The energy gradient is a fundamental physical quantity of flow motion. To date, many studies have concentrated on uniform flow or fully developed curved flow, with the energy gradient approximated as the bed slope. This paper presents a new method to assess the lateral distribution of the apparent energy gradient in curved channels when curved flow is not fully developed. A dimensionless apparent energy gradient (K) is presented. An expression for K is explicitly formulated based on the Reynolds-averaged Navier–Stokes (RANS) equations and the lateral distribution of K is derived from measured velocity data. The method was applied in a 120° curved flume with asymmetric trapezoidal cross-sections. The results showed a bilinear distribution of K; that is, K remained nearly constant in the central region of the channel while, in the inner bank region, K increased linearly as the inner bank was approached. These results were derived for specific cases for curved channels with a side-slope, but the method for deriving K can be applied to other cases, thus providing a new way to study energy loss in curved channels to contribute to river management, such as estimation of discharge capacity and navigation improvement.

中文翻译：

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一种评估弯道能量梯度横向分布的新方法

能量梯度是流动运动的基本物理量。迄今为止，许多研究都集中在均匀流或完全发展的弯曲流上，能量梯度近似为床层斜率。本文提出了一种新的方法，当弯曲流没有完全展开时，可以评估弯曲通道中视在能量梯度的横向分布。提出了无量纲的视在能量梯度（K）。根据雷诺平均Navier-Stokes（RANS）方程显式制定K的表达式，并从测得的速度数据中得出K的横向分布。该方法应用于具有不对称梯形横截面的120°弯曲槽中。结果表明K的双线性分布; 也就是说，在通道的中央区域，K几乎保持恒定，而在内部堤岸区域，随着接近内部堤岸，K呈线性增加。这些结果是针对具有边坡的弯曲河道的特定情况得出的，但是推导K的方法可以应用于其他情况，从而为研究弯曲河道的能量损失以有助于河流管理提供了一种新方法，例如估算容量和航行改善。