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Stochastic modelling in fluid dynamics: Itô versus Stratonovich.

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This study addresses transforming Itô stochastic processes to Stratonovich processes for fluid dynamics. It clarifies whether frame transformations impact stochastic fluid equation solutions.

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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.