Scalar transport in compressible flow
/ Authors
/ Abstract
Abstract 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 v are derived by using multi-scale techniques. Ballistic transport generally takes place when both the solenoidal and the potential components of v do not vanish, despite of the fact that v has zero average value. The calculation of the effective ballistic velocity V b 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 comoving 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.
Journal: Physica D: Nonlinear Phenomena