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A primer on turbulence in hydrology and hydraulics: The power of dimensional analysis

机译：水文和液压湍流的底漆：维度分析的力量

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摘要

The apparent random swirling motion of water is labeled “turbulence,” which is a pervasive state of the flow in many hydrological and hydraulic transport phenomena. Water flow in a turbulent state can be described by the momentum conservation equations known as the Navier–Stokes (NS) equations. Solving these equations numerically or in some approximated form remains a daunting task in applications involving natural systems thereby prompting interest in alternative approaches. The apparent randomness of swirling motion encodes order that may be profitably used to describe water movement in natural systems. The goal of this primer is to illustrate the use of a technique that links aspects of this ordered state to conveyance and transport laws. Thistechnique is “dimensional analysis”, which can unpack much of the complications associated with turbulence into surprisingly simplified expressions. The use of this technique to describing water movement in streams as well as water vapor movement in the atmosphere is featured. Particular attention is paid to bulk expressions that have received support from a large body of experiments such as flow‐resistance formulae, the Prandtl‐von Karman log‐law describing the mean velocity shape, Monin‐Obukhov similarity theory that corrects the mean velocity shape for thermal stratification, and evaporation from rough surfaces. These applications illustrate how dimensional analysis offers a pragmatic approach to problem solving in sciences and engineering.
机译：水的明显随机旋转运动被标记为“湍流”，这是许多水文和水力运输现象中流动的普遍状态。在湍流状态下的水流可以通过称为Navier -Stokes（NS）方程的动量保护方程来描述。在涉及自然系统的应用中，以数值或某些近似形式求解这些方程仍然是一项艰巨的任务，从而引起了对替代方法的兴趣。旋转运动的明显随机性编码可以利用来描述自然系统中的水运动的顺序。该底漆的目的是说明使用该命令状态方面与运输和运输法联系的技术的使用。 Thistechnique是“维度分析”，它可以将与湍流相关的许多并发症分解为令人惊讶的简化表达式。特征是使用该技术来描述溪流中的水运动以及大气中的水蒸气运动。特别关注大量表达式，这些表达式得到了大量实验的支持，例如流动抗性公式，prandtl -von karman logaw -law描述了平均速度形状，Monin -Obukhov的相似性理论，可纠正平均速度形状的平均速度形状。热分层和粗糙表面蒸发。这些应用程序说明了维度分析如何为科学和工程中的问题解决问题提供务实的方法。

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