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Buoyancy Effects in the Turbulence Kinetic Energy Budget and Reynolds Stress Budget for a Katabatic Jet over a Steep Alpine Slope
Boundary-Layer Meteorology ( IF 4.3 ) Pub Date : 2020-08-11 , DOI: 10.1007/s10546-020-00549-2
Claudine Charrondière , Christophe Brun , Jean-Emmanuel Sicart , Jean-Martial Cohard , Romain Biron , Sébastien Blein

Katabatic winds are very frequent but poorly understood or simulated over steep slopes. This study focuses on a katabatic jet above a steep alpine slope. We assess the buoyancy terms in both the turbulence kinetic energy (TKE) and the Reynolds shear-stress budget equations. We specifically focus on the contribution of the slope-normal and along-slope turbulent sensible heat fluxes to these terms. Four levels of measurements below and above the maximum wind-speed height enable analysis of the buoyancy effect along the vertical profile as follow: (i) buoyancy tends to destroy TKE, as expected in stable conditions, and the turbulent momentum flux in the inner-layer region of the jet below the maximum wind-speed height zj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_j$$\end{document}; (ii) results also suggest buoyancy contributes to the production of TKE in the outer-layer shear region of the jet (well above zj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_j$$\end{document}) while consumption of the turbulent momentum flux is observed in the same region; (iii) In the region around the maximum wind speed where mechanical shear production is marginal, buoyancy tends to destroy TKE and our results suggest it tends to increase the momentum flux. The present study also provides an analytical condition for the limit between production and consumption of the turbulent momentum flux due to buoyancy as a function of the slope angle, similar to the condition already proposed for TKE. We reintroduce the stress Richardson number, which is the equivalent of the flux Richardson number for the Reynolds shear-stress budget. We point out that the flux Richardson number and the stress Richardson number are complementary stability parameters for characterizing the katabatic flow apart from the region around the maximum wind-speed height.

中文翻译:

湍流动能收支和雷诺应力收支的浮力效应在陡峭的高山斜坡上消散射流

衰减风非常频繁,但在陡坡上却知之甚少或模拟得很少。这项研究的重点是陡峭的高山斜坡上方的下降气流。我们评估了湍流动能 (TKE) 和雷诺剪应力预算方程中的浮力项。我们特别关注斜坡法向和沿斜坡湍流感热通量对这些项的贡献。低于和高于最大风速高度的四个级别的测量能够分析沿垂直剖面的浮力效应,如下所示:(i) 浮力往往会破坏 TKE,正如在稳定条件下所预期的那样,以及最大风速高度以下的喷流内层区域的湍流动量通量 zj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_j$$\end{document}; (ii) 结果还表明浮力有助于在喷流的外层剪切区域产生 TKE(远高于 zj\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$z_j$$\end{document}) 而消费在同一区域观察到湍流动量通量;(iii) 在最大风速附近,机械剪切产生的边缘区域,浮力往往会破坏 TKE,我们的结果表明它往往会增加动量通量。本研究还提供了由于浮力作为倾斜角的函数而产生的湍流动量通量的产生和消耗之间的限制的分析条件,类似于已经为 TKE 提出的条件。我们重新引入应力理查森数,它相当于雷诺剪应力预算的通量理查森数。我们指出,通量理查森数和应力理查森数是表征除最大风速高度附近区域外的衰减流的互补稳定性参数。浮力往往会破坏 TKE,我们的结果表明它往往会增加动量通量。本研究还提供了由于浮力作为倾斜角的函数而产生的湍流动量通量的产生和消耗之间的限制的分析条件,类似于已经为 TKE 提出的条件。我们重新引入应力理查森数,它相当于雷诺剪应力预算的通量理查森数。我们指出,通量理查森数和应力理查森数是表征除最大风速高度附近区域外的衰减流的互补稳定性参数。浮力往往会破坏 TKE,我们的结果表明它往往会增加动量通量。本研究还提供了由于浮力作为倾斜角的函数而产生的湍流动量通量的产生和消耗之间的限制的分析条件,类似于已经为 TKE 提出的条件。我们重新引入应力理查森数,它相当于雷诺剪应力预算的通量理查森数。我们指出,通量理查森数和应力理查森数是表征除最大风速高度附近区域外的衰减流的互补稳定性参数。本研究还提供了由于浮力作为倾斜角的函数而产生的湍流动量通量的产生和消耗之间的限制的分析条件,类似于已经为 TKE 提出的条件。我们重新引入应力理查森数,它相当于雷诺剪应力预算的通量理查森数。我们指出,通量理查森数和应力理查森数是表征除最大风速高度附近区域外的衰减流的互补稳定性参数。本研究还提供了由于浮力作为倾斜角的函数而产生的湍流动量通量的产生和消耗之间的限制的分析条件,类似于已经为 TKE 提出的条件。我们重新引入应力理查森数,它相当于雷诺剪应力预算的通量理查森数。我们指出,通量理查森数和应力理查森数是表征除最大风速高度附近区域外的衰减流的互补稳定性参数。
更新日期:2020-08-11
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