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.

scholarly journals A numerical study of tsunami wave impact and run-up on coastal cliffs using a CIP-based model

2017 ◽  
Vol 17 (5) ◽  
pp. 641-655 ◽  
Author(s):  
Xizeng Zhao ◽  
Yong Chen ◽  
Zhenhua Huang ◽  
Zijun Hu ◽  
Yangyang Gao
Keyword(s):  
Incident Wave ◽  
Tsunami Wave ◽  
Critical Value ◽  
Tsunami Source ◽  
Solid Boundary ◽  
Wave Impact ◽  
Submarine Slope ◽  
Coastal Cliffs ◽  
Run Up ◽  
The Impact

Abstract. There is a general lack of understanding of tsunami wave interaction with complex geographies, especially the process of inundation. Numerical simulations are performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of gentle submarine slopes and coastal cliffs, using an in-house code, a constrained interpolation profile (CIP)-based model. The model employs a high-order finite difference method, the CIP method, as the flow solver; utilizes a VOF-type method, the tangent of hyperbola for interface capturing/slope weighting (THINC/SW) scheme, to capture the free surface; and treats the solid boundary by an immersed boundary method. A series of incident waves are arranged to interact with varying coastal geographies. Numerical results are compared with experimental data and good agreement is obtained. The influences of gentle submarine slope, coastal cliff and incident wave height are discussed. It is found that the tsunami amplification factor varying with incident wave is affected by gradient of cliff slope, and the critical value is about 45°. The run-up on a toe-erosion cliff is smaller than that on a normal cliff. The run-up is also related to the length of a gentle submarine slope with a critical value of about 2.292 m in the present model for most cases. The impact pressure on the cliff is extremely large and concentrated, and the backflow effect is non-negligible. Results of our work are highly precise and helpful in inverting tsunami source and forecasting disaster.

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 TRANSFORMATION, BREAKING AND RUN-UP OF A LONG WAVE OF FINITE HEIGHT

2011 ◽  
Vol 1 (8) ◽  
pp. 5
Author(s):  
Tsutomu Kishi
Keyword(s):  
Approximate Solutions ◽  
Wave Transformation ◽  
Beach Profile ◽  
Parabolic Profile ◽  
Long Wave ◽  
Short Period ◽  
Run Up ◽  
Sloping Beach ◽  
Linear Shallow Water Theory ◽  
Considerable Deformation

On studying the transformation, breaking and run-up of a relatively steep wave of a short period, the theory for waves of permanent type has given us many fruitful results. However, the theory gradually loses its applicability as a wave becomes flat, since a considerable deformation of the wave profile is inevitable in its propagation. In § 1, a discussion concerning the transformation of a long wave in a channel of variable section is presented based on the non-linear shallow water theory. Approximate solutions obtained by G. B. Whitham's method (1958) are shown. Further, some brief considerations are given to the effects of bottom friction on wave transformation. In § 2, breaking of a long wave is discussed. Breakings on a uniformly sloping beach and on a beach of parabolic profile are considered and the effects of beach profile on breaking are clarified. Finally in § 3, experimental results on wave run-up over l/30 slope are described in comparing with the Kaplan's results.

 The tsunami energy radiation directivity on the example of the 1994, 2006 and 2007 events

2021 ◽  
Author(s):  
Anastasia Ivanova
Keyword(s):  
Continental Slope ◽  
Wave Energy ◽  
Energy Flow ◽  
Tsunami Wave ◽  
Source Zone ◽  
Tsunami Source ◽  
Bottom Relief ◽  
Edge Waves ◽  
Tsunami Energy ◽  
Kuril Ridge

<p>Determining the tsunami source danger is currently one of the most urgent tasks. The vast majority of recorded tsunamis are of seismic origin. Part of the energy released during an earthquake passes into the energy of the initial tsunami source. The tsunami excitation efficiency depends on a number of factors: the depth of the sea above the source and its location relative to the coast and continental slope; the shape and area of residual post-seismic bottom displacements, as well as the bottom relief directly in the zone of the seismic source; inhomogeneities of the ocean floor relief along the path of tsunami propagation (for estimating wave heights in the zone farthest from the source); time inhomogeneities of tsunami wave radiation from the source zone; non-isotropy of the tsunami radiation spectrum.</p><p>To study the tsunami source efficiency, we considered three tsunamis in the Kuril ridge region: the Shikotan tsunami of 1994, and two Simushir tsunamis of 2006 and 2007. The choice of events was largely determined by the close geographical location – all of them belong to the Kuril-Kamchatka subduction zone. Also, these events are well studied, and there is quite a large amount of data on tsunami measurements onshore and in the deep ocean. At the same time, all three sources differ in the mechanisms of the seismic focus and location relative to the coast and the continental slope.</p><p>We analyzed the tsunami wave field for three events near the Russian Pacific coast. Tsunami energy flow calculations show that frontal energy flow is mainly directed to the southeast. The flux magnitude decreases with distance from the source as a result of geometric divergence and scattering. At longer distances, the effect of refraction becomes more significant – the flow is divided into separate rays due to the focusing on the irregular bottom relief.</p><p>The radiation patterns of each source that also were created show the part of wave energy that penetrated the Sea of Okhotsk through the Kuril Straits. It is easy to indicate the effect of the capture of tsunami waves by the shelf and the formation of edge waves that carry the wave energy away from the source area along the Kuril Ridge shelf. For 2006 and 2007 events a relatively small part of the wave energy went into the captured waves, but for 1994 the initial sea surface displacement area was in the shelf zone and a significant part of the energy was transferred to the captured edge waves, radiated mainly in the northeast direction.</p>

scholarly journals On the breaking of water waves of finite amplitude on a sloping beach

1958 ◽  
Vol 4 (3) ◽  
pp. 330-334 ◽  
Author(s):  
H. P. Greenspan
Keyword(s):  
Particle Velocity ◽  
Water Waves ◽  
Initial Conditions ◽  
Finite Amplitude ◽  
Shallow Water Theory ◽  
Wave Shape ◽  
Compressive Wave ◽  
Sloping Beach ◽  
Explicit Relation ◽  
Linear Shallow Water Theory

In a recent paper Carrier & Greenspan (1958) showed that, within the framework of the non-linear shallow-water theory, there exist waves which do not break as they climb a sloping beach. The formation of a shock or bore is dependent on a variety of factors (wave shape, particle velocity, etc.) and, as yet, no general criteria for breaking have been found. In this paper, we consider waves which propagate shoreward into quiescent water; it is shown that any compressive wave (a wave of positive amplitude) which has a non-zero slope at the wave-front eventually breaks before reaching the coastline. In fact, an explicit relation is obtained between the initial conditions and the position where breaking occurs.

scholarly journals The Tsunami Wave Energy

2020 ◽  
Vol 18 (4) ◽  
pp. 39-53
Author(s):  
Andrey G. Marchuk
Keyword(s):  
Wave Energy ◽  
Water Surface ◽  
Tsunami Wave ◽  
Opposite Sign ◽  
Surface Displacement ◽  
Tsunami Source ◽  
Energy Radiation ◽  
Long Wave ◽  
Axis Length ◽  
Radiation Directivity

The basic formulae for calculating the moving long wave energy were derived and presented. The problems related to the energy counting in the course of numerical modeling of tsunami wave generation and propagation. Through a number of computational experiments, the wave energy radiation directivity of tsunami generated by an ellipsoidal source with a various axis length ratio was studied. The wave energy radiation directivity of the dipole tsunami source consisting of two ellipsoidal sources with opposite sign of the water surface displacement is considered.

scholarly journals A numerical study of tsunami wave run-up and impact on coastal cliffs using a CIP-based model

2017 ◽  
Author(s):  
Xizeng Zhao ◽  
Yong Chen ◽  
Zhenhua Huang ◽  
Yangyang Gao
Keyword(s):  
Incident Wave ◽  
Tsunami Wave ◽  
Numerical Study ◽  
Tsunami Source ◽  
Solid Boundary ◽  
Wave Impact ◽  
Gentle Slope ◽  
Coastal Cliffs ◽  
Run Up ◽  
The Impact

Abstract. There is a general lack of the understanding of tsunami wave interacting with complex geographies, especially the process of inundation. Numerical simulations are performed to understand the effects of several factors on tsunami wave impact and run-up in the presence of submarine gentle slopes and coastal cliffs, using an in-house code, named a Constrained Interpolation Profile (CIP)-based model in Zhejiang University (CIP-ZJU). The model employs a high-order finite difference method, the CIP method as the flow solver, utilizes a VOF-type method, the Tangent of hyperbola for interface capturing/Slope weighting (THINC/SW) scheme to capture the free surface, and treats the solid boundary by an immersed boundary method. A series of incident waves are arranged to interact with varying coastal geographies. Numerical results are compared with experimental data and good agreement is obtained. The influences of submarine gentle slope, coastal cliff and incident wave height are discussed. It is found that the rule of tsunami amplification factor varying with incident wave is affected by angle of cliff slope, and there is a critical angle about 45°. The run-up on a toe-erosion cliff is smaller than that on a normal cliff. The run-up is also related to the length of submarine gentle slope with a critical about 2.292 m in the present study. The impact pressure on the cliff is extremely large and concentrated, and the backflow effect is nonnegligible. Results of our work are in high precision and helpful in inversing tsunami source and forecasting disaster.

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.

Tsunami wave run-up load reduction inside a building array

2021 ◽  
pp. 103910
Author(s):  
Joaquin P. Moris ◽  
Andrew B. Kennedy ◽  
Joannes J. Westerink
Keyword(s):  
Tsunami Wave ◽  
Load Reduction ◽  
Building Array ◽  
Run Up
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