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Article

Closure Schemes for Stably Stratified Atmospheric Flows without Turbulence Cutoff

Dan Li1, Gabriel G. Katul2, and Sergej S. Zilitinkevich3
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  • 1 Department of Earth and Environment, Boston University, Boston, Massachusetts
  • | 2 Nicholas School of the Environment, and Department of Civil and Environmental Engineering, Duke University, Durham, North Carolina
  • | 3 Finnish Meteorological Institute, and Division of Atmospheric Sciences, University of Helsinki, Helsinki, Finland, and Department of Radio Physics, N.I. Lobachevski State University of Nizhniy Novgorod, Nizhniy Novgorod, and Faculty of Geography, Moscow University, and Institute of Geography, Russian Academy of Sciences, Moscow, Russia, and Nansen Environmental and Remote Sensing Center/Bjerknes Centre for Climate Research, Bergen, Norway
Print Publication:
01 Dec 2016
DOI:
https://doi.org/10.1175/JAS-D-16-0101.1
Page(s):
4817–4832
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Abstract

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

Corresponding author address: Dan Li, Department of Earth and Environment, Boston University, 685 Commonwealth Ave., Boston, MA 02215. E-mail: lidan@bu.edu

Abstract

Two recently proposed turbulence closure schemes are compared against the conventional Mellor–Yamada (MY) model for stably stratified atmospheric flows. The Energy- and Flux-Budget (EFB) approach solves the budgets of turbulent momentum and heat fluxes and turbulent kinetic and potential energies. The Cospectral Budget (CSB) approach is formulated in wavenumber space and integrated across all turbulent scales to obtain flow variables in physical space. Unlike the MY model, which is subject to a “critical gradient Richardson number,” both EFB and CSB models allow turbulence to exist at any gradient Richardson number and predict a saturation of flux Richardson number () at sufficiently large . The CSB approach further predicts the value of and reveals a unique expression linking the Rotta and von Kármán constants. Hence, all constants in the CSB model are nontunable and stability independent. All models agree that the dimensionless sensible heat flux decays with increasing . However, the decay rate and subsequent cutoff in the MY model appear abrupt. The MY model further exhibits an abrupt cutoff in the turbulent stress normalized by vertical velocity variance, while the CSB and EFB models display increasing trends. The EFB model produces a rapid increase in the ratio of turbulent potential energy and vertical velocity variance as is approached, suggesting a strong self-preservation mechanism. Vertical anisotropy in the turbulent kinetic energy is parameterized in different ways in MY and EFB, but this consideration is not required in CSB. Differences between EFB and CSB model predictions originate from how the vertical anisotropy is specified in the EFB model.

Corresponding author address: Dan Li, Department of Earth and Environment, Boston University, 685 Commonwealth Ave., Boston, MA 02215. E-mail: lidan@bu.edu
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