An analytical model of wave overtopping flow velocities on dike crests and landward slopes

Abstract

A B S T R A C TAn accurate description of the maximum flow velocity across flood-protective structures is necessary in order to determine the stability of the landward slope and the amount of cover erosion. In this paper, two new formulas are derived to describe the change in the maximum overtopping flow velocity along the dike crest and the adjacent landward slope. These formulas are coupled in an effort to accurately predict the velocities in wave overtopping events. This analytical model is validated using 244 data points from flume tests and 300 data points from field tests on river dikes in the Netherlands. The modelled flow velocity shows good agreement with the measured flow velocity, with a Nash-Sutcliffe efficiency factor varying from 0.49 to 0.87. Also, the derived formulas are compared with existing formulas for wave overtopping flow velocities and overall showed a better performance for a wide range of geometries and covers.

Flow Depths and Velocities across a Smooth Dike Crest

“…The decay of h is strictly dependent on the crest freeboard, varying approximately between the 20% and the 35% for over-washed (R c /H s = −1.5) and for emerged (R c /H s = 1.5) conditions respectively. To account for the effect of R c /H s , a new coefficient c 3 for the decay formulation of h was proposed in Equation (10). For submerged dikes (R c < 0 and wet landward conditions), the decay of h is almost negligible.…”

“…Recently, a new analytical model [10] was proposed to describe the evolution of the maximum flow velocities (U) on the dike crest and landward slope. The model consists of two coupled formulae to be applied in sequence for the dike crest and the landward slope, respectively.…”

“…, R c > 0 (10) where based on the "momentary discharge Q;" i.e., the discharge calculated at the instant of occurrence of the maximum flow velocity U. The approach by article [10] gives also a formulation for the evolution of the "momentary layer thickness", h U , derived from the continuity equation of Q, but no validation is given for this formula. So far, no predicting method exists for the evolution of h and u in case of R c < 0.…”

“…Both h and u exponentially decay along the dike crest due to frictional losses and overtopping volume deformation [9]. Recently, an analytical model to predict h and u along the dike crest and the landward slope, offering two new decay functions for h and u over the crest, was proposed by Van Bergeijk et al [10]. Both the studies [9,10] indicate that the entity of the decay increases with increasing the roughness and the width of the dike crest.…”

Overtopping Metrics and Coastal Safety: A Case of Study from the Catalan Coast

“…There is already plenty of literature dealing with the estimation of overtopping flow parameters [10], [15], [16]. The equations for overtopping flow depth and velocity at the dike crest can be expressed in a general form as follows:…”