Model of the Height Variation of the Turbulence Kinetic Energy Budget in the Unstable Planetary Boundary Layer

Abstract

A model is proposed for the variation with height of the terms in the turbulence kinetic energy budget throughout an unstably stratified barotrople planetary boundary layer. The model is based upon aircraft measurements throughout the boundary layer that are presented here and previous results from surface layer measurements. The model assumes that at the limit of neutral stability, the transport term in the budget equation is at a minimum. When the height above the ground is greater than about ten times the absolute value of the Obukhov length, the shear-generation term is negligible, while the rate of dissipation of turbulence energy becomes almost constant, and the transport term increases almost linearly with height to balance the almost linear decrease of the buoyancy-generation term. Measurements of the ratio of the vertical flux of the horizontal part of the turbulence kinetic energy to the vertical part show good agreement with a model based upon surface layer observations and a laboratory tank experiment. One set of observations was taken over a lake from just downwind of the shore to about 30 km offshore and the assumption of horizontal homogeneity was found to be unjustified.