The role of consistent turbulence energetics in the representation of dry and shallow convection

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2019

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Abstract

In this doctoral dissertation, the role of consistent turbulence energetics is examined in the context of sub-grid turbulence, convection, and cloud condensation parameterizations for numerical weather and climate models. The property of energetic consistency is formally defined and divided into two categories, local and non-local, and various common parameterization approaches are classified according this framework. I show theoretically that the basis of local energetic consistency is the inclusion of mean-gradient transport and buoyancy acceleration terms in the diagnostic and prognostic budget equations of all second-order statistical moments, including fluxes. Effectively, these terms account for the conversion between turbulent kinetic energy (TKE) and turbulent potential energy (TPE) under stably stratified conditions. With simple numerical experiments, I show that if local energetic consistency is not satisfied, then thermodynamic profiles cannot be correctly predicted under stably conditions, such as in the boundary layer capping inversion. I then extend the concept of energetic consistency from local turbulent mixing to non-local convective transport. I show that the popular eddy diffusivity-mass flux (EDMF) approach for unified parameterization of turbulence and convection treats the turbulent transport of turbulent energy in two parallel but inconsistent ways: advectively and diffusively. I introduce a novel parameterization approach, inspired by EDMF, that consistently partitions all second-order moments, including TKE, between convective and non-convective parts of a grid cell and show that this approach predicts significantly more realistic depths of convective boundary layers than conventional EDMF schemes. Finally, I introduce a novel method for validating this parameterization approach, based on Langragian particle tracking in large-eddy simulations.

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