Estimation of wave run-up on smooth, impermeable slopes using the wave momentum flux parameter

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Received 23 April 2003; received in revised form 29 June 2004; accepted 16 July 2004

Available online 3 October 2004

Abstract

This paper re-examines existing wave run-up data for regular, irregular and solitary waves on smooth, impermeable plane

slopes. A simple physical argument is used to derive a new wave run-up equation in terms of a dimensionless wave parameter

representing the maximum, depth-integrated momentum flux in a wave as it reaches the toe of the structure slope. This

parameter is a physically relevant descriptor of wave forcing having units of force. The goal of the study was to provide an

estimation technique that was as good as existing formulas for breaking wave run-up and better at estimating nonbreaking wave

run-up. For irregular waves breaking on the slope, a single formula for the 2% run-up elevation proved sufficient for all slopes

in the range 2/3VtanaV1/30. A slightly different formula is given for nonbreaking wave run-up. In addition, two new equations

for breaking and nonbreaking solitary maximum wave run-up on smooth, impermeable plane slopes are presented in terms of

the wave momentum flux parameter for solitary waves. This illustrates the utility of the wave momentum flux parameter for

nonperiodic waves.

Keywords: Coastal structures; Impermeable slopes; Iribarren number; Irregular wave run-up; Solitary waves; Solitary wave run-up; Wave

momentum flux; Wave run-up

flooding are related, in part, to wave run-up. Being

1. Introduction

able to estimate maximum wave run-up accurately can

Maximum wave run-up is an important design

lead to more economical design. For example, the

criterion for several types of coastal structures such as

upper limit of expected wave run-up determines the

revetments, breakwaters and dikes. Also, beach

crest elevation of a coastal structure designed to

processes such as beach/dune erosion and storm

prevent wave overtopping. Overestimating maximum

wave run-up could add significant cost to a rubble-

mound breakwater. Below is a sampling of published

papers related to wave run-up on coastal structures to

* Tel.: +1 601 634 2026; fax: +1 601 634 3433.

give an idea of how predictive capability has

E-mail address: Steven.A.Hughes@erdc.usace.army.mil.

doi:10.1016/j.coastaleng.2004.07.026