A two Turbulence Kinetic Energy model as a scale-adaptive approach to modeling 
the planetary boundary layer

Bhattacharya, Ritthik; Stevens, Bjorn

doi:10.1002/2015MS000548

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A two Turbulence Kinetic Energy model as a scale-adaptive approach to modeling the planetary boundary layer

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Bhattacharya, Ritthik
Hans Ertel Research Group Clouds and Convection, The Atmosphere in the Earth System, MPI for Meteorology, Max Planck Society;
IMPRS on Earth System Modelling, MPI for Meteorology, Max Planck Society;

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Stevens, Bjorn
Director’s Research Group AES, The Atmosphere in the Earth System, MPI for Meteorology, Max Planck Society;

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Citation

Bhattacharya, R., & Stevens, B. (2016). A two Turbulence Kinetic Energy model as a scale-adaptive approach to modeling the planetary boundary layer. Journal of Advances in Modeling Earth Systems, 8, 224-243. doi:10.1002/2015MS000548.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0029-65BD-B

Abstract

A two Turbulence Kinetic Energy (2TKE) model is developed to address the boundary layer “grey zone” problem. The model combines ideas from local and nonlocal models into a single energetically consistent framework. By applying the Reynolds averaging to the large eddy simulation (LES) equations that employ Deardorff's subgrid TKE, we arrive at a system of equations for the boundary layer quantities and two turbulence kinetic energies: one which encapsulates the TKE of large boundary-layer-scale eddies and another which represents the energy of eddies subgrid to the vertical grid size of a typical large-scale model. These two energies are linked via the turbulent cascade of energy from larger to smaller scales and are used to model the mixing in the boundary layer. The model is evaluated for three dry test cases and found to compare favorably to large eddy simulations. The usage of two TKEs for mixing helps reduce the dependency of the model on the vertical grid scale as well as on the free tropospheric stability and facilitates a smoother transition from convective to stable regimes. The usage of two TKEs representing two ranges of scales satisfies the prerequisite for modeling the boundary layer in the “grey zone”: an idea that is explored further in a companion paper.