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Stochastic modelling in fluid dynamics: Itô versus Stratonovich
1Mathematics Department, Imperial College London, London, UK.
Proceedings. Mathematical, Physical, and Engineering Sciences
|June 11, 2020
Summary
This study addresses transforming Itô stochastic processes to Stratonovich processes for fluid dynamics. It clarifies whether frame transformations impact stochastic fluid equation solutions.
Area of Science:
- Fluid dynamics
- Stochastic processes
- Mathematical physics
Background:
- Lagrangian trajectories in fluid flow can be modeled using Itô stochastic processes.
- Hamilton's principle requires Stratonovich processes for deriving stochastic fluid equations.
Purpose of the Study:
- To investigate the transformation from Itô to Stratonovich noise in fluid dynamics.
- To determine if frame transformations affect the interpretation of stochastic fluid equations.
Main Methods:
- Utilizing variational calculus and Hamilton's principle.
- Transforming Itô noise to Stratonovich noise.
- Analyzing the impact of frame transformations on drift velocity.
Main Results:
- The transformation shifts drift velocity, introducing non-inertial frame considerations.
- Elementary analysis is used to resolve the impact of these forces.
Conclusions:
- The study resolves the question of whether non-inertial forces from frame transformations influence stochastic fluid equation solutions.
- Provides clarity on the interpretation of solutions derived from transformed stochastic processes.
Keywords:
stochastic Kelvin circulation theoremstochastic geometric mechanicsstochastic geophysical fluid dynamicsMore Related Videos
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