Analytical solution for katabatic flow induced by an isolated cold strip

An analytical model for katabatic flow induced by cold strip of finite width in the cross-slope direction but of infinite extent in the downslope direction is presented. The fluid is assumed to have a constant (eddy) viscosity, and the Coriolis force is neglected. A numerical simulation has been used to verify the model, which is shown to revert to the classical Prandtl model if the strip width goes to infinity. The effects of the strip width and slope angle on the katabatic flow are studied. The buoyancy and downslope velocity reach maximum values at the centre of the strip, and spread outwards in the cross-slope direction. The downslope wind maximum weakens for narrow strips and shallow slopes. In contrast to the Prandtl solution, which shows a counter flow above the wind maximum, our model predicts the counter flow to occur outside the strip. The cross-slope variation in the surface forcing induces cross-slope and slope-normal velocities, which are manifested in vortices at the strip edges. Below the wind maximum, the fluid above the cooling surface descends and moves toward the strip edge where it is detrained from the strip region. Replenishment of fluid into the strip region takes place above the wind maximum.