Gravity wave refraction by islands

1970 ◽  
Vol 41 (3) ◽  
pp. 655-672 ◽  
Author(s):  
Conrad C. Lautenbacher
Keyword(s):  
Differential Equation ◽  
Integral Equation ◽  
Bottom Topography ◽  
Practical Importance ◽  
Shallow Water Theory ◽  
One Dimensional ◽  
Wave Refraction ◽  
Long Wave ◽  
Run Up ◽  
Tsunami Run Up

The refractive influence on tsunami run-up of the offshore bottom topography of islands is analyzed. Shallow water theory is used to treat problems in which the geometry resembles that of individual Hawaiian islands and in which the incident wave is plane and monochromatic.Mathematically, the differential equation for long-wave propagation is converted into an integral equation to which numerical methods are applied. Results of practical importance include the run-up on island coastal areas. The results are used in conjunction with earlier one-dimensional analyses to estimate the total tsunami run-up.

Simplified formulae for designing coastal forest against tsunami run-up: one-dimensional approach

2018 ◽  
Vol 92 (1) ◽  
pp. 327-346 ◽  
Author(s):  
Nguyen Ba Thuy ◽  
N. A. K. Nandasena ◽  
Vu Hai Dang ◽  
Norio Tanaka
Keyword(s):  
Coastal Forest ◽  
Dimensional Approach ◽  
One Dimensional ◽  
Run Up ◽  
Tsunami Run Up

scholarly journals Run-up of nonlinear monochromatic wave on a plane beach in presence of a tide

2019 ◽  
Vol 59 (4) ◽  
pp. 529-532
Author(s):  
I. I. Didenkulova ◽  
E. N. Pelinovsky
Keyword(s):  
Exact Solution ◽  
Shallow Water ◽  
Nonlinear Problem ◽  
Incident Wave ◽  
Wave Amplitude ◽  
Monochromatic Wave ◽  
Shallow Water Theory ◽  
Long Wave ◽  
Run Up

The nonlinear problem of long wave run-up on a plane beach in a presence of a tide is solved within the shallow water theory using the Carrier-Greenspan approach. The exact solution of the nonlinear problem for wave run-up height is found as a function of the incident wave amplitude. Influence of tide on characteristics of wave run-up on a beach is studied.

scholarly journals NUMERICAL AND EXPERIMENTAL STUDY ON TSUNAMI RUN-UP AND INUNDATION INFLUENCED BY MACRO ROUGHNESS ELEMENTS

2011 ◽  
Vol 1 (32) ◽  
pp. 13 ◽  
Author(s):  
Nils Goseberg ◽  
Torsten Schlurmann
Keyword(s):  
Effective Area ◽  
Second Step ◽  
Wave Channel ◽  
Long Wave ◽  
Roughness Elements ◽  
First Results ◽  
Alternative Methodology ◽  
Run Up ◽  
Tsunami Run Up ◽  
Flow Cross

This research study considers long wave run-up experimentally and numerically. At first, an alternative methodology in long wave physical modeling is presented by means of a set of pipe pumps forcing the inflow of a controlled volume of water into a wave channel mimicking a tsunami-like wave shape that is consistently contained by a proportional plus integral plus derivative controller (PID) controller. Arbitrary wave lengths are persistently generated by means of the proposed methodology. First results are compared to tsunami data stemming from conventional experimental configurations with solitary waves as well as with recent numerical modeling results. Comparisons are thoroughly discussed and – in a second step – numerical simulations are accomplished taking the interaction of long wave run-up and macro-roughness elements into account. Four different experimental configurations of macro-roughness elements are carried out while spacing between elements and numbers of obstacle rows are alternated. A fundamental correlation analysis reveals that a correlation of the number of macro-roughness rows, effective area of flow cross section and a grouping factor of different element configurations exists in principle.

A one-dimensional shock-capturing model for long wave run-up on sloping beaches

2012 ◽  
Vol 18 (2) ◽  
pp. 65-79 ◽  
Author(s):  
Soumendra Nath Kuiry ◽  
Weiming Wu ◽  
Yan Ding
Keyword(s):  
Shock Capturing ◽  
One Dimensional ◽  
Long Wave ◽  
Run Up

scholarly journals Resonance phenomena at the long wave run-up on the coast

2013 ◽  
Vol 1 (2) ◽  
pp. 561-582
Author(s):  
A. Ezersky ◽  
D. Tiguercha ◽  
E. Pelinovsky
Keyword(s):  
Particle Velocity ◽  
Tsunami Wave ◽  
Earthquake Magnitude ◽  
Tsunami Source ◽  
Bottom Relief ◽  
Shallow Water Theory ◽  
Resonance Effects ◽  
Long Wave ◽  
Run Up ◽  
Linear Shallow Water Theory

Abstract. Run-up of long wave on a beach consisting of three pieces of constant but different slopes is studied. Linear shallow-water theory is used for incoming impulse evolution and non-linear corrections are obtained for the run-up stage. It is demonstrated that bottom profile influences the run-up characteristics and can lead to the resonance effects: increasing of wave height, particle velocity, and number of oscillations. Simple parameterization of tsunami source through an earthquake magnitude is used to calculate the run-up height versus earthquake magnitude. It is shown that resonance effects lead to the sufficient increasing of run-up heights for weakest earthquakes and tsunami wave does not break on chosen bottom relief if the earthquake magnitude does not exceed 7.8.

scholarly journals Resonance phenomena at the long wave run-up on the coast

2013 ◽  
Vol 13 (11) ◽  
pp. 2745-2752 ◽  
Author(s):  
A. Ezersky ◽  
D. Tiguercha ◽  
E. Pelinovsky
Keyword(s):  
Particle Velocity ◽  
Tsunami Wave ◽  
Earthquake Magnitude ◽  
Tsunami Source ◽  
Bottom Relief ◽  
Shallow Water Theory ◽  
Resonance Effects ◽  
Long Wave ◽  
Run Up ◽  
Linear Shallow Water Theory

Abstract. Run-up of long waves on a beach consisting of three pieces of constant but different slopes is studied. Linear shallow-water theory is used for incoming impulse evolution, and nonlinear corrections are obtained for the run-up stage. It is demonstrated that bottom profile influences the run-up characteristics and can lead to resonance effects: increase of wave height, particle velocity, and number of oscillations. Simple parameterization of tsunami source through an earthquake magnitude is used to calculate the run-up height versus earthquake magnitude. It is shown that resonance effects lead to the sufficient increase of run-up heights for the weakest earthquakes, and a tsunami wave does not break on chosen bottom relief if the earthquake magnitude does not exceed 7.8.

On Improved Approximate Solution of the Fredholm Integral Equation

2006 ◽  
Vol 6 (3) ◽  
pp. 264-268
Author(s):  
G. Berikelashvili ◽  
G. Karkarashvili
Keyword(s):  
Integral Equation ◽  
Approximate Solution ◽  
Fredholm Integral Equation ◽  
Algebraic Equations ◽  
Order Convergence ◽  
One Dimensional ◽  
Averaging Operator ◽  
Linear Algebraic Equations ◽  
Convergence Solution

AbstractA method of approximate solution of the linear one-dimensional Fredholm integral equation of the second kind is constructed. With the help of the Steklov averaging operator the integral equation is approximated by a system of linear algebraic equations. On the basis of the approximation used an increased order convergence solution has been obtained.

scholarly journals On the Numerical Simulation of HPDEs Using θ-Weighted Scheme and the Galerkin Method

Mathematics ◽  
2020 ◽  
Vol 9 (1) ◽  
pp. 78
Author(s):  
Haifa Bin Jebreen ◽  
Fairouz Tchier
Keyword(s):  
Differential Equation ◽  
Galerkin Method ◽  
Linear Ordinary Differential Equation ◽  
Time Interval ◽  
Hyperbolic Partial Differential Equation ◽  
Time Step ◽  
Numerical Examples ◽  
One Dimensional ◽  
The Stability ◽  
The Galerkin Method

Herein, an efficient algorithm is proposed to solve a one-dimensional hyperbolic partial differential equation. To reach an approximate solution, we employ the θ-weighted scheme to discretize the time interval into a finite number of time steps. In each step, we have a linear ordinary differential equation. Applying the Galerkin method based on interpolating scaling functions, we can solve this ODE. Therefore, in each time step, the solution can be found as a continuous function. Stability, consistency, and convergence of the proposed method are investigated. Several numerical examples are devoted to show the accuracy and efficiency of the method and guarantee the validity of the stability, consistency, and convergence analysis.

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