On the Budget of Turbulence Kinetic Energy in the Unstable Atmospheric Surface Layer

This paper presents a new account of the turbulence kinetic energy budget in the unstable atmospheric surface layer beneath a convective outer layer. It is based on the structural model of turbulence introduced by McNaughton (Boundary-Layer Meteorology, 112: 199-221, 2004). In this model the turbulence is described as a self-organizing system with a highly-organized structure that resists change by instability. Thus local buoyant production in the surface layer adds energy to the turbulence and so increases its velocity scale and momentum transport, but the tendency for buoyancy to alter the structure of the eddies is opposed by pressure reaction forces, so the buoyant (gravitational) potential energy is simply converted to pressure potential energy. Thus pressure production equals buoyant production in the TKE budget equation. The model is developed to consider the variable driving of the whole surface layer by the larger-scale eddies of the outer layer. The divergence of the downwards flux of TKE from the outer layer can be divided into mean and fluctuating shear production terms. The variable shear production has usually been included within the turbulent transport term, causing an apparent imbalance between total production and dissipation. The extra shear production increases the dissipation rate without changing the momentum flux. The velocity scale for turbulent transport processes in the surface layer should be based on the dissipation rate rather than the friction velocity for all purposes but scaling the mean wind profile and mean momentum flux. These findings are in direct opposition to the principles of Monin-Obukhov similarity theory.