ABSTRACT

A simple diagnostic narrow channel shallow water model for the cross-channel distribution of the depth average velocity is developed. It is diagnostic, because the slope of the stream-wise free surface is specified and it models the cross-channel distribution of the depth average velocity without any knowledge of the velocity field. A non-dimensional parameter that encapsulates the channel dimensions and the relative importance of bottom friction to horizontal eddy viscosity is defined. Numerical solutions for the cross-channel distribution of the depth average velocity are obtained using values of this non-dimensional parameter for different cross-channel topographies. Numerical solutions for the depth average velocity are in turn used to find the cross-channel distribution for secondary flow and vertical velocity. Two-dimensional distributions of the vertical velocity in the n–z-plane show that changes in topography dominate the vertical velocity distribution. Three-dimensional tracers in a hypothetical open channel using scaling values from geophysical observations show that secondary circulation has a loose helical flow pattern of approximately one full rotation for every ${360}^{\circ }$${360}^{\circ }$ of curvature. It is not unreasonable to suggest that this 1:1 relationship describes the looseness of secondary circulation in geophysical data.

摘要

一个简单的诊断窄通道浅水模型针对跨通道分布的深度平均速度进行了开发。这是诊断性的，因为指定了流向自由表面的斜率，并且它在不了解速度场的情况下对深度平均速度的跨通道分布进行了建模。定义了一个无量纲参数，该参数封装了通道尺寸以及底部摩擦对水平涡流粘度的相对重要性。对于不同的跨通道地形，使用该无量纲参数的值可获得深度平均速度的跨通道分布的数值解。深度平均速度的数值解又被用于寻找二次流和垂直速度的跨通道分布。垂直速度的二维分布n – z平面表明，地形变化控制着垂直速度分布。假设的明渠中的三维示踪剂使用地球物理观测的标度值显示，二次循环的松散螺旋流模式大约为每转一圈${360}^{\circ }$${360}^{\circ }$曲率。建议这一1：1关系描述地球物理数据中二次循环的松动并不是没有道理的。