The effective equation describing the transport of passive tracers in non-solenoidal velocity fields is determined, assuming that the velocity field is a function of both position and time, albeit remaining locally random. Assuming a strong separation of scales, and applying the method of homogenization, we find a Fickian constitutive relation for the coarse-grained particle flux, as the sum of a convective part, and a diffusive term, expressed in terms of an Eulerian mean tracer velocity, and an effective diffusivity. We show that the motion of a tracer particle is a Stratonovich random process, where the smoothly-varying mean tracer velocity equals the microscale mean tracer velocity and the fluctuating term is described through the cross velocity correlation dyadics.
|Titolo:||Heat and Mass Transport in Nonhomogeneous Random Velocity Fields|
|Anno del prodotto:||2003|
|Digital Object Identifier (DOI):||10.1103/PhysRevE.68.066306|
|Appare nelle tipologie:||1.1 Articolo in rivista|