一种三次多项式湍黏性底边界层的流场分布

The velocity distribution of a cubic polynomial form turbulent eddy viscosity in bottom boundary layer

本文通过假定底边界层湍黏性的三次多项式参数化形式,基于简化的Navier–Stokes方程,并利用超几何方程的性质,推导出了湍流粗糙底边界层的速度解析解。同时,得到了底边界层内其他的动力参数,如底剪应力、Ekman传输、Ekman抽吸及近底部速度分布场,从理论上讨论了均匀混合底边界层特征量分布特征。通过数值结果分析,进一步得出底边界层的总速度、亏损速度及其剪应力受平均流的角频率和地球自转影响比较大;而底边界层的动力结构对于底边界层顶部粗糙度不敏感。该涡黏性模式从理论上丰富了底边界层涡黏性的形式,为底边界层的动力系统研究提供了借鉴和理论参考。

The analytical solutions for the velocity distribution within the turbulent bottom boundary layer BBL are deduced by supposing an eddy viscosity of cubic polynomial form. Based on the simplified Navior-Stokes equations, the property of the hypergeometric function is used to this model. Moreover, other dynamic parameters of BBL are also obtained, such as the bottom shear stress, the Ekman transport, Ekman pumping and the velocity fields near the bottom. Thus the dynamic characteristics of well-mixed turbulent bottom boundary are discussed theoretically. Furthermore, numerical results show that the total velocity profile, Ekman velocity and shear stress are sensitive to the ratio of the tidal frequency and the Coriolis parameter, but are less influenced by the strength of capping in BBL. The mode will provide valuable information for how to select the eddy viscosity forms in the BBL theoretically and provide theoretical references for the dynamics in the BBL.