A bound on scalar variance for the advection – diffusion equation

@inproceedings{PLASTING2006ABO,
  title={A bound on scalar variance for the advection – diffusion equation},
  author={S. C. PLASTING and William R. Young},
  year={2006}
}
We study the statistics of a passive scalar T (x, t) governed by the advection–diffusion equation with variations in the scalar produced by a steady source. Two important statistical properties of the scalar are the variance, σ 2 ≡ 〈T 〉, and the entropy production, χ ≡ κ〈|∇T |〉. Here 〈〉 denotes a space–time average and κ is the molecular diffusivity of T . Using variational methods we show that the system must lie above a parabola in the (χ, σ )-plane. The location of the bounding parabola… CONTINUE READING