Stochastic Geometric Models with Non-stationary Spatial Correlations in Lagrangian Fluid Flows.

Area of Science:

• Geophysical Fluid Dynamics
• Oceanography
• Stochastic Modeling

Background:

• Satellite observations of ocean surface drifters provide insights into oceanic current dynamics.
• Existing models often assume stationary spatial correlations, limiting their ability to capture complex current behavior.

Purpose of the Study:

• To develop novel data-driven stochastic models for geophysical fluid dynamics.
• To incorporate non-stationary spatial correlations representing advected oceanic currents.
• To introduce symmetry-breaking mechanisms into models of oceanic dynamics.

Main Methods:

• Review of a time-independent spatial correlation model (Holm, 2015).
• Development of two new models (Model 2 and Model 3) using reduction by symmetry of stochastic variational principles.
• Application of stochastic Hamiltonian systems, momentum maps, conservation laws, and Lie-Poisson bracket structures.

Main Results:

• Introduction of two new stochastic Hamiltonian models (Model 2 and Model 3).
• These models incorporate symmetry-breaking mechanisms to advect spatial correlations with the flow.
• The models provide a more dynamic representation of oceanic current behavior.

Conclusions:

• The developed models offer enhanced capabilities for simulating geophysical fluid dynamics.
• Non-stationary spatial correlations are crucial for accurately representing oceanic current dynamics.
• Stochastic Hamiltonian systems provide a robust framework for these advanced GFD models.