Hydraulic resistance to overland flow on surfaces with partially submerged vegetation

Abstract

This study investigates numerically the characteristics of upscaling the Manning resistance coefficient (nt) for areas covered by partially submerged vegetation elements, such as shrub or tree stems. A number of high‐resolution hydrodynamic simulations were carried out corresponding to scenarios with different domain slopes (S), inflow rates (Q), bed roughness (nb), and vegetation cover fractions (Vf). Using simulations performed at fine space‐time scales, two methods were developed for computing the upscaled Manning coefficient, termed “Equivalent Roughness Surface (ERS)” and “Equivalent Friction Slope (EFS).” Results obtained with these two methods indicate that both yield highly correlated estimates of nt. The effects of four independent variables (Vf, S, Q, and nb) on nt were further investigated. First, as Vf increases, nt also grows. Second, two distinct modes of the relationship between S and nt for a fixed Vf and Q emerge: a positive dependence at low‐flow rates and a negative dependence at high‐flow rates. For a fixed Vf and S, two distinct modes of the relationship between Q and nt are also identified: a positive dependence at mild domain slopes and a negative dependence at steep slopes. A regression analysis shows that the two conflicting trends can occur depending on whether the variability of flow depth with respect to S (or Q) is greater than the ratio of h and S (or Q). Third, a rougher soil bed (i.e., larger values of nb) implies a higher resistance due to vegetation. Last, the study argues that nt increases as h increases and decreases as V increases. A generic regression relation that includes all four of the above variables and the difference nt − nb (i.e., the additional resistance due to partially submerged vegetation representing the sum of the form and wave resistances) was developed. The range of applicability of this relation is given by the following conditions: Vf ≤ 0.5, 0.1 ≤ S ≤ 1.1, and 0.0001 ≤ Q ≤ 0.01. The difference nt − nb computed from the developed regression relation was compared with estimates reported by five different studies. Furthermore, the simulated wave resistance coefficients were compared with those predicted from an equation in a previous study; the estimates were consistent in the range of experimental conditions for which the latter equation was developed. The relationship is sufficiently general and applicable to other flow conditions with partially submerged roughness elements.