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.
Heat and Mass Transport in Nonhomogeneous Random Velocity Fields
MAURI, ROBERTO
2003-01-01
Abstract
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.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
