| Abstract: | Lawrence argued that the inundation ratio Λ, defined as the mean flow depth d divided by the roughness height k, is the dominant control of flow resistance f and should be used as the primary variable when evaluating the hydraulics of overland flow on rough surfaces. Lawrence defined three flow regimes on the basis of Λ and developed an expression for f in terms of Λ for each regime. Common sense, however, suggests that f is independent of Λ where Λ < 1 because when roughness elements protrude through the flow, the value of f for the flow is the same regardless of the height of the elements. The error appears to have crept in as a result of Lawrence's representation of roughness elements by hemispheres. Lawrence found that f ∝ d/k, which she interpreted to mean f ∝ Λ. However, in her model the length dimension denoted by k is in fact half the breadth b/2 of the roughness elements. The distinction between k and b/2 is important, especially for roughness elements where k ≠ b/2. Thus, contrary to Lawrence's claim, f is not generally a function of Λ. Instead, f is a function of Λ only where Λ > 1. Where Λ < 1, f is a function of d/(b/2) or d/b. © 1998 John Wiley & Sons, Ltd. |
