Predicting uncertainty in geometric fluid mechanics

François Gay-Balmaz; Darryl D. Holm

doi:10.3934/dcdss.2020071

Article Contents

2020, Volume 13, Issue 4: 1229-1242. Doi: 10.3934/dcdss.2020071

This issue Previous Article On the geometry of twisted prolongations, and dynamical systems Next Article Sub-Riemannian geometry and finite time thermodynamics Part 1: The stochastic oscillator

Predicting uncertainty in geometric fluid mechanics

François Gay-Balmaz^1, and
Darryl D. Holm^2, ,

1.
CNRS - LMD - IPSL, École Normale Supérieure de Paris, 24 Rue Lhomond, 75005, Paris, France
2.
Department of Mathematics, Imperial College, London SW7 2AZ, UK, Springfield, MO 65810, USA

^* Corresponding author: Darryl D. Holm
^* Corresponding author: Darryl D. Holm

Received: December 2017

Revised: August 2018

Published: April 2020

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Abstract

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 scales of fluid motion, due to unresolvable, small, rapid scales of fluid motion.

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Mathematics Subject Classification: Primary: 58F15, 58F17; Secondary: 53C35.

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References

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