On the analytical solution for two-dimensional convective plume and analytical modeling of the entrainment zone thickness |
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| Institution: | 1. Institute of Oceanography, Hellenic Centre for Marine Research, PO Box 712, Anavyssos, Attica GR-190 13, Greece;2. Institute of Marine Biological Resources and Inland Waters, Hellenic Centre for Marine Research, Anavyssos, Attica GR-190 13, Greece;1. Department of Sustainable Landscape Development, Institute for Geosciences and Geography, Martin Luther University Halle-Wittenberg, Halle (Saale), Germany;2. Department of Biosystems Engineering, Institute of Technology, Hawassa University, Hawassa, Ethiopia |
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| Abstract: | Analytical solution for two-dimensional thermal plume updraft velocity is obtained under the assumption of a uniform temperature excess inside the plume. In this way, the thermal plume motion is modeled in both mixed layer and entrainment zone. Also, a semi-analytical solution is obtained using an empirical model for the plume temperature excess in the mixed layer. In addition, an analytical model for entrainment zone thickness is obtained by computing the overshoot distance of the modeled plumes, and a semi-analytical model by using the empirical model for plume temperature. By using a nonlinear profile for the lapse rate in the surface layer based on the Monin–Obukhov similarity theory, our model predicts that the characteristics of the surface layer plays an important role in the structure of the entrainment zone. Finally, our solutions for plume velocity allow us to consider the effect of the lateral entrainment on the plume excess temperature and velocity in the convective boundary layer. It is shown that the lateral entrainment has an important role on the plume dynamics and the solutions in the zero entrainment limit offer large overestimated values for the plume velocity, which also result in overestimated values of the entrainment zone thickness. |
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| Keywords: | Analytical model Convective boundary layer Convective rolls Entrainment zone thickness Thermal plume |
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