Abstract
Accurate estimation of head loss introduced via randomly placed roughness elements found in natural or constructed streams (e.g., fish passages) is essential in order to estimate flow variables in mountain streams, understand formation of niches for aquatic life, and model flow structure. Owing to the complexity of the involved processes and the often missing detailed data regarding the roughness elements, the head loss in such streams is mostly approximated using empirical models. In our study, we utilize flume experiments to analyze the effects of the spatial distribution of roughness elements on water surface levels and head loss and, moreover, use the produced data to test three empirical models estimating head loss. The experiments were performed in a 15 m long, 0.9 m wide flume with a slope of 5% under large Froude numbers (2.5–2.8). Flow velocities and water levels were measured with different flow rates at 58 points within a 3.96 m test section of the flume. We could show that different randomly arranged patterns of roughness elements significantly affected head loss (differences up to 33.6%), whereas water jumps occurred when flow depths were in the same size range as the roughness elements. The roughness element position and its size influenced water surface profiles. None of the three tested empirical models were able to well reproduce the differences in head loss due to the different patterns of roughness elements, with overestimated head loss from 12 to 94.7%, R2 from 41 to 73%, NSE from −21.1 to 0.09, and RRMSE from 18.4 to 93%. This generally indicates that these empirical models are conditionally suitable to consider head loss effects of random patterns of roughness elements.
Highlights
The spatio-temporal dynamics of the flow depths and velocities in mountainous streams are influenced by cobbles, boulders, and step pools
In the Pagliaria and Chincacinin [23] model: (i) fi is a function of cluster density alone and the model does not address the effects of the approaching flow (Froude number and relative submergence); (ii) it assumes constant empirical coefficients for any random pattern of roughness elements; and (iii) hemispherical roughness elements were used in the study
Model: (iv) the semi-analytical model is originally developed for the staggered pattern with uniform size roughness elements, where the present study focused on non-uniform size random patterns; and (v) both studies considered sub and superficial flows for the model development, Froude number (Fu) : 0.14–1.8 [27] and Fu : 0.8–2.8 [23]. (vi) λ, Fu of Cassan et al [27]
Summary
The spatio-temporal dynamics of the flow depths and velocities in mountainous streams are influenced by cobbles, boulders, and step pools. The cobbles, boulders, and step pools cause head loss along the stream flow pathway [1,2,3,4,5], and understanding the spatio-temporal flow dynamics is essential for modelling [6]. The Mannings and Darcy–Weisbach models are generally used for estimating head loss in open-channel flows. These models cannot be used when vortices formed in the wake region of macro-roughness elements [18,19].
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