Multiscale turbulence models based on convected fluid microstructure

Holm, Darryl D.; Tronci, Cesare

doi:10.1063/1.4754114

Cited by 14 publications

(19 citation statements)

References 22 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The multi-space-scale approach of [35] follows one step in Richardson's cascade metaphor [51], which describes fluid dynamics as a sequence of whorls within whorls, in which each space/time scale is carried by a bigger/slower one. LF Richardson's cascade in scales (sizes) of nested interacting "whorls" .…”

Section: Objectives Of This Workmentioning

confidence: 99%

Stochastic Parametrization of the Richardson Triple

Holm

2018

J Nonlinear Sci

Self Cite

View full text Add to dashboard Cite

A Richardson triple is an ideal fluid flow map g t/ ,t, t = h t/ k t l t composed of three smooth maps with separated time scales: slow, intermediate and fast, corresponding to the big, little and lesser whorls in Richardson's well-known metaphor for turbulence. Under homogenization, as lim → 0, the composition h t/ k t of the fast flow and the intermediate flow is known to be describable as a single stochastic flow d t g. The interaction of the homogenized stochastic flow d t g with the slow flow of the big whorl is obtained by going into its non-inertial moving reference frame, via the composition of maps (d t g)l t . This procedure parameterizes the interactions of the three flow components of the Richardson triple as a single stochastic fluid flow in a moving reference frame. The Kelvin circulation theorem for the stochastic dynamics of the Richardson triple reveals the interactions among its three components. Namely, (1) the velocity in the circulation integrand is kinematically swept by the large scales and (2) the velocity of the material circulation loop acquires additional stochastic Lie transport by the small scales. The stochastic dynamics of the composite homogenized flow is derived from a stochastic Hamilton's principle and then recast into Lie-Poisson bracket form with a stochastic Hamiltonian. Several examples are given, including fluid flow with stochastically advected quantities and rigid body motion under gravity, i.e. the stochastic heavy top in a rotating frame.

show abstract

Section: Objectives Of This Workmentioning

confidence: 99%

Stochastic Parametrization of the Richardson Triple

Holm

2018

J Nonlinear Sci

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, we have contrasted the model (3.22) with existing approaches from the literature and established several connections. Our model should also be compared with [18,21] where (deterministic) advection of fluid microstructure is studied. The Kinematic Sweeping Ansatz of [21] is to consider deterministic turbulence parameters which are swept along a mean flow, while (3.22) is a model for stochastic particles along a mean flow.…”

Section: Discussionmentioning

confidence: 99%

“…I am grateful to Darryl Holm for useful remarks and explanations. The referee reports are also gratefully acknowledged, in particular for pointing out references [18,21,28,32,33,34].…”

mentioning

confidence: 99%

A Hamiltonian mean field system for the Navier–Stokes equation

Hochgerner¹

2018

Proc. R. Soc. A.

View full text Add to dashboard Cite

We use a Hamiltonian interacting particle system to derive a stochastic mean field system whose McKean–Vlasov equation yields the incompressible Navier–Stokes equation. Since the system is Hamiltonian, the particle relabeling symmetry implies a Kelvin Circulation Theorem along stochastic Lagrangian paths. Moreover, issues of energy dissipation are discussed and the model is connected to other approaches in the literature.

show abstract

“…In Theorem 4.1, we found equations of motion on the space T X (k) ⊕g (the Lagrange-Poincaré equations). These equations of motion are given by a horizontal equation, (24), which describes the dynamics on T X (k) , and a vertical equation, (25), which describes the dynamics of theg (k) -component. In particular, (24) is similar to an Euler-Lagrange equation except for the coupling term involving the curvature on the right hand side and the (x (k) , ξ (k)…”

Section: Particle Methodsmentioning

confidence: 99%

“…If L is a G -invariant Lagrangian, then there is an extra symmetry in the horizontal equations(24). In particular, the group J k (G ) ≡ G /G (k) is a residual symmetry left over by a G (k) reduction.…”

mentioning

confidence: 99%

On the coupling between an ideal fluid and immersed particles

Jacobs

Raţiu

Desbrun

2013

Physica D: Nonlinear Phenomena

View full text Add to dashboard Cite

In this paper we use Lagrange-Poincare reduction to understand the coupling between a fluid and a set of Lagrangian particles that are supposed to simulate it. In particular, we reinterpret the work of Cendra et al. by substituting velocity interpolation from particle velocities for their principal connection. The consequence of writing evolution equations in terms of interpolation is two-fold. First, it gives estimates on the error incurred when interpolation is used to derive the evolution of the system. Second, this form of the equations of motion can inspire a family of particle and hybrid particle-spectral methods where the error analysis is "built-in". We also discuss the influence of other parameters attached to the particles, such as shape, orientation, or higher-order deformations, and how they can help with conservation of momenta in the sense of Kelvin's circulation theorem.Comment: to appear in Physica D, comments and questions welcom

show abstract

Multiscale turbulence models based on convected fluid microstructure

Cited by 14 publications

References 22 publications

Stochastic Parametrization of the Richardson Triple

Stochastic Parametrization of the Richardson Triple

A Hamiltonian mean field system for the Navier–Stokes equation

On the coupling between an ideal fluid and immersed particles

Contact Info

Product

Resources

About