The effect of density gradient on boundary flow
The effect of density gradient on boundary flow
复制标题
密度梯度对边界流的影响
DOI：
10.1016/j.ecss.2016.10.025
复制
发表时间：
2016-12
期刊：
影响因子：
--
通讯作者：
Hu Di
中科院分区：
文献类型：
--
作者：
Chen Cheng;Guo Fei;Zhang Dong;Hu Di
基于Prandtl的混合长度理论，本文提出了非分层和稳定分层流动中水平浮力梯度恒定的强迫作用下速度剖面的新理论公式。基于一维水柱动量方程，发现垂直湍流剪应力剖面偏离线性分布，服从抛物线分布，与中性水流不同。剪切应力随电流沿密度梯度向上弯曲，随电流与密度梯度相反而向下弯曲。对于恒定的涡动粘性，众所周知的河口环流是通过抛物线切变分布得到的。对于垂直抛物型涡粘性，得到了Burchard&Hetland(2010)新提出的速度分布。本文根据Prandtl的混合长度理论估算了粘性分布，并导出了新的速度分布公式。通过与数值湍流模型的比较，本文给出的速度分布与数值结果吻合较好。此外，新的速度剖面还可用于确定斜压边界流测井拟合的有效范围和评定误差。
Based on Prandtl's mixing-length theory, this study proposes new theoretical formulae of velocity profiles resulting from the forcing by a constant horizontal buoyancy gradient in unstratified and stably stratified flows. Based on the one-dimensional water column momentum equation, the vertical turbulent shearing stress profile is found to deviate from a linear distribution and follow a parabolic distribution, differing from that in neutral flow. The shearing stress curves upward with the current following the density gradient, and curves downward with the currents opposite to the density gradient. For a constant eddy viscosity, the well-known estuarine circulation is obtained through the parabolic shearing distribution. For a vertically parabolic eddy viscosity, the new-proposed velocity profile by Burchard & Hetland (2010) is obtained. In this paper, we estimate the viscosity profile based on Prandtl's mixing-length theory and then derive the new formulae of the velocity profiles. Through comparison with the numerical turbulence model, the velocity profiles presented in the paper agree well with the numerical results. In addition, the new velocity profiles can be applied to determine the valid range and evaluate errors of the log-fit in baroclinic boundary flows.
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