Ineffective diffusivity

An important problem in passive scalar transport is to parametrize the effect of a fluctuating component of the flow, in order to overcome a limited resolution. A local effective diffusivity is one such parametrization, and over the years there have been many different suggestions for 'closures' that relate the advective flux to gradients of the mean concentration. Souza et al. (J. Fluid Mech., 2023, in press) introduce a stochastic framework where the local effective diffusivity is replaced by an exact effective diffusivity operator. By computing this operator for various examples, they quantify deviations from the local approximation, which can suggest areas of improvement and novel closure models.

Automated summary

In passive scalar transport, it is important to parameterize the effect of a fluctuating component of the flow to overcome limited resolution. One commonly used parameterization is the local effective diffusivity, which relates the advective flux to gradients of the mean concentration. Souza et al. introduce a stochastic framework where the local effective diffusivity is replaced by an exact effective diffusivity operator, allowing for quantification of deviations from the local approximation and suggesting areas for improvement and novel closure models.