We show that the decay of a passive scalar θ 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 freedom. The Schrödinger equation is derived and its solution is analyzed for the case when at the beginning the scalar has Gaussian statistics with correlation function...

We study the statistics of the relative separation between two fluid particles in a random flow. We confine ourselves to the Batchelor regime, i.e. we only examine the evolution of distances smaller than the smallest active scale of the flow, where the latter is spatially smooth. The Lagrangian strain is assumed as given in its statistics and is modelled by a telegraph noise. This is a stationa...

Two dimensional passive scalar turbulence is studied by means of a k-space diffusion model based on third order differential approximation. This simple description local nonlinear interactions in Fourier space shown to present general expression, line with previous seminal works, and appears be suitable for various 2D problems. Steady state solutions the spectral energy density flow are recover...

Passive scalars advected by three-dimensional Navier-Stokes turbulence exhibit a fundamental anomaly in odd-order moments because of the characteristic ramp-cliff structures, violating small-scale isotropy. We use data from direct numerical simulations with grid resolution up to $8192^3$ at high P\'eclet numbers understand this as scalar diffusivity, $D$, diminishes, or Schmidt number, $Sc = \n...

fill this seat, the choice lies between a career grade officer, a general practitioner, or a hospital junior doctor with a number of house appointments behind him. If staffing is to be entirely by career grade officers, then the minimum number is five and not four as suggested by Mr. F. C. Durbin and Mr. J. S. Batchelor (14 August, p. 432). To staff with only four would mean a 42-hour week with...

The dynamics of the two{dimensional turbulence is studied by a stochastic simulation method. The latter is based on a representation of the random vorticity eld and stream function by a multivariate stochastic process de-ned by a discrete master equation. It is demonstrated that in the continuum limit the complete hierarchy of coupled moment equations for the statistical formulation of the 2D N...

The latest experimental evidence indicates that acetylation of p53 at K164 (lysine 164) and K120 may induce directly cell apoptosis under severe DNA damage. However, previous cell apoptosis models only studied the effects of active and/or inactive p53, that is, phosphorylation/dephosphorylation of p53. In the present paper, based partly on Geva-Zatorsky et al. (2006) and Batchelor et al. (2008)...

Mixing and transport in turbulent flows-which have strong local concentration fluctuations-are essential in many natural and industrial systems including reactions in chemical mixers, combustion in engines and burners, droplet formation in warm clouds, and biological odor detection and chemotaxis. Local concentration fluctuations, in turn, are intimately tied to the problem of the separation of...

Pressure spectra at large wave numbers are calculated for Lundgren-Townsend vortex models of the fine scales of homogeneous turbulence. Specific results are given for the Burgers vortex and also for the Lundgren-strained spiral vortex. For the latter case, it is fqund that the contribution to the shell-summed spectrum produced by the interaction between the axisymmetric and nonaxisymmetric comp...

We consider an emulsion of two Stokes uids, one of which is periodically distributed in the form of small spherical bubbles. The e ects of surface tension on the bubble boundaries are modelled mathematically, as in the work of G. I. Taylor, by a jump only in the normal component of the traction. For a given volume fraction of bubbles we consider the two-scale convergence, and in the ne phase li...