Sticky Issues in Turbulent Transport

We investigate the role of partial stickiness among particles or with a surface for turbulent transport. For the former case, we re-derive known results for the case of the compressible Kraichnan model by using a method based on bi-orthogonality for the expansion of the propagator in terms of left and right eigenvectors. In particular, we show that enforcing the constraints of orthogonality and normalization yields results that were previously obtained by a rigorous, yet possibly less intuitive method. For the latter case, we introduce a general model of transport within the atmospheric boundary layer. As suggested by experimental observations on the transport of atmospheric tracers, both drift and diffusivity scale with the height to the ground. The strength of the drift is parameterized by a velocity V. We use the bi-orthogonality method to show that for V in the range -1<V<0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$-1<V<0$$\end{document} and 0<V<1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0<V<1$$\end{document} there is a one-parameter family of boundary conditions that are a priori admissible. Outside of that range, there is a single boundary condition that is admissible. In physical terms, the one-parameter family is parametrized by the degree to which particles stick to the ground.