The models that are based of fractional derivatives should be highlighted among promising new models to describe turbulent fluid flows. In the present work, a steadystate flow in a duct is considered under the condition that the turbulent diffusion is governed by a fractional power of the Laplace operator. To study numerically flows in rectangular channels, finite-difference approximations are ...

A simple, semi-analytic representation is developed for nuclear burning in Type Ia supernovae in the special case where turbulent eddies completely disrupt the flame. The speed and width of the “distributed” flame front are derived. For the conditions considered, the burning front can be considered as a turbulent flame brush composed of corrugated sheets of well-mixed flames. These flames are a...

We propose a simple empirical model to describe the Rayleigh–Taylor RT turbulent mixing of immiscible, miscible and stratified fluids. For immiscible fluids, the rate of momentum loss is an invariant of the flow, whereas the energy dissipation rate increases linearly with time. Turbulent diffusion, accounted for through temperature fluctuations, does not terminate mixing but slows it down signi...

We investigate the dynamics of the Fisher equation for the spreading of micro-organisms in one dimenison subject to both turbulent convection and diffusion. We show that for strong enough turbulence, bacteria , for example, track in a quasilocalized fashion (with remakably long persistance times) sinks in the turbulent field. An important consequence is a large reduction in the carrying capacit...

The effect of turbulence on mixing in prototype reaction-diffusion systems is analyzed here in the special situation where the turbulence is modeled ideally with two separated scales consisting of a large-scale mean flow plus a small-scale spatiotemporal periodic flow. In the limit of fast reaction and slow diffusion, it is rigorously proved that the turbulence does not contribute to the locati...

The physical similarity and mathematical equivalence of continuous diffusion and particle random walk forms one of the cornerstones of modern physics and the theory of stochastic processes. The randomly walking particles do not need to posses any properties other than location in physical space. However, particles used in many models dealing with simulating turbulent transport and turbulent com...

Aims. We present global 3D MHD simulations of disks of gas and solids, aiming at developing models that can be used to study various scenarios of planet formation and planet-disk interaction in turbulent accretion disks. Methods. We employ the PENCIL CODE, a 3D high-order finite-difference MHD code using Cartesian coordinates. We solve the equations of ideal MHD with a local isothermal equation...

The paper describes the propagation of a thin laser beam which passes through a hot turbulent jet, perpendicularly to the flow direction, using geometrical optics approximation. From the modelling of the random propagation direction of the laser beam along its whole path, the diffusion coefficient of the turbulent jet is determined by means of a shape optimization technique in which a genetic a...

Most numerical investigations on the role of magnetic fields in turbulent molecular clouds (MCs) are based on ideal magneto-hydrodynamics (MHD). However, MCs are weakly ionized, so that the time scale required for the magnetic field to diffuse through the neutral component of the plasma by ambipolar diffusion (AD) can be comparable to the dynamical time scale. We have performed a series of 256 ...