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Flow Regimes of Nonlinear Heat Island Circulation

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  • 1 Ocean Research Institute, University of Tokyo, Tokyo, Japan
  • | 2 Department of Astronomy and Earth Sciences, Tokyo Gakugei University, Tokyo, Japan
  • | 3 Division of Earth and Planetary Sciences, Graduate School of Science, Kyoto University, Kyoto, Japan
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Abstract

Previous laboratory and numerical experiments show that the nonlinear heat island circulation has two different flow regimes: One has two maximums of updraft at both edges of the heat island (type E), while the other has a single maximum of updraft at the center of the island (type C). Our theoretical consideration shows that the heat island circulation is principally governed by two nondimensional parameters: a nonlinear parameter εN = Δθ/(Γδ) and a Prandtl number Pr = ν/κ, where Δθ is the surface temperature anomaly of the heat island, Γ the vertical gradient of the basic potential temperature, δ the thickness of the thermal boundary layer, ν the kinematic viscosity, and κ the temperature diffusivity. For a given fluid, the Prandtl number is fixed, so that the flow regime is principally determined by the nonlinear parameter εN.

Numerical experiments are performed to confirm the theoretical prediction. The steady-state flows obtained from the numerical experiments are categorized into either of the two regimes. In accordance with the theoretical prediction, the transition between the two regimes occurs at a critical value of εN(∼3.4). When εN is larger (smaller) than this critical value, type C (type E) is realized. The physical mechanism for the transition is interpreted in the light of the authors' previous theoretical study.

* Current affiliation: Head Office, Suntory Ltd., Osaka, Japan

Corresponding author address: Prof. Hiroshi Niino, Ocean Research Institute, University of Tokyo, Nakano, Tokyo 164-8639, Japan. Email: niino@ori.u-tokyo.ac.jp

Abstract

Previous laboratory and numerical experiments show that the nonlinear heat island circulation has two different flow regimes: One has two maximums of updraft at both edges of the heat island (type E), while the other has a single maximum of updraft at the center of the island (type C). Our theoretical consideration shows that the heat island circulation is principally governed by two nondimensional parameters: a nonlinear parameter εN = Δθ/(Γδ) and a Prandtl number Pr = ν/κ, where Δθ is the surface temperature anomaly of the heat island, Γ the vertical gradient of the basic potential temperature, δ the thickness of the thermal boundary layer, ν the kinematic viscosity, and κ the temperature diffusivity. For a given fluid, the Prandtl number is fixed, so that the flow regime is principally determined by the nonlinear parameter εN.

Numerical experiments are performed to confirm the theoretical prediction. The steady-state flows obtained from the numerical experiments are categorized into either of the two regimes. In accordance with the theoretical prediction, the transition between the two regimes occurs at a critical value of εN(∼3.4). When εN is larger (smaller) than this critical value, type C (type E) is realized. The physical mechanism for the transition is interpreted in the light of the authors' previous theoretical study.

* Current affiliation: Head Office, Suntory Ltd., Osaka, Japan

Corresponding author address: Prof. Hiroshi Niino, Ocean Research Institute, University of Tokyo, Nakano, Tokyo 164-8639, Japan. Email: niino@ori.u-tokyo.ac.jp

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