Nonlinear run-ups of regular waves on sloping structures

T.-W Hsu,S.-J Liang,B.-D Young,S.-H Ou

doi:10.5194/nhess-12-3811-2012

Abstract

Abstract. For coastal risk mapping, it is extremely important to accurately predict wave run-ups since they influence overtopping calculations; however, nonlinear run-ups of regular waves on sloping structures are still not accurately modeled. We report the development of a high-order numerical model for regular waves based on the second-order nonlinear Boussinesq equations (BEs) derived by Wei et al. (1995). We calculated 160 cases of wave run-ups of nonlinear regular waves over various slope structures. Laboratory experiments were conducted in a wave flume for regular waves propagating over three plane slopes: tan α =1/5, 1/4, and 1/3. The numerical results, laboratory observations, as well as previous datasets were in good agreement. We have also proposed an empirical formula of the relative run-up in terms of two parameters: the Iribarren number ξ and sloping structures tan α. The prediction capability of the proposed formula was tested using previous data covering the range ξ ≤ 3 and 1/5 ≤ tan α ≤ 1/2 and found to be acceptable. Our study serves as a stepping stone to investigate run-up predictions for irregular waves and more complex geometries of coastal structures.

Highlights

As a wave propagates toward relatively shallow water prior to breaking, a part of its energy is dissipated on the slope of shore structures or on beaches
For regular waves breaking on a sloping beach, the dimensionless equation for the maximum run-up Ru is given by Ru/√H = ξ ; here ξ is the Iribarren number defined as ξ = tan α/ H /L0 (e.g., Battjes, 1974), where L0 is the wavelength for the deep water condition
The design formula for estimation run-ups of regular waves is given in the Shore Protection Manual (SPM) (1984), in which some extensions have been made based on a reanalysis

Summary

Introduction

As a wave propagates toward relatively shallow water prior to breaking, a part of its energy is dissipated on the slope of shore structures or on beaches. For regular waves breaking on a sloping beach, the dimensionless equation for the maximum run-up Ru is given by Ru/√H = ξ ; here ξ is the Iribarren number defined as ξ = tan α/ H /L0 (e.g., Battjes, 1974), where L0 is the wavelength for the deep water condition. Hughes (2004) re-examined wave run-up data for regular, irregular, and solitary waves breaking on smooth impermeable plane slopes Numerical results obtained from a series of calculations for regular wave run-ups on a slope from a seawall were obtained, and empirical equations were derived by regression analysis for practical applications. The present paper provides limited but useful information that may be valuable and serve as a stepping stone to investigate run-up predictions for irregular wave run-ups on both plane and more complex sloping structures

Governing equations and numerical method

Laboratory experiments

Results and discussions

Findings

Conclusions