Katabatic flow: Analytic solution for gradually varying eddy diffusivities

A simple form of the Prandtl model addressing pure katabatic flows is solve d. The new analytic solution is valid for almost any assigned eddy diffusiv ity K(z) and constant Prandtl number. This model assumes a one-dimensional steady state for momentum and heat balance. Its approximate solution, obtai ned using the WKB method, appears as a generalization and improvement of th e classic analytic solution for the constant-K case. It is compared favorab ly against a numerical solution. A comparison with observations from PASTEX , Austria 1994, shows that the new solution is much closer to the data than the constant-K solution. The dynamics revealed with this new solution is d iscussed (relatively sharper near-surface profiles, their gradients, and th e low-level jet), and a suggestion toward improving boundary layer paramete rizations is offered.