We elucidate the effect of noise on dynamics N point charges in a Vlasov‐Poisson model with singular bounded interaction force. A too simple does not affect structure inherited from deterministic system and, particular, cannot prevent coalescence charges. Inspired by theory random transport passive scalars, we identify class fields generating pulses that are chaotic enough to disorganize and any collapse particles. obtain strong unique solvability stochastic for initial configuration...

We show that, at low inertia and large elasticity, shell models of viscoelastic fluids develop a chaotic behaviour with properties similar to those elastic turbulence. The dimensionality allows us explore wide range both in polymer concentration Weissenberg number. Our results demonstrate that the physical mechanisms origin turbulence do not rely on boundary conditions or geometry mean flow.

We present an overview of the statistical properties turbulence in two-dimensional (2D) fluids. After a brief recapitulation well-known results for statistically homogeneous and isotropic 2D fluid turbulence, we give recent progress this field such conducting fluids, fluids with polymer additives, binary-fluid mixtures, superfluids; also discuss particles advected by turbulent

Shell models allow much greater scale separations than those presently achievable with direct numerical simulations of the Navier–Stokes equations. Consequently, they are an invaluable tool for testing new concepts and ideas in theory fully developed turbulence. They also successfully display energy cascades intermittency homogeneous isotropic turbulent flows. Moreover, great interest to mathematical analysts because, while retaining some key features Euler equations, more tractable. A...

We present measurements of fluid particle accelerations in turbulent water flow between counterrotating disks using three-dimensional Lagrangian tracking. By simultaneously following multiple particles with sub-Kolmogorov-time-scale temporal resolution, we measured the spatial correlation acceleration at Taylor microscale Reynolds numbers 200 and 690. also obtained indirect, nonintrusive Eulerian pressure structure functions by integrating correlations. Our are good agreement theoretical...

The issue of intermittency in numerical solutions the 3D Navier-Stokes equations on a periodic box $[0,\,L]^{3}$ is addressed through four sets simulations that calculate new set variables defined by $D_{m}(t) = \left(\varpi_{0}^{-1}\Omega_{m}\right)^{\alpha_{m}}$ for $1 \leq m \infty$ where $\alpha_{m}= \frac{2m}{4m-3}$ and $\left[\Omega_{m}(t)\right]^{2m} L^{-3}\I |\bom|^{2m}dV$ with $\varpi_{0} \nu L^{-2}$. All unexpectedly show $D_{m}$ are ordered $m 1\,,...,\,9$ such $D_{m+1} < D_{m}$....

Polymer stretching in random smooth flows is investigated within the framework of FENE dumbbell model. The advecting flow Gaussian and short-correlated time. stationary probability density function polymer extension derived exactly. characteristic time needed for system to attain regime computed as a Weissenberg number maximum length polymers. transient relaxation predicted be exceptionally slow proximity coil–stretch transition.

We study the impact of Peterlin approximation on statistics end-to-end separation polymers in a turbulent flow. The finitely extensible nonlinear elastic (FENE) model and FENE with (FENE-P) are numerically integrated along large number Lagrangian trajectories resulting from direct numerical simulation three-dimensional homogeneous isotropic turbulence. Although FENE-P yields results qualitative agreement those model, quantitative differences emerge. steady-state probability extensions is...

Abstract The dynamics of non-spherical rigid particles immersed in an axisymmetric random flow is studied analytically. motion the described by Jeffery’s equation; Gaussian and has short correlation time. stationary probability density function orientations calculated exactly. Four regimes are identified depending on statistical anisotropy geometrical shape particle. If $\boldsymbol{\lambda} $ axis symmetry flow, four are: rotation about , tumbling between $- \boldsymbol{\lambda} combination...

Elastic turbulence is a chaotic regime that emerges in polymer solutions at low Reynolds numbers. A common way to ensure stability numerical simulations of add artificially large polymer-stress diffusion. In order assess the accuracy this approach elastic regime, we compare two-dimensional Oldroyd-B and FENE-P models sustained by cellular force with without artificial We find diffusion can have dramatic effect even on large-scale properties flow show some spurious phenomena may arise when used.

The effects of a large-scale shear on the energy spectrum passively advected scalar field are investigated. is superimposed turbulent isotropic flow, yielding an Obukhov-Corrsin $k^{-5/3}$ at small scales. Shear appear large scales, where different, anisotropic behavior observed. shown to behave as $k^{-4/3}$ for fixed in intensity and direction. For other types characteristics, slope generally intermediate between -5/3 Obukhov-Corrsin's -1 Batchelor's values. physical mechanisms origin this...

We present a new closure for the mean rate of stretching dissolved polymer by homogeneous isotropic turbulence. The is modeled bead-spring-type model (e.g., Oldroyd B, FENE-P, Giesekus) and analytical obtained assuming Lagrangian velocity gradient can be as Gaussian, white-noise stochastic process. resulting depends upon ratio correlation time strain rotation. Additionally, we derived second-order expression circumstances when rotation have finite time. Finally, base level shown to reproduce...

The periodic 3D Navier–Stokes equations are analyzed in terms of dimensionless, scaled, L2m-norms vorticity Dm (1 ⩽ m < ∞). first this hierarchy, D1, is the global enstrophy. Three regimes naturally occur D1 − plane. Solutions regime, which lie between two concave curves, shown to be regular, owing strong nonlinear depletion. Moreover, numerical experiments have suggested, so far, that all dynamics heavily depleted regime [1]; new evidence for presented. Estimates dimension a attractor and...

Abstract

We consider the kinematic fluctuation dynamo problem in a flow that is random, white-in-time, with both solenoidal and potential components. This model generalization of well-studied Kazantsev model. If parts have same scaling exponent, then, as compressibility increases, growth rate decreases but remains positive. exponents for differ, particular if they correspond to typical Kolmogorov Burgers values, we again find an increase slows down does not turn it off. The slow is, however, weaker...

A string of tracers, interacting elastically, in a turbulent flow is shown to have dramatically different behaviour when compared the non-interacting case. In particular, such an elastic chain shows strong preferential sampling unlike usual tracer limit: trapped vortical regions and not straining ones. The degree its dependence on elasticity quantified via Okubo-Weiss parameter. effect modifying deformability chain, number links that form it, also examined.

Simulations of elastic turbulence, the chaotic flow highly and inertialess polymer solutions, are plagued by numerical difficulties: chaotically advected conformation tensor develops extremely large gradients can lose its positive-definiteness, which triggers instabilities. While efforts to tackle these issues have produced a plethora specialized techniques – decompositions, artificial diffusion, shock-capturing advection schemes we still lack an unambiguous route accurate efficient...

We study the deformation of flexible polymers whose contour length lies in inertial range a homogeneous and isotropic turbulent flow. By using elastic dumbbell model stochastic velocity field with nonsmooth spatial correlations, we obtain probability density function extension as Weissenberg number scaling exponent structure functions. In spatially rough flow, turbulence, statistics polymer stretching differs from that observed laminar flows or smooth chaotic flows. particular, distribution...

We investigate the non-equilibrium dynamics of an isolated polymer in a stationary elongational flow. compute relaxation time to steady-state configuration as function Weissenberg number. A strong increase is found around coil–stretch transition, which attributed large number configurations. The solved analytically terms central two-point connection problem for singly confluent Heun equation.

We show and explain how a long bead-spring chain, immersed in homogeneous, isotropic turbulent flow, preferentially samples vortical flow structures. begin with an elastic, extensible chain which is stretched out by the up to inertial-range scales. This filamentary object, known sample circular coherent vortices of two-dimensional (2D) turbulence, shown here also intense, tubular, vortex filaments 3D turbulence. In 2D case, collapses into tracer inside vortices. 3D, on contrary, extended...

The bending dynamics of trimers depends strongly on whether the flow is laminar or turbulent and, in latter case, sensitive to dimension. Trimers are found be mainly fully extended 3D turbulence and either folded 2D turbulence.

The present study investigates the dynamics of an inertialess rigid dumbbell in a steady two-dimensional vortex. This system goes beyond point-particle approximation but remains analytically solvable. For any vortex, follows from existence constant motion that is independent form In particular, if fluid angular velocity decreases with radial distance, performs spirographic trajectories around vortex center, shape which highly sensitive to initial position and orientation dumbbell.

The growth of magnetic fluctuations in the inertial range turbulence is investigated terms fluid particle dynamics. existence dynamo effect related to time behaviour correlations between tangent vectors evolving along Lagrangian trajectories. In presence effect, grow exponentially time; absence they decay as power laws. above behaviours are intimately statistical conservation laws for