scholarly journals A UNIFIED RUNUP FORMULA FOR BREAKING SOLITARY WAVES ON A UNIFORM BEACH

2018 ◽  
pp. 3
Author(s):  
Yun-Ta Wu ◽  
Philip Li-Fan Liu ◽  
Philip Li-Fan Liu ◽  
Kao-Shu Hwang ◽  
Kao-Shu Hwang ◽  
...  
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Large Scale ◽  
Storm Surges ◽  
Research Area ◽  
Easy Access ◽  
Wave Runup ◽  
Wave Flume ◽  
Long Wave ◽  
Analytical Approaches

For coastal management, it is of great importance to understand long-wave induced runup processes and predict maximum runup heights. Long-wave in nature could take different forms, such as swells, storm surges and tsunamis. One of the fundamental waveforms is solitary wave, which has a permanent form in a constant depth. Thus, the issue of solitary wave propagation, shoaling, breaking and runup has been an active research area in coastal engineering community, using experimental, numerical and analytical approaches. Among existing runup experiments, only limited numbers of experiments were conducted in large-scale wave flume facilities because of the lack of easy access. To enhance the range of surf parameters for breaking solitary waves, new laboratory experiments were carried out in a large-scale wave flume with a 1/100 slope. Several wave conditions in the experiments were on the borderline of plunging and spilling breakers. The main objective of this paper is twofold. The first aim is to present a new dataset for solitary wave runup. The second objective aims to develop a unified empirical formula, based on the available runup data in the literature and the present new data, for the runup of breaking solitary waves on a uniform slope.

Radiation of short waves from the resonantly excited capillary–gravity waves

2016 ◽  
Vol 810 ◽  
pp. 5-24 ◽  
Author(s):  
M. Hirata ◽  
S. Okino ◽  
H. Hanazaki
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Gravity Waves ◽  
Wave Pattern ◽  
Short Wave ◽  
Bond Number ◽  
Linear Wave ◽  
Cnoidal Wave ◽  
Short Waves ◽  
Long Wave

Capillary–gravity waves resonantly excited by an obstacle (Froude number: $Fr=1$) are investigated by the numerical solution of the Euler equations. The radiation of short waves from the long nonlinear waves is observed when the capillary effects are weak (Bond number: $Bo<1/3$). The upstream-advancing solitary wave radiates a short linear wave whose phase velocity is equal to the solitary waves and group velocity is faster than the solitary wave (soliton radiation). Therefore, the short wave is observed upstream of the foremost solitary wave. The downstream cnoidal wave also radiates a short wave which propagates upstream in the depression region between the obstacle and the cnoidal wave. The short wave interacts with the long wave above the obstacle, and generates a second short wave which propagates downstream. These generation processes will be repeated, and the number of wavenumber components in the depression region increases with time to generate a complicated wave pattern. The upstream soliton radiation can be predicted qualitatively by the fifth-order forced Korteweg–de Vries equation, but the equation overestimates the wavelength since it is based on a long-wave approximation. At a large Bond number of $Bo=2/3$, the wave pattern has the rotation symmetry against the pattern at $Bo=0$, and the depression solitary waves propagate downstream.

LARGE SCALE EXPERIMENTS ON EVOLUTION AND RUN-UP OF BREAKING SOLITARY WAVES

2007 ◽  
Vol 01 (03) ◽  
pp. 257-272 ◽  
Author(s):  
KAO-SHU HWANG ◽  
YU-HSUAN CHANG ◽  
HWUNG-HWENG HWUNG ◽  
YI-SYUAN LI
Keyword(s):  
Solitary Wave ◽  
Wave Height ◽  
Solitary Waves ◽  
Water Depth ◽  
Large Scale ◽  
Scale Effects ◽  
Wave Heights ◽  
Run Up ◽  
Hydraulics Laboratory ◽  
The Waves

The evolution and run-up of breaking solitary waves on plane beaches are investigated in this paper. A series of large-scale experiments were conducted in the SUPER TANK of Tainan Hydraulics Laboratory with three plane beaches of slope 0.05, 0.025 and 0.017 (1:20, 1:40 and 1:60). Solitary waves of which relative wave heights, H/h0, ranged from 0.03 to 0.31 were generated by two types of wave-board displacement trajectory: the ramp-trajectory and the solitary-wave trajectory proposed by Goring (1979). Experimental results show that under the same relative wave height, the waveforms produced by the two generation procedures becomes noticeably different as the waves propagate prior to the breaking point. Meanwhile, under the same relative wave height, the larger the constant water depth is, the larger the dimensionless run-up heights would be. Scale effects associated with the breaking process are discussed.

scholarly journals BREAKING AND WASH UP OF SOLITARY WAVES ON A COMPOSITE BEACH

2020 ◽  
pp. 29
Author(s):  
Hajo von Hafen ◽  
Jacob Stolle ◽  
Nils Goseberg ◽  
Ioan Nistor
Keyword(s):  
Solitary Waves ◽  
Horizontal Plane ◽  
Large Scale ◽  
Propagation Path ◽  
Rock Falls ◽  
Damage Potential ◽  
Large Wave ◽  
Beach Slope ◽  
Wave Flume ◽  
Run Up

Hazardous events, such as landslides, rock slides, rock falls or avalanches often generate extreme, impulsive waves when entering water bodies (Fuchs & Hager, 2015). These waves are approximated by solitary waves and researchers investigate their damage potential when inundating built environment. Deepening the understanding of solitary waves running up a uniform beach slope and propagating over a subsequent horizontal plane can help to reduce and mitigate damage and the number of casualties caused by such a hazardous event. So far, few authors addressed this specific setting near-shore (Fuchs & Hager, 2015; Zelt & Raichlen, 1991). In this study, large scale solitary waves propagate about 200 m in in the Large-Wave Flume (GWK, 307 m 5 m 7 m) at the Coastal Research Center in Hannover, Germany then they run up a beach slope and subsequently break, generating a bore which advances onto a subsequent, initially dry, horizontal surface. Unlike previous studies, the generated solitary waves broke close to the edge between the beach slope and the horizontal plane section. The overall aim of this study is to investigate the characteristics of the broken waves' dynamics. In addition, their surge profile and front celerity are compared to those of the non-breaking solitary waves. Subsequently, the differences between the velocity regimes along the bore propagation path are presented and linked to the fundamental physical processes behind.

Long wave runup on piecewise linear topographies

1998 ◽  
Vol 374 ◽  
pp. 1-28 ◽  
Author(s):  
UTKU KÂNOĞLU ◽  
COSTAS EMMANUEL SYNOLAKIS
Keyword(s):  
Solitary Waves ◽  
Numerical Models ◽  
Piecewise Linear ◽  
Physical Parameters ◽  
Wave Runup ◽  
Asymptotic Results ◽  
Tidal Waves ◽  
Topographic Slope ◽  
Long Wave ◽  
Time Histories

We study long-wave evolution and runup on piecewise linear one- and two-dimensional bathymetries analytically and experimentally with the objective of understanding certain coastal effects of tidal waves. We develop a general solution method for determining the amplification factor of different ocean topographies consisting of linearly varying and constant-depth segments to study how spectral distributions evolve over bathymetry, and apply our results to study the evolution of solitary waves. We find asymptotic results which suggest that solitary waves often interact with piecewise linear topographies in a counter-intuitive manner. We compare our analytical predictions with numerical results, with results from a new set of laboratory experiments from a physical model of Revere Beach, and also with the data on wave runup around an idealized conical island. We find good agreement between our theory and the laboratory results for the time histories of free-surface elevations and for the maximum runup heights. Our results suggest that, at least for simple piecewise linear topographies, analytical methods can be used to calculate effectively some important physical parameters in long-wave runup. Also, by underscoring the effects of the topographic slope at the shoreline, this analysis qualitatively suggests why sometimes predictions of field-applicable numerical models differ substantially from observations of tsunami runup.

On the existence of solitary waves in rotating fluids

1995 ◽  
Vol 125 (5) ◽  
pp. 1105-1129
Author(s):  
S. M. Sun
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Solitary Wave Solutions ◽  
Rotating Fluid ◽  
Rotating Fluids ◽  
First Order ◽  
Wave Solutions ◽  
Long Wave ◽  
Long Wave Approximation ◽  
Conditions At Infinity

This paper considers the existence of axisymmetric solitary waves in an inviscid and incompressible rotating fluid bounded by a rigid cylinder. It has been obtained by many experiments and formal derivations that this flow has internal solitary waves in the fluid when equilibrium state at infinity satisfies certain conditions. This paper gives a rigorous proof of the existence of solitary wave solutions for the exact equations governing the flow under such conditions at infinity, and shows that the first-order approximations of the solitary wave solutions for the exact equations are solitary wave solutions derived formally using long-wave approximation. The ideas in the proof of the existence of solitary waves in two-dimensional stratified fluids are used and a main difficulty from the singularity at axis of rotation is overcome.

scholarly journals Magma ascent mechanisms in the transition regime from solitary porosity waves to diapirism

2020 ◽  
Author(s):  
Janik Dohmen ◽  
Harro Schmeling
Keyword(s):  
Solitary Wave ◽  
Solitary Waves ◽  
Large Scale ◽  
Two Phase Flow ◽  
Grid Size ◽  
Magma Ascent ◽  
Phase Flow ◽  
Two Phase ◽  
Porosity Wave ◽  
Wide Range

Abstract. In partially molten regions inside the earth melt buoyancy may trigger upwelling of both solid and fluid phases, i.e. diapirism. If the melt is allowed to move separately with respect to the matrix, melt perturbations may evolve into solitary porosity waves. While diapirs may form on a wide range of scales, porosity waves are restricted to sizes of a few times the compaction length. Thus, the size of a partially molten perturbation controls whether a diapir or a porosity wave will emerge. We study the transition from diapiric rise to solitary porosity waves by solving the two-phase flow equations of conservation of mass and momentum in 2D with porosity dependent matrix viscosity. We systematically vary the initial size of a porosity perturbation from 1 to 100 times the compaction length. If the perturbation is much larger than a regular solitary wave, its Stokes velocity is large and therefore faster than the segregating melt. Consequently, the fluid is not able to form a porosity wave and a diapir emerges. For small perturbations solitary waves emerge, either with a positive or negative vertical matrix velocity inside. In between the diapir and solitary wave regimes we observe a third regime of solitary wave induced focusing of melt. In these cases, diapirism is dominant but the fluid is still fast enough to locally build up small solitary waves which rise slightly faster than the diapir and form finger like structures at the front of the diapir. In our numerical simulations the width of these fingers is controlled by the compaction length or the grid size, whichever is larger. In cases where the compaction length becomes similar to or smaller than the grid size the finger-like leading solitary porosity waves are no more properly resolved, and too big and too fast waves may be the result. Therefore, one should be careful in large scale two-phase flow modelling with melt focusing especially when compaction length and grid size are of similar order.

scholarly journals ARE SOLITARY WAVES THE LIMITING WAVES IN LONG WAVE RUNUP?

1988 ◽  
Vol 1 (21) ◽  
pp. 14 ◽  
Author(s):  
Costas Emmanuel Synolakis
Keyword(s):  
Solitary Waves ◽  
Laboratory Data ◽  
Long Waves ◽  
Wave Runup ◽  
Long Wave ◽  
Limiting Condition

This is a study of the maximum runup of single long waves on plane beaches. Laboratory data are presented that suggest that solitary waves attain the higher runup distances than other single long waves with identical generation characteristics, such as energy or momentum. These results suggest that solitary waves may provide a limiting condition for long wave runup on plane beaches.

scholarly journals On Galilean Invariant and Energy Preserving BBM-Type Equations

Symmetry ◽  
2021 ◽  
Vol 13 (5) ◽  
pp. 878
Author(s):  
Alexei Cheviakov ◽  
Denys Dutykh ◽  
Aidar Assylbekuly
Keyword(s):  
Wave Equation ◽  
Conservation Laws ◽  
Numerical Simulations ◽  
Solitary Waves ◽  
Local Symmetry ◽  
Symmetry And Conservation Laws ◽  
Higher Order ◽  
Special Equation ◽  
Long Wave ◽  
Local Symmetries

We investigate a family of higher-order Benjamin–Bona–Mahony-type equations, which appeared in the course of study towards finding a Galilei-invariant, energy-preserving long wave equation. We perform local symmetry and conservation laws classification for this family of Partial Differential Equations (PDEs). The analysis reveals that this family includes a special equation which admits additional, higher-order local symmetries and conservation laws. We compute its solitary waves and simulate their collisions. The numerical simulations show that their collision is elastic, which is an indication of its S−integrability. This particular PDE turns out to be a rescaled version of the celebrated Camassa–Holm equation, which confirms its integrability.

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