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

Abstract

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. This technique 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.This article is categorized under: Science of Water > Methods Science of Water > Hydrological Processes