Particle pair diffusion and persistent streamline topology in two-dimensional turbulence
نویسنده
چکیده
From observations of direct numerical simulations (DNS) of twodimensional turbulence with inverse energy cascade, two physical pictures of particle pair diffusion are proposed based on persistent streamline topology associated with stagnation points. One picture describes the step-by-step separation process of individual pairs in a local frame moving with them, whereas the other serves as a statistical description of particle pair diffusion in a global frame which we define. These two pictures lead to the same characteristic time scale for particle pair diffusion. Based on this time scale, a new model of particle pair diffusion is proposed which predicts the temporal evolutions of the mean square separation, and of the probability density function (PDF) of separations. Our PDF equation turns out to be a generalization of Richardson’s diffusion equation (Richardson L F 1926 Proc. R. Soc. A 110 709). DNS verifications support all the predictions of our model. A generalization of our approach to d-dimensional turbulence with energy spectrum proportional to k−p is given for the purpose of demonstrating that the PDF equation and the exponent of mean square separation are directly related with the fractal dimension of the spatial distribution of stagnation points. 1 Permanent address: Theory and Computer Simulation Center, National Institute for Fusion Science, 322-6 Oroshi-cho, Toki, 509-5292, Japan. New Journal of Physics 6 (2004) 65 PII: S1367-2630(04)78254-3 1367-2630/04/010065+35$30.00 © IOP Publishing Ltd and Deutsche Physikalische Gesellschaft 2 DEUTSCHE PHYSIKALISCHE GESELLSCHAFT
منابع مشابه
The streamline diffusion method with implicit integration for the multi-dimensional Fermi Pencil Beam equation
We derive error estimates in the appropriate norms, for the streamlinediffusion (SD) finite element methods for steady state, energy dependent,Fermi equation in three space dimensions. These estimates yield optimal convergencerates due to the maximal available regularity of the exact solution.High order SD method together with implicit integration are used. The formulationis strongly consistent...
متن کاملSimulation of particle diffusion and heat transfer in a two-phase turbulent boundary layer using the Eulerian-Eulerian approach
This work investigates the response of two-dimensional, turbulent boundary layer characteristics over a flat plate to the presence of suspended particulate matter. Both phases are assumed to be interacting continua. That is, the carrier fluid equations are considered to be coupled with the particle-phase equations. A finite-difference technique with non-uniform grid has been employed for the so...
متن کاملModelling the catalyst fragmentation pattern in relation to molecular properties and particle overheating in olefin polymerization
A two-dimensional single particle finite element model was used to examine the effects of particle fragmental pattern on the average molecular weights, polymerization rate and particle overheating in heterogeneous Ziegler-Natta olefin polymerization. A two-site catalyst kinetic mechanism was employed together with a dynamic two-dimensional molecular species in diffusion-reaction equation. The i...
متن کاملKinematic Simulation for stably stratified and rotating turbulence
The properties of one-particle and particle-pair diffusion in rotating and stratified turbulence are studied by applying the Rapid Distortion Theory to a Kinematic Simulation of the Boussinesq equation with a Coriolis term. Scalings for oneand two-particle horizontal and vertical diffusions in purely rotating turbulence are proposed for small Rossby numbers. Particular attention is given to the...
متن کاملTaylor particle dispersion during transition to fully developed two-dimensional turbulence.
We report new measurements of single particle dispersion in turbulent two-dimensional (2D) flows. Laboratory experiments in electromagnetically driven and Faraday wave driven turbulence reveal a transition from weakly dispersing superdiffusive regime to strongly dispersing Brownian diffusion as the flow energy is increased in a broad range. The transition to fully developed 2D turbulence is cha...
متن کامل