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Computational Modeling of the Turbulent Penetrative Convection above the Urban Heat Island in a Stably Stratified Environment

Albert F. KurbatskiiInstitute of Theoretical and Applied Mechanics, Russian Academy of Sciences, Novosibirsk State University, Novosibirsk, Russia

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Abstract

A three-equation model of the turbulent transport of momentum and heat for simulating a circulation structure over the heat island in a stably stratified environment under nearly calm conditions is formulated. The turbulent kinetic energy E = (1/2)〈uiui〉 (where 〈 〉 indicates averaging), its spectral flux ϵ (dissipation), and the dispersion of turbulent fluctuations of temperature 〈θ2〉 are found from differential equations; thus the correct modeling of transport processes in the interface layer with the countergradient heat flux is assured. Turbulent fluxes of momentum, −〈uiuj〉, and heat, −〈uiθ〉, are determined from fully explicit “gradient diffusion” models. The Eϵ–〈θ2〉 turbulence model minimizes difficulties in simulating the turbulent transport in a stably stratified environment and reduces efforts needed for the numerical implementation of the model. Numerical simulation of the turbulent structure of the penetrative convection over the heat island under conditions of stably stratified atmosphere demonstrates that the three-equation model is able to predict the circulation induced by the heat island, temperature distribution, root-mean-square fluctuations of the turbulent velocity and temperature fields, and spectral turbulent kinetic energy flux that are in good agreement with the experimental data and results of large-eddy simulations.

Corresponding author address: Dr. Albert Kurbatskii, Institute of Theoretical and Applied Mechanics, Siberian Division of Russian Academy of Sciences, 630090 Novosibirsk, Russia. kurbat@nsu.ru

Abstract

A three-equation model of the turbulent transport of momentum and heat for simulating a circulation structure over the heat island in a stably stratified environment under nearly calm conditions is formulated. The turbulent kinetic energy E = (1/2)〈uiui〉 (where 〈 〉 indicates averaging), its spectral flux ϵ (dissipation), and the dispersion of turbulent fluctuations of temperature 〈θ2〉 are found from differential equations; thus the correct modeling of transport processes in the interface layer with the countergradient heat flux is assured. Turbulent fluxes of momentum, −〈uiuj〉, and heat, −〈uiθ〉, are determined from fully explicit “gradient diffusion” models. The Eϵ–〈θ2〉 turbulence model minimizes difficulties in simulating the turbulent transport in a stably stratified environment and reduces efforts needed for the numerical implementation of the model. Numerical simulation of the turbulent structure of the penetrative convection over the heat island under conditions of stably stratified atmosphere demonstrates that the three-equation model is able to predict the circulation induced by the heat island, temperature distribution, root-mean-square fluctuations of the turbulent velocity and temperature fields, and spectral turbulent kinetic energy flux that are in good agreement with the experimental data and results of large-eddy simulations.

Corresponding author address: Dr. Albert Kurbatskii, Institute of Theoretical and Applied Mechanics, Siberian Division of Russian Academy of Sciences, 630090 Novosibirsk, Russia. kurbat@nsu.ru

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