An Eddy Diffusivity–Mass Flux Approach to the Vertical Transport of Turbulent Kinetic Energy in Convective Boundary Layers

Marcin L. Witek Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Joao Teixeira Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Georgios Matheou Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California

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Abstract

In this study a new approach to the vertical transport of the turbulent kinetic energy (TKE) is proposed. The principal idea behind the new parameterization is that organized updrafts or convective plumes play an important role in transferring TKE vertically within convectively driven boundary layers. The parameterization is derived by applying an updraft environment decomposition to the vertical velocity triple correlation term in the TKE prognostic equation. The additional mass flux (MF) term that results from this decomposition closely resembles the features of the TKE transport diagnosed from the large-eddy simulation (LES) and accounts for 97% of the LES-diagnosed transport when the updraft fraction is set to 0.13. Another advantage of the MF term is that it is a function of the updraft vertical velocity and can be readily calculated using already existing parameterization. The new MF approach, combined with several eddy diffusivity (ED) formulations, is implemented into a simplified 1D TKE prognostic model. The 1D model results, compared against LES simulations of dry convective boundary layers, show substantial improvement in representing the vertical structure of TKE. The new combined ED–MF parameterization, as well as the MF term alone, surpasses in accuracy the ED parameterizations. The proposed TKE transport parameterization shows large potential of improving TKE simulations in mesoscale and global circulation models.

Corresponding author address: Marcin L. Witek, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109. E-mail: marcin.l.witek@jpl.nasa.gov

Abstract

In this study a new approach to the vertical transport of the turbulent kinetic energy (TKE) is proposed. The principal idea behind the new parameterization is that organized updrafts or convective plumes play an important role in transferring TKE vertically within convectively driven boundary layers. The parameterization is derived by applying an updraft environment decomposition to the vertical velocity triple correlation term in the TKE prognostic equation. The additional mass flux (MF) term that results from this decomposition closely resembles the features of the TKE transport diagnosed from the large-eddy simulation (LES) and accounts for 97% of the LES-diagnosed transport when the updraft fraction is set to 0.13. Another advantage of the MF term is that it is a function of the updraft vertical velocity and can be readily calculated using already existing parameterization. The new MF approach, combined with several eddy diffusivity (ED) formulations, is implemented into a simplified 1D TKE prognostic model. The 1D model results, compared against LES simulations of dry convective boundary layers, show substantial improvement in representing the vertical structure of TKE. The new combined ED–MF parameterization, as well as the MF term alone, surpasses in accuracy the ED parameterizations. The proposed TKE transport parameterization shows large potential of improving TKE simulations in mesoscale and global circulation models.

Corresponding author address: Marcin L. Witek, Jet Propulsion Laboratory, California Institute of Technology, 4800 Oak Grove Drive, Pasadena, CA 91109. E-mail: marcin.l.witek@jpl.nasa.gov
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