A single-column model of the dry, shear-free, convective boundary layer is presented
in which nonlocal transports by coherent structures such as thermals are represented
by the partitioning of the fluid into two components, updraft and environment, each
with a full set of prognostic dynamical equations. Local eddy diffusive transport ...
A single-column model of the dry, shear-free, convective boundary layer is presented
in which nonlocal transports by coherent structures such as thermals are represented
by the partitioning of the fluid into two components, updraft and environment, each
with a full set of prognostic dynamical equations. Local eddy diffusive transport and
entrainment and detrainment are represented by parameterizations similar to those
used in Eddy Diffusivity Mass Flux schemes. The inclusion of vertical diffusion of the
vertical velocity is shown to be important for suppressing an instability inherent in the
governing equations. A semi-implicit semi-Lagrangian numerical solution method is
presented and shown to be stable for large acoustic and diffusive Courant numbers,
though it becomes unstable for large advective Courant numbers. The solutions are
able to capture key physical features of the dry convective boundary layer. Some of the
numerical challenges posed by sharp features in the solution are discussed, and areas
where the model could be improved are highlighted.
