2 research outputs found
Scalar transport in compressible flow
Transport of scalar fields in compressible flow is investigated. The
effective equations governing the transport at scales large compared to those
of the advecting flow are derived by using multi-scale techniques. Ballistic
transport generally takes place when both the solenoidal and the potential
components of the velocity do not vanish, despite of the fact that it has zero
average value. The calculation of the effective ballistic velocity is
reduced to the solution of one auxiliary equation. An analytic expression for
is derived in some special instances, i.e. flows depending on a single
coordinate, random with short correlation times and slightly compressible
cellular flow. The effective mean velocity vanishes for velocity fields
which are either incompressible or potential and time-independent. For generic
compressible flow, the most general conditions ensuring the absence of
ballistic transport are isotropy and/or parity invariance. When vanishes
(or in the frame of reference moving with velocity ), standard diffusive
transport takes place. It is known that diffusion is always enhanced by
incompressible flow. On the contrary, we show that diffusion is depleted in the
presence of time-independent potential flow. Trapping effects due to potential
wells are responsible for this depletion. For time-dependent potential flow or
generic compressible flow, transport rates are enhanced or depleted depending
on the detailed structure of the velocity field.Comment: 27 pages, submitted to Physica
Resonant enhanced diffusion in time dependent flow
Explicit examples of scalar enhanced diffusion due to resonances between
different transport mechanisms are presented. Their signature is provided by
the sharp and narrow peaks observed in the effective diffusivity coefficients
and, in the absence of molecular diffusion, by anomalous transport. For the
time-dependent flow considered here, resonances arise between their
oscillations in time and either molecular diffusion or a mean flow. The
effective diffusivities are calculated using multiscale techniques.Comment: 18 latex pages, 11 figure