Estimates of the Manning's coefficient for ice-covered rivers

Abstract

The management of ice-covered rivers presents special issues with respect to planning, design and operation of a water resources project. To address these issues properly entails a good understanding of the hydraulics of icecovered rivers, where the composite Manning's coefficient is a fundamental parameter. The aim of this paper is to obtain field estimates of the composite coefficient associated with the ice cover and riverbed. Using four different methods, this paper analyses a large volume of winter measurements of water velocities made from shallow icecovered rivers in Canada. The results show that the composite Manning's coefficient ranges from 0 . 013 to 0 . 040 as winter averages, but can vary up to seven-fold through the winter. The slope of the energy grade line is difficult to measure in the field and thus is rarely available; it appears to be about 30% of the water slope. The method for determining the coefficient based on the logarithmic velocity distribution fitted to measurements has shown advantages, as revealed by comparing the results of the four methods. The estimates of the composite Manning's coefficient reported in this paper are useful for modelling ice-covered river flow and determining winter discharges. This is particularly true when site-specific data are unavailable. Notation a slope of a semi-log velocity profile b intercept of a semi-log velocity profile (m/s) g gravity (m/s 2 ) J total number of subsections across the channel width j index for subsection k s average roughness height of the ice underside (m) n i ice Manning's coefficient corresponding to an individual velocity profile n c ice Manning's coefficient for the entire cross-section n b bed Manning's coefficient n o composite Manning's coefficient associated with the ice and riverbed P i wetted perimeter of an individual subsection (m) R hydraulic radius of the ice-affected layer (m) Re Reynolds number R h hydraulic radius of a river section (m) S slope of the energy grade line (m/m) s water slope (m/m) V cross-sectionally averaged velocity (m/s) v velocity at a given depth (m/s) v i depth-averaged velocity of the ice-affected layer (m/s) v m maximum velocity of a velocity profile (m/s) v* friction velocity (m/s) x cross-channel distance (m) Y local flow depth (m) y depth below the ice underside (m) y i thickness of the ice-affected layer (m) å ratio of the energy-grade-line slope to water slope k Karman constant í kinematic viscosity of water (m 2 /s)

Momentum, Energy and Drag Coefficients for Ice‐covered Rivers

“…The hydraulic parameters include the energy coefficient, α , and the momentum coefficient, β (Chow, ), which are needed for predictions of (one‐dimensional) cross‐sectionally averaged flow, the Manning's coefficient, n , or equivalent resistance coefficients, which are required for predictions of (two‐dimensional) depth‐averaged flow, and the drag coefficient, C D (Wu, ) for predictions of fully three‐dimensional flow. Discussion of the Manning's n for ice‐covered rivers can be found in Larsen (), Calkins () and Li (). The purpose of this study is to obtain good estimates of α , β and C D , which are not available from previous studies of ice‐covered river flows.…”

Discussion: Estimates of the Manning's coefficient for ice-covered rivers

“…However, the author meant to deal with the flow field in a relatively short channel section, not the reach-scale flow field. In the former case, the assumption of uniform flow would be acceptable, taking into consideration the relatively simple hydraulic and geometric conditions described in the second paragraph of section 2 in Li (2012).…”

“…The use of reported Manning's n values for flow modelling (based on the Saint-Venant equations) would be appropriate if the river channel of interest has basic hydraulic parameters within the range of values given in Table 1 of Li (2012) and is under similar field conditions as described in the second paragraph of section 2 of Li (2012). For modelling one-dimensional ice-covered river flow, the composite Manning's n ranging between 0 .…”

“…04 may be used to calculate flow resistance distributed along the channel length. For modelling two-dimensional flow, the results shown in Figure 5 of Li (2012) may be used to derive crosschannel distribution of ice Manning's n, in addition to alongchannel distribution. Neill and Andres (1984) presented an interesting case of icecovered river flow, in which the basic hydraulic parameters appear to be outside the range of values given in Table 1 of Li (2012) and the field conditions (slush, ice floes and very large ice thickness) are complicated in comparison with those described in section 2 of Li (2012).…”

Non-iterative design method for flexible channels with bends

“…The American Association of State Highway and Transportation Officials (Aashto) states that the type of lining should be consistent with the degree of protection required, overall cost, safety requirements and aesthetic considerations (Aashto, 2007). Besides channel lining design, a number of related design aspects have been addressed in the literature, including the direct design of grass-lined and stable channels (Easa and Vatankhah, 2012;Easa et al, 2011), estimation of Manning roughness (Li, 2012;Neill, 2012), reliability analysis (Adarsh and Sahana, 2013;Easa, 1992Easa, , 1994, and evaluation of riprap performance (Cardoso et al, 2010;Martín-Vide et al, 2010).…”