Related papers: The Batchelor spectrum for a deterministically dri…
We consider transport of dynamically passive quantities in the Batchelor regime of smooth in space velocity field. For the case of arbitrary temporal correlations of the velocity we formulate the statistics of relevant characteristics of…
Steady statistics of a passive scalar advected by a random two-dimensional flow of an incompressible fluid is described in the range of scales between the correlation length of the flow and the diffusion scale. That corresponds to the…
The stationary distribution of passive tracers chaotically advected by a two-dimensional large-scale flow is investigated. The tracer field is force by resetting the value of the tracer in certain localised regions. This problem is…
Forced advection of passive tracer, $\theta $, in nonlinear relaxational medium by large scale (Batchelor problem) incompressible velocity field at scales less than the correlation length of the flow and larger than the diffusion scale is…
The Batchelor passive advection is an advection by a smooth velocity field. If the velocity field is a delta-correlated in time random Gaussian process, then the problem is reduced to quantum mechanics of fluctuating velocity gradient…
In 1959, Batchelor predicted that the stationary statistics of passive scalars advected in fluids with small diffusivity $\kappa$ should display a $|k|^{-1}$ power spectrum along an inertial range contained in the viscous-convective range…
We show that the decay of a passive scalar $\theta$ advected by a random incompressible flow with zero correlation time in Batchelor limit can be mapped exactly to a certain quantum-mechanical system with a finite number of degrees of…
We consider statistics of the passive scalar on distances much larger than the pumping scale. Such statistics is determined by statistics of Lagrangian contraction that is by probabilities of initially distant fluid particles to come close.…
In 1959, Batchelor gave a prediction for the power spectral density of a passive scalar advected by an incompressible fluid exhibiting shear-straining, a mechanism for the creation of small scales in the scalar [Bat59]. Recently, a…
Given a velocity field $u(x,t)$, we consider the evolution of a passive tracer $\theta$ governed by $\partial_t\theta + u\cdot\nabla\theta = \Delta\theta + g$ with time-independent source $g(x)$. When $\|u\|$ is small in some sense,…
This study is concerned with the decay behaviour of a passive scalar $\theta$ in three-dimensional flows having bounded velocity gradients. Given an initially smooth scalar distribution, the decay rate $d<\theta^2>/dt$ of the scalar…
We study the evolution of passive scalars in both rigid and moving slab-like domains, in both horizontally periodic and infinite contexts. The scalar is required to satisfy Robin-type boundary conditions corresponding to Newton's law of…
Passive scalar equation is considered in a turbulent homogeneous incompressible Gaussian velocity field. The turbulent nature of the field results in non-smooth coefficients in the equation. A strong, in the stochastic sense, solution of…
We present results of direct numerical simulations of passive scalar advection and diffusion in turbulent rotating flows. Scaling laws and the development of anisotropy are studied in spectral space, and in real space using an axisymmetric…
We consider the behaviour of a passive tracer $\theta$ governed by $\partial_t\theta + u\cdot\nabla\theta = \Delta\theta + g$ in two space dimensions with prescribed smooth random incompressible velocity $u(x,t)$ and source $g(x)$. In 1959,…
Given a velocity field $u(x,t)$, we consider the evolution of a passive tracer $\theta$ governed by $\partial_t\theta + u\cdot\nabla\theta = \Delta\theta + g$ with time-independent source $g(x)$. When $\|u\|$ is small, Batchelor, Howells…
We investigate the large-scale statistics of a passive scalar transported by a turbulent velocity field. At scales larger than the characteristic lengthscale of scalar injection, yet smaller than the correlation length of the velocity, the…
Batchelor predicted that a passive scalar $\psi^\nu$ with diffusivity $\nu$, advected by a smooth fluid velocity, should typically have Fourier mass distributed as $|\hat \psi^\nu|^2(k) \approx |k|^{-d}$ for $|k| \ll \nu^{-1/2}$. For a…
Bounds on high-order derivative moments of a passive scalar are obtained for large values of the Schmidt number, $Sc$. The procedure is based on the approach pioneered by Batchelor for the viscous-convective range. The upper bounds for…
A phenomenological model for the dissipation of scalar fluctuations due to the straining by the fluid motion is proposed in this letter. An explicit equation is obtained for the time evolution of the probability distribution function of a…