Hydraulic resistance in overland flow during partial and marginal surface inundation: Experimental observations and modeling

Abstract

Abstract. Hydraulic resistance as a function of surface roughness inundation was evaluated in a set of experiments designed to simulate overland flow on a rough, granular surface. The data are compared with an additive drag model based on the contribution of individual elements to flow resistance and a mixing length model for estimating bulk flow resistance. During partial inundation of the surface roughness the observed coefficient of drag per element is much higher than for an isolated element, and a model based on element form drag alone underestimates the observed friction. These high resistance values are strongly correlated with the hydrostatic wave drag estimated from the free surface deformation around elements. The mixing length model, incorporating a multiplier setting the hydraulically effective roughness height, reliably reproduces the trends in resistance during marginal inundation. This multiplier is shown to have a value similar to the root-mean-square of the surface height. IntroductionOverland flow is an important mechanism for the surface transport of particulate and dissolved nutrients and contaminants and contributes to surface erosion and, potentially, land degradation in environments where it is an active runoff process. Many physically based and quasi-empirical methods designed to assess transport and erosion processes assume that overland flow hydraulics are well understood and can be readily characterized in terms of simple resistance models. This is, however, not generally the case. During a single storm event, overland flow hydraulics are quite complex because of, in part, the varying contribution of boundary roughness to total flow resistance as a surface is progressively inundated. In many cases, the surface will only be partially or marginally inundated, so that the roughness disrupts the flow throughout its depth and classical boundary layer theory cannot be invoked to model the flow. The moderate Reynolds number of these flows (often of order 100-10, 000) introduces significant variability in the occurrence and interaction of wakes behind roughness elements and, for the case ofRe • 500, further invalidates the assumptions underlying boundary layer approximations. The pronounced distortion of the free surface around and over roughness elements is difficult to model hydrodynamically and also hinders the development of alternative approximate models based on the momentum balance equations. Each of these physical factors may have a significant effect on transport, mixing, and dispersion in the flow as well as on the most suitable form of a hydraulic approximation for characterizing mean flow behavior.Hydraulic approximations are used to estimate mean flow velocity and depth for a given specific discharge over a surface of known roughness. They are required when hydrodynamic modeling is either unfeasible or the data for it are not avail-

A Semi-Analytical Model for the Hydraulic Resistance Due to Macro-Roughnesses of Varying Shapes and Densities

“…This result makes our model equivalent to other approaches for this type of roughness element with low confinement (h/k > 10) [20,34,35].…”

“…The data from [20] (Figure 5) show the continuity of the model since it works for the emergent (h/k < 1), partially, and completely submerged cases even though each behavior is modeled differently ( [20]). Compared with the model proposed by [20], where C d is adjusted using an experimental correlation, we obtain a change in f for the emergent case based on the functions f h * (h * ) and f F (F).…”

“…For a given shape of roughness element, D is assumed to be constant and we therefore assume that its change will be taken into account in the value of C d0 ( Figure 7). Hence, for the same diameter used in the model, the frontal area of the circular cylinder [17] is greater than that of the hemisphere [20], which is itself greater than that of the truncated cone [24]. To a first approximation, the value for ellipsoidal shape appears to correspond to several "cobble" forms of bed roughness element, and it will be taken as the reference for "natural" beds in the remainder of this article.…”

“…Moreover, the friction model is not only available for flow above vegetation [2,6,13] but also for rock, gravel, and sand beds. To illustrate the ability of the model for various hydraulic conditions, it is applied to experiments that provide the stage-discharge relationship for steep mountains stream [18,19], for flood plains [20], for prediction of the biological response to management actions [21,22], or for river restoration [1].…”

“…The values of C d0 are 0.7 using the data from [20] obtained from hemispheres and 0.3 using the data from [24] obtained from truncated cones.…”