Hydraulic resistance of vegetation : predictions of average flow velocities based on a rigid-cylinders analogy

River flows can be described in all detail by the Navier-Stokes equation, however, for practical purposes the complexity of the flow description needs to be reduced.The objective of this study is to find an appropriate way of describing the vegetation roughness.For river management purposes floodplain roughness is relevant because it has an effect on water levels.Too much resistance causes high water levels, which increases flood risk.To be able to predict the effect on water levels of future changes in floodplains an appropriate independent predictor is required.In this study we compared existing and a newly developed descriptor for vegetation roughness on their performance under different conditions.Based on this analyses the most appropriate description of vegetation resistance is deduced for different conditions.The Chzy or Manning equations are commonly used to describe steady uniform flows and the associated flow resistance in open channels (e.g.rivers).Although these two equations are fundamentally different, they behave similar when the relative flow depth (R/k) is large.A stronger theoretical foundation is often attributed to the Chzy equation and the Manning equation is usually considered to be entirely empirical.However, Gioia and Bombardelli (2002) showed that the Manning/Strickler equation can be derived theoretically based on (i) a force balance between gravitational pull and bottom shear stress and (ii) a relation between small scale velocities and the mean velocity that includes relative roughness.Another requirement in the derivation is that flow is hydraulically rough.In general river flows can be considered hydraulically rough, which justifies the application of the Manning equation.In chapter 2 it was pointed out that for flow over a flat (rough) surface the Manning coefficient is a true measure of wall roughness, while the Chzy coefficient is inversely related to the roughness via the White-Colebrook relation.The appearance of the hydraulic radius in this formula complicates the applicability of Chzy for complicated river geometries, e.g. when the calculation of a composite roughness for compound channels is desired.Therefore, it is easier to construct a composite resistance parameter based on addition of Manning coefficients instead of Chzy coefficients.The resultant composite Manning coefficient is no longer a measure of wall resistance only, but also depends on depth variations.Even if the material of the bounding wall is the same everywhere, then the composite resistance parameter is depth-dependent.Therefore, if field measurements indicate that hydraulic resistance is depth-dependent, this does not necessarily imply that wall-roughness or friction is complicated.It could also be the result of the cross-section geometry.In chapters 3 and 4 two different descriptions for the hydraulic resistance of vegetation are put forward.The principal assumption in both of these methods is that separate plants may be treated as rigid cylinders (i.e. the rigid cylinder analogy).Because the Manning and Chzy coefficients are typically associated with flows affected by wall roughness, flow resistance caused by rigid cylinders is described in terms of resulting average flow velocities.For the situation of submerged vegetation, the flow field can be divided in flow over the vegetation, the surface layer, and flow through the vegetation, the vegetation layer.Klopstra et al. (1997) derived an analytical solution for the velocity profile for this case, which is the topic of chapter 3. Originally the turbulent characteristics in this description were not treated consistently and the necessary turbulent length scale was described empirically.Therefore, the same data as used by Klopstra et al. (1997) was analyzed further to arrive at the following expression for average velocity (equation numbering refers to numbering in subsequent chapters):Hydraulic resistance of vegetation