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Predicting uncertainty in geometric fluid mechanics

  • * Corresponding author: Darryl D. Holm

    * Corresponding author: Darryl D. Holm
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  • 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.

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

    Citation:

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  • [1] S. Albeverio, A. B. Cruzeiro and D. D. Holm, Stochastic Geometric Mechanics, Springer, 2017.
    [2] A. ArnaudonA. L. de Castro and D. D. Holm, Noise and dissipation on coadjoint orbits, J. Nonlin. Sci., 28 (2018), 91-145.  doi: 10.1007/s00332-017-9404-3.
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    [7] C. J. Cotter, G. A. Gottwald and D. D. Holm, Stochastic partial differential fluid equations as a diffusive limit of deterministic Lagrangian multi-time dynamics, Proc. Roy. Soc. A, 473 (2017), 20170388, 10pp. doi: 10.1098/rspa.2017.0388.
    [8] C. J. Cotter, D. Crisan, D. D. Holm, W. Pan and I. Shevchenko, Modelling uncertainty using circulation-preserving stochastic transport noise in a 2-layer quasi-geostrophic model, arXiv preprint, arXiv: 1802.05711.
    [9] D. Crisan, F. Flandoli and D. Holm, Solution properties of a 3d stochastic Euler fluid equation, arXiv: 1704.06989, [math-ph], 2017. doi: 10.1007/s00332-018-9506-6.
    [10] A. B. CruzeiroD. D. Holm and T. S. Ratiu, Momentum maps and stochastic Clebsch action principles, Commun. in Math. Phys., 357 (2018), 873-912.  doi: 10.1007/s00220-017-3048-x.
    [11] F. Gay-Balmaz and D. D. Holm, Stochastic geometric models with non-stationary spatial correlations in Lagrangian fluid flows, J. Nonlin. Sci., 28 (2018), 873-904.  doi: 10.1007/s00332-017-9431-0.
    [12] F. Gay-Balmaz and V. Putkaradze, On noisy extensions of nonholonomic constraints, J. Nonlin. Sci., 26 (2016), 1571-1613.  doi: 10.1007/s00332-016-9313-x.
    [13] D. D. Holm, Variational principles for stochastic fluid dynamics, Proceedings of the Royal Society of London A: Mathematical, Physical and Engineering Sciences, 471 (2015), 20140963, 19 pp. doi: 10.1098/rspa.2014.0963.
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