Splitting integrators for stochastic Lie–Poisson systems ⋮ A geometric framework for stochastic shape analysis ⋮ Well-posedness and wave-breaking for the stochastic rotation-two-component Camassa-Holm system ⋮ Well-posedness for a stochastic 2D Euler equation with transport noise ⋮ Variational integrators for stochastic Hamiltonian systems on Lie groups ⋮ Noise and dissipation on coadjoint orbits ⋮ Numerically Modeling Stochastic Lie Transport in Fluid Dynamics ⋮ Solution properties of a 3D stochastic Euler fluid equation ⋮ 2D Euler equations with Stratonovich transport noise as a large-scale stochastic model reduction ⋮ Stochastic closures for wave-current interaction dynamics ⋮ Circulation and Energy Theorem Preserving Stochastic Fluids ⋮ Modelling the climate and weather of a 2D Lagrangian-averaged Euler-Boussinesq equation with transport noise ⋮ Lagrangian averaged stochastic advection by Lie transport for fluids ⋮ Lyapunov exponents of two stochastic Lorenz 63 systems ⋮ Stochastic effects of waves on currents in the ocean mixed layer

Uses Software

• jLab

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Dirac reduction for nonholonomic mechanical systems and semidirect products
• Reduction theory for symmetry breaking with applications to nematic systems
• Dirac structures in Lagrangian mechanics. II: Variational structures
• The Euler-Poincaré equations and semidirect products with applications to continuum theories
• Sur la géométrie différentielle des groupes de Lie de dimension infinite et ses applications à l'hydrodynamique des fluides parfaits
• Lagrangian Analysis and Prediction of Coastal and Ocean Dynamics
• Stochastic variational integrators
• Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics
• Stochastic Navier--Stokes Equations for Turbulent Flows
• A stable particle filter for a class of high-dimensional state-space models
• Variational principles for stochastic fluid dynamics
• Lagrangian averages, averaged Lagrangians, and the mean effects of fluctuations in fluid dynamics
• Geometric Mechanics
• White noise in space and time and the cylindrical wiener process
• The Navier-Stokes-alpha model of fluid turbulence
• The three dimensional viscous Camassa-Holm equations, and their relation to the Navier-Stokes equations and turbulence theory

This page was built for publication: Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows