A Generalized Mixing Length Closure for Eddy-Diffusivity Mass-Flux
Schemes of Turbulence and Convection
Abstract
Because of their limited spatial resolution, numerical weather
prediction and climate models have to rely on parameterizations to
represent atmospheric turbulence and convection. Historically, largely
independent approaches have been used to represent boundary layer
turbulence and convection, neglecting important interactions at the
subgrid scale. Here we build on an eddy-diffusivity mass-flux (EDMF)
scheme that represents all subgrid-scale mixing in a unified manner,
partitioning subgrid-scale fluctuations into contributions from local
diffusive mixing and coherent advective structures and allowing them to
interact within a single framework. The EDMF scheme requires closures
for the interaction between the turbulent environment and the plumes and
for local mixing. A second-order equation for turbulence kinetic energy
(TKE) provides one ingredient for the diffusive local mixing closure,
leaving a mixing length to be parameterized. A new mixing length
formulation is proposed, based on constraints derived from the TKE
balance. It expresses local mixing in terms of the same physical
processes in all regimes of boundary layer flow. The formulation is
tested at a range of resolutions and across a wide range of boundary
layer regimes, including a stably stratified boundary layer, a
stratocumulus-topped marine boundary layer, and dry convection.
Comparison with large eddy simulations (LES) shows that the EDMF scheme
with this diffusive mixing parameterization accurately captures the
structure of the boundary layer and clouds in all cases considered.