This paper investigates global integrals of the volumetric, momentum and temperature fluxes for turbulent natural convection over a vertical plate (TNCVP). The global integral of the mean continuity equation gives a relation for the mean wall-normal velocity outside the boundary layer as W_∞ = − d(∫₀^∞Udz)/dx where U is the mean velocity in the streamwise x direction and z is the wall-normal direction. The global integral of the mean momentum equation gives a relation for the specific wall momentum flux as u_τ² = gβ∫₀^∞(Θ_∞ − Θ)dz − d(∫₀^∞U²dz)/dx where u_τ is the friction velocity, g is the gravitational acceleration and β is the thermal expansion coefficient. Θ = T_w − T is the difference between the wall temperature T_w and the fluid temperature, and Θ_∞ = T_w − T_∞ is the difference between the wall temperature and the ambient fluid temperature. Finally, the global integral of the mean heat equation gives a relation for the wall temperature flux as u_τθ_τ = − W_∞Θ_∞ − d(∫₀^∞UΘdz)/dx where θ_τ is the frictional temperature. Based on the global integrals of the momentum and heat fluxes, we propose an indirect determination of u_τ and θ_τ. Given the extreme challenge in direct measurement of u_τ and θ_τ in wall-bounded turbulent flows, the indirect determination proposed here offers a powerful tool to subsequent experimental studies of TNCVP.

本文研究了垂直板（TNCVP）上湍流自然对流的体积，动量和温度通量的整体积分。平均连续性方程的全局积分给出了平均壁正常速度边界层作为外部的关系W¯¯ _∞  = -  d（∫ ₀ ^∞ UDZ）/ DX其中ü是在流向平均速度X方向和ž是墙法线方向。平均动量方程的全局积分给出了特定壁动量通量的关系作为Ù _τ ²  =  Gβ ∫ ₀ ^∞（Θ _∞  - Θ）DZ  -  d（∫ ₀ ^∞ Ù ² DZ）/ DX其中Ú _τ为摩擦流速，克为重力加速度和β是热膨胀系数。Θ=  Ť_瓦特 -  Ť是壁温度之间的差Ť_瓦特和流体温度，并且Θ _∞  =  Ť_瓦特 -  Ť _∞是壁温和环境流体温度之间的差。最后，平均热传导方程的全球积分给出了壁温磁通的关系作为ü _τ θ _τ  = -  w ^ _∞ Θ _∞  -  d（∫ ₀ ^∞ Ù Θ DZ）/ DX其中θ _τ是摩擦温度。基于动量和热通量的全球积分，我们提出的间接测定ü _τ和θ _τ。鉴于在直接测量的极限挑战ü _τ和θ _τ在界壁的紊流，这里提出了间接测定提供了一个强大的工具，TNCVP随后的实验研究。