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28 March 2024
 
  » arxiv » 1510.0784

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Dispersion in rectangular networks: effective diffusivity and large-deviation rate function
Alexandra Tzella ; Jacques Vanneste ;
Date 3 Oct 2015
AbstractWe investigate the dispersion of a passive scalar released in a fluid flowing within a rectangular, Manhattan-style network. We use large-deviation theory to approximate the scalar concentration as it evolves under the combined action of advection and diffusion and derive an expression for the rate function that controls the form of the concentration at large times $t$. For moderately large distances $O(t^{1/2})$ from the centre of mass, this form reduces to a Gaussian parameterised by a (tensorial) effective diffusivity given in closed form. Further away, at distances $O(t)$, a more complex form reveals the strong imprint of the network geometry. Our theoretical predictions are verified against Monte Carlo simulations of Brownian particles.
Source arXiv, 1510.0784
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