Non-local mixing

The eddy flux of a tracer can, in general, be represented as integral of a weighting kernel times the mean gradient. In terms of the Fourier components of the gradient, this implies that the effective diffusivity depends on the wavenumber. We present a one-dimensional analytical model of mixing by stochastic flow where we can calculate the effective diffusivity as a function of k and the form of the kernel. We describe the dependence on the statistics of the flow (the variance of the velocity and the correlation time). We then describe a 2D flow field and show that the kernel has similar properties.