Stochastic Modelling of Small-Scale Perturbation

Flandoli, Franco; Pappalettera, Umberto

doi:10.3390/w12102950

Cited by 10 publications

(4 citation statements)

References 35 publications

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“…Of particular interest in fluid dynamics and also for geophysical flows is a noise of transport type which appears naturally when stochastic models are derived from Hamiltonian principles as proposed in [33] (see also [4] for a brief description) and yield a physically relevant randomization [2] with energy conservation. Recently, the importance of transport noise was discussed in the connection with unresolved small scales, see [17,18] and the references therein.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity

Saal¹,

Slavík²

2021

Preprint

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We establish the existence and uniqueness of pathwise strong solutions to the stochastic 3D primitive equations with only horizontal viscosity and diffusivity driven by transport noise on a cylindrical domain M = (−h, 0) × G, G ⊂ R 2 bounded and smooth, with the physical Dirichlet boundary conditions on the lateral part of the boundary. Compared to the deterministic case where the uniqueness of z-weak solutions holds in L 2 , more regular initial data are necessary to establish uniqueness in the anisotropic space H 1 z L 2 xy so that the existence of local pathwise solutions can be deduced from the Gyöngy-Krylov theorem. Global existence is established using the logarithmic Sobolev embedding, the stochastic Gronwall lemma and an iterated stopping time argument.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Stochastic Primitive Equations with Horizontal Viscosity and Diffusivity

Saal¹,

Slavík²

2021

Preprint

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“…This is a burgeoning area of research in fluid dynamics. For recent introductory surveys of stochastic fluid dynamics with applications, see, e.g., [17,23,28].…”

Section: Motivating Question and Main Results Of The Papermentioning

confidence: 99%

Stochastic effects of waves on currents in the ocean mixed layer

Holm,

2020

Preprint

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How does one guarantee that a stochastic approach for modelling fluid dynamics will preserve its fundamental deterministic properties, such as (i) energy conservation, (ii) Kelvin circulation theorem and (iii) conserved quantities arising from the Lagrangian particle relabelling symmetry? In fact, a choice must be made. For example, the approach of stochastic advection by Lie transport (SALT) preserves the latter two properties, but SALT does not conserve the deterministic energy. This paper introduces an energypreserving stochastic model for studying wave effects on currents in the ocean mixing layer. The model is called stochastic forcing by Lie transport (SFLT). The SFLT model is derived here from a stochastic constrained variational principle, so it has a Kelvin circulation theorem. The examples of SFLT given here treat 3D Euler fluid flow, rotating shallow water dynamics and the Euler-Boussinesq equations. In each example, one sees the effect of stochastic Stokes drift and material entrainment in the generation of fluid circulation. Moreover, we present an Eulerian-averaged SFLT model (EA SFLT), based on the Eulerian decomposition of solutions of the energy-conserving SFLT model into the sums of their expectations and fluctuations.

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“…in good agreement with Monte Carlo simulations. Flandoli and Pappalettera (2020) used a stochastic model to identify the noise required to reduce the complexity of interaction between different scales.…”

Section: Uncertainty Analysis and Numerical Derived Distribution Methodsmentioning

confidence: 99%