scholarly journals An Efficient Two-Layer Non-Hydrostatic Model for Investigating Wave Run-Up Phenomena

Computation ◽  
2019 ◽  
Vol 8 (1) ◽  
pp. 1 ◽  
Author(s):  
Ikha Magdalena ◽  
Novry Erwina
Keyword(s):  
Solitary Waves ◽  
Hydrodynamic Pressure ◽  
Shape Preservation ◽  
Layer System ◽  
Flat Bottom ◽  
Hydrostatic Model ◽  
Run Up ◽  
Set Up ◽  
Volume Method ◽  
Sloping Beach

In this paper, we study the maximum run-up of solitary waves on a sloping beach and over a reef through a non-hydrostatic model. We do a modification on the non-hydrostatic model derived by Stelling and Zijlema. The model is approximated by resolving the vertical fluid depth into two-layer system. In contrast to the two-layer model proposed by Stelling, here, we have a block of a tridiagonal matrix for the hydrodynamic pressure. The equations are then solved by applying a staggered finite volume method with predictor-corrector step. For validation, several test cases are presented. The first test is simulating the propagation of solitary waves over a flat bottom. Good results in amplitude and shape preservation are obtained. Furthermore, run-up simulations are conducted for solitary waves climbing up a sloping beach, following the experimental set-up by Synolakis. In this case, two simulations are performed with solitary waves of small and large amplitude. Again, good agreements are obtained, especially for the prediction of run-up height. Moreover, we validate our numerical scheme for wave run-up simulation over a reef, and the result confirms the experimental data.

Non-Hydrostatic Model for Solitary Waves Passing Through a Porous Structure

2016 ◽  
Vol 11 (5) ◽  
pp. 957-963 ◽  
Author(s):  
Ikha Magdalena ◽  
◽  
Keyword(s):  
Porous Structure ◽  
Solitary Waves ◽  
Hydrodynamic Pressure ◽  
Flat Bottom ◽  
Boussinesq Model ◽  
Free Region ◽  
Hydrostatic Model ◽  
Pass Through ◽  
Predictor Corrector ◽  
Wave Transmission Coefficient

The non-hydrostatic depth-integrated model we developed to study solitary waves passing undisturbed in shape through a porous structure, involves hydrodynamic pressure. The equations are nonlinear, diffusive, and weakly dispersive wave equation for describing solitary wave propagation in a porous medium. We solve the equation numerically using a staggered finite volume with a predictor-corrector method. To demonstrate our non-hydrostatic scheme’s performance, we implement our scheme for simulating solitary waves over a flat bottom in a free region to examine the balance between dispersion and nonlinearity. Our computed waves travel undisturbed in shape as expected. Furthermore, the numerical scheme is used to simulate the solitary waves pass through a porous structure. Results agree well with results of a central finite difference method in space and a fourth-order Runge-Kutta integration technique in time for the Boussinesq model. When we quantitatively compare the wave amplitude reduction from our numerical results to experimental data, we find satisfactory agreement for the wave transmission coefficient.

scholarly journals Can small islands protect nearby coasts from tsunamis? An active experimental design approach

2014 ◽  
Vol 470 (2172) ◽  
pp. 20140575 ◽  
Author(s):  
T. S. Stefanakis ◽  
E. Contal ◽  
N. Vayatis ◽  
F. Dias ◽  
C.E. Synolakis
Keyword(s):  
Coastal Communities ◽  
Physical Parameters ◽  
Small Islands ◽  
Nonlinear Shallow Water Equations ◽  
Run Up ◽  
Set Up ◽  
Sloping Beach ◽  
Focusing Lens ◽  
Selection Of ◽  
Island Slope

Small islands in the vicinity of the mainland are widely believed to offer protection from wind and waves and thus coastal communities have been developed in mainland areas behind small islands. However, whether they offer protection from tsunamis is unclear. Do islands act as natural barriers? Recent post-tsunami survey data, supported by numerical simulations, reveal that the run-up on coastal areas behind small islands was significantly higher than on neighbouring locations not affected by the presence of the islands. To study the conditions of this run-up amplification, we solve numerically the nonlinear shallow water equations. We use the simplified geometry of a conical island sitting on a flat seafloor in front of a uniform sloping beach. By doing so, the experimental set-up is defined by five physical parameters, namely the island slope, the beach slope, the water depth, the distance between the island and the plane beach and the incoming wavelength, while the wave height was kept fixed. The objective is to find the maximum run-up amplification with the least number of simulations. To achieve this goal, we build an emulator based on Gaussian Processes to guide the selection of the query points in the parameter space. We thus reduce substantially the computations required to identify the run-up amplification. Our results show that the island acts as a focusing lens for energy and amplifies the run-up along the coastline behind its lee side, instead of protecting it, as popular beliefs suggest.

Wave set-up, percolation and undertow in the surf zone

1983 ◽  
Vol 390 (1799) ◽  
pp. 283-291 ◽  
Keyword(s):  
Surf Zone ◽  
Bottom Current ◽  
Straight Tube ◽  
Mean Flow ◽  
Mean Water Level ◽  
The Mean ◽  
Run Up ◽  
Set Up ◽  
Sloping Beach ◽  
The Waves

Waves approaching a sloping beach induce a tilt in the mean water level within the surf zone. The existence of this ‘set-up’ is here demonstrated by observing the mean flow in a straight tube laid parallel to the incoming waves; also by showing that the waves induce a siphon in a U-tube laid on the sloping bottom. It is argued theoretically, and confirmed by experiment, that the set-up should help to drive an offshore bottom current (the undertow) between the shoreline and the breaker line. Seawards from the breaker line the bottom current is reversed. The consequent convergence of the bottom currents may contribute to building up the ‘breaker bar’. Further experiments show that the mean onshore pressure gradient drives a circulation of water within a porous beach. The associated pattern of streamlines also extends into the land, inshore from the run-up line. Theoretically, the injection of dye at the sediment-water interface might be used to probe the porosity of the beach material.

On the evolution and run-up of breaking solitary waves on a mild sloping beach

2008 ◽  
Vol 55 (12) ◽  
pp. 975-988 ◽  
Author(s):  
Shih-Chun Hsiao ◽  
Tai-Wen Hsu ◽  
Ting-Chieh Lin ◽  
Yu-Hsuan Chang
Keyword(s):  
Solitary Waves ◽  
Run Up ◽  
Sloping Beach

scholarly journals Head-on collision between capillary–gravity solitary waves

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Marin Marin ◽  
M. M. Bhatti
Keyword(s):  
Surface Tension ◽  
Solitary Waves ◽  
Water Waves ◽  
Free Parameter ◽  
Order Approximation ◽  
Third Order ◽  
Boussinesq Model ◽  
Run Up ◽  
Physical Features ◽  
Third Order Approximation

AbstractThe present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.

scholarly journals Run-Up Simulation of Impulse-Generated Solitary Waves

2018 ◽  
Vol 144 (2) ◽  
pp. 04017170
Author(s):  
Viljami Laurmaa ◽  
Marco Picasso ◽  
Gilles Steiner ◽  
Frederic M. Evers ◽  
Willi H. Hager
Keyword(s):  
Solitary Waves ◽  
Run Up

scholarly journals On the numerical simulation of the nonbreaking solitary waves run up on sloping beaches

2015 ◽  
Vol 70 (9) ◽  
pp. 2270-2281 ◽  
Author(s):  
Asghar Farhadi ◽  
Homayoun Emdad ◽  
Ebrahim Goshtasbi Rad
Keyword(s):  
Numerical Simulation ◽  
Solitary Waves ◽  
Run Up

scholarly journals INTERACTION OF IDEALIZED URBAN INFRASTRUCTURE AND LONG WAVES DURING RUN-UP AND ON-LAND FLOW PROCESS IN COASTAL REGIONS

2012 ◽  
Vol 1 (33) ◽  
pp. 18 ◽  
Author(s):  
Nils Goseberg ◽  
Torsten Schlurmann
Keyword(s):  
Shock Wave ◽  
Urban Infrastructure ◽  
Coastal Regions ◽  
Flow Process ◽  
Long Wave ◽  
Roughness Elements ◽  
Shock Wave Generation ◽  
Run Up ◽  
Sloping Beach ◽  
Good Agreement

This paper reports experimental results of long wave run-up climbing up a 1:40 sloping beach. The resulting maximum run-up is compared with analytical results and a good agreement is found for single sinusoidal waves with uniform wave period and varying amplitude. Subsequently, the interaction with macro-roughness elements on the beach is investigated for different long-shore obstruction ratios. The reduction in wave run-up is expressed by means of a nomogram relating the wave run-up without macro-roughness elements present to those cases where on-land flow is modified by macro-roughness. The presented results mainly focus on a non-staggered and non-rotated macro-roughness configuration. In addition to the run-up reduction, surface elevation profiles on the shore are presented, that address the shock wave generation when the wave tongue approaches the first row of macro-roughness elements.

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