Countergradient Fluxes of Conserved Variables in the Clear convective and Stratocumulus-topped Boundary Layer: The role of the Entrainment Flux

Large-eddy simulations of a clear convective boundary layer (CBL)and a stratocumulus-topped boundary layer are studied. Bottom-upand a top-down scalars were included in the simulations, and theprinciple of linear superposition of variables was applied toreconstruct the fields of any arbitrary conserved variable.This approach allows a systematic analysis of countergradient fluxesas a function of the flux ratio, which is defined as the ratio betweenthe entrainment flux and the surface flux of the conserved quantity.In general, the turbulent flux of an arbitrary conserved quantityis counter to the mean vertical gradient if the heights where thevertical flux and the mean vertical gradient change sign do notcoincide. The regime where the flux is countergradient is thereforebounded by the so-called zero-flux and zero-gradient heights. Becausethe vertical flux changes sign only if the entrainment flux has anopposite sign to the surface flux, countergradient fluxes arepredominantly found for negative flux ratios. In the CBL the fluxratio for the virtual potential temperature is, to a good approximation,constant, and equal to -0.2. Only if the moisture contribution to thevirtual potential temperature is negligibly small will the flux ratio forthe potential temperature be equal to this value. Otherwise, theflux ratio for the potential temperature can have any arbitrary(negative) value, and, as a consequence, the fluxes for thepotential temperature and the virtual potential temperature willbe countergradient at different heights. As a practical application ofthe results, vertical profiles of the countergradient correction termfor different entrainment-to-surface-flux ratios are discussed.     

Length Scales of Scalar Diffusion in the Convective Boundary Layer: Laboratory Observations

A laboratory study of scalar diffusion in the convective boundary layer has found results that are consistent with a 1999 large-eddy simulation (LES) study by Jonker, Duynkerke and Cuijpers. For bottom-up and top-down scalars (introduced as ‘infinite’ area sources of passive tracer at the surface and inversion, respectively) the dominant length scale was found to be much larger than the length scale for density fluctuations, the latter being equal to the boundary-layer depth h. The variance of the normalized passive scalar grew continuously with time and its magnitude was about 3–5 times larger for the top-down case than for the bottom-up case. The vertical profiles of the normalized passive scalar variance were found to be approximately constant through the convective boundary layer (CBL) with a value of about 3–8c_*² for bottom-up and 10–50c_*² for top-down diffusion. Finally, there was some evidence of a minimum in the variance and dominant length scale for scalar flux ratios (top-down to bottom-up flux) close to −0.5. All these convection tank results confirm the LES results and support the hypothesis that there is a distinct difference in behaviour between the dynamic and passive variables in the CBL.