RESEARCH ARTICLE


A Harbor Resonance Numerical Model with Reflecting, Absorbing and Transmitting Boundaries



Yansheng Chang1, Edward H. Wang2, *
1 College of Civil Engineering, Putian University, Fujian, China
2 Department of Civil Engineering and Environmental Informatics, Minghsin University of Science and Technology Hsin-Chu, Taiwan


© 2017 Chang and Wang.

open-access license: This is an open access article distributed under the terms of the Creative Commons Attribution 4.0 International Public License (CC-BY 4.0), a copy of which is available at: https://creativecommons.org/licenses/by/4.0/legalcode. This license permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.

* Address correspondence to this author at the Department of Civil Engineering and Environmental Informatics, Minghsin University of Science and Technology, No. 1 Hsin-Hsin Rd, Hsin-Fong, Hsin-Chu County, Taiwan 304; Tel: +886-3-5593142, ext 3315; Fax: +886-3-5573718; E-mail: edwang313@gmail.com


Abstract

Background:

A very important aspect in the planning and design of a harbor is to determine the response of the harbor basin to incident waves. Many previous investigators have studied various aspects of the harbor resonance problem, though correct to a certain extent, have some disadvantages.

Objective:

To calculate wave response in an offshore or coastal harbor of arbitrary shape, this research develops a two-dimensional linear, inviscid, dispersive, hybrid finite element harbor resonance model using conservation of energy approach. Based on the mild-slope wave equation, the numerical model includes wave refraction, diffraction, and reflection. The model also incorporates the effects of variable bathymetry, bottom friction, variable, full or partial absorbing boundaries, and wave transmission through permeable breakwaters.

Methods:

Based on the mild-slope wave equation, the numerical model includes wave refraction, diffraction, and reflection. The model also incorporates the effects of variable bathymetry, bottom friction, variable, full or partial absorbing boundaries, and wave transmission through permeable breakwaters. The Galerkin finite element method is used to solve the functional which was obtained using the governing equations. This model solves both long-waves as well as short-wave problems. The accuracy and efficiency of the present model are verified by comparing different cases of rectangular harbor numerical results with analytical and experimental results.

Results:

There said results indicate that reduction in wave amplitude inside a harbor caused by energy dissipation due to water depth, linearly sloping bottom, and bottom friction is quite small for a deep harbor. But for a shallow harbor, these factors are critical. They also show that reduction in wave amplitude inside a harbor due to boundary absorption, permeable transmission, harbor entrance width, and horizontal dimensions.

Conclusion:

Those factors are very important for both deep and shallow harbors as proven by accurate agreement with the prediction of this numerical model. The model presented herein is a realistic method for solving harbor resonance problems.

Keywords: Harbor resonance, Mild-slope wave equation, Conservation of energy, Variable depth, Bottom friction, Absorbing and transmitting boundaries.