Effect of helicity on the effective diffusivity for incompressible random flows - art. no. 061205

The advection of a passive scaler by a quenched (frozen) incompressible vel ocity field is studied by extensive high precision numerical simulation and various approximation schemes. We show that second-order self-consistent p erturbation theory, in the absence of helicity, perfectly predicts the effe ctive diffusivity of a tracer particle in such a field. In the presence of helicity in the Row, simulations reveal an unexpectedly strong enhancement of the effective diffusivity which is highly nonperturbative and most visib le when the bare molecular diffusivity of the particle is small. We develop and analyze a series of approximation schemes which indicate that this enh ancement of the diffusivity is due to a second order effect, whereby the he lical component of the field, which does not directly renormalize the effec tive diffusivity, enhances the strength of the nonhelical part of the flow, which in turn renormalizes the molecular diffusivity. We show that this re normalization is most important at a low bare molecular diffusivity, in agr eement with numerical simulations.