The solitary waves of the barotropic quasi-geostrophic model with the large-scale orography

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.

Download Full-text

BREAKING AND WASH UP OF SOLITARY WAVES ON A COMPOSITE BEACH

Coastal Engineering Proceedings ◽

10.9753/icce.v36v.waves.29 ◽

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.

Download Full-text

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

Coastal Engineering Proceedings ◽

10.9753/icce.v36.currents.3 ◽

2018 ◽

pp. 3

Author(s):

Yun-Ta Wu ◽

Philip Li-Fan Liu ◽

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.

Download Full-text

Runup of solitary waves on a circular Island

Journal of Fluid Mechanics ◽

10.1017/s0022112095004095 ◽

1995 ◽

Vol 302 ◽

pp. 259-285 ◽

Cited By ~ 278

Author(s):

Philip L. -F. Liu ◽

Yong-Sik Cho ◽

Michael J. Briggs ◽

Utku Kanoglu ◽

Costas Emmanuel Synolakis

Keyword(s):

Numerical Model ◽

Solitary Waves ◽

Large Scale ◽

Wave Equations ◽

Laboratory Data ◽

Two Dimensional ◽

Wave Trapping ◽

Shallow Water Wave Equations ◽

Circular Island ◽

Run Up

This is a study of the interactions of solitary waves climbing up a circular island. A series of large-scale laboratory experiments with waves of different incident height-to-depth ratios and different crest lengths is described. Detailed two-dimensional run-up height measurements and time histories of surface elevations around the island are presented. A numerical model based on the two-dimensional shallow-water wave equations including runup calculations was developed. Numerical model predictions agreed very well with the laboratory data and the model was used to study wave trapping and the effect of slope. Under certain conditions, enhanced runup and wave trapping on the lee side of the island were observed, suggesting a possible explanation for the devastation reported by field surveys in Babi Island off Flores, Indonesia, and in Okushiri Island, Japan.

Download Full-text

Evolution of large-scale magnetosonic structures to trains of solitary waves

Journal of Geophysical Research Atmospheres ◽

10.1029/2011ja016565 ◽

2011 ◽

Vol 116 (A7) ◽

pp. n/a-n/a ◽

Cited By ~ 4

Author(s):

M. Strumik ◽

K. Stasiewicz ◽

C. Z. Cheng ◽

B. Thidé

Keyword(s):

Solitary Waves ◽

Large Scale

Download Full-text

Satellite Altimetry Observations of Large-Scale Internal Solitary Waves

IEEE Geoscience and Remote Sensing Letters ◽

10.1109/lgrs.2017.2655621 ◽

2017 ◽

Vol 14 (4) ◽

pp. 534-538 ◽

Cited By ~ 6

Author(s):

J. M. Magalhaes ◽

J. C. B. da Silva

Keyword(s):

Solitary Waves ◽

Satellite Altimetry ◽

Large Scale ◽

Internal Solitary Waves

Download Full-text

The swash of solitary waves on a plane beach: flow evolution, bed shear stress and run-up

Journal of Fluid Mechanics ◽

10.1017/jfm.2015.435 ◽

2015 ◽

Vol 779 ◽

pp. 556-597 ◽

Cited By ~ 17

Author(s):

Nimish Pujara ◽

Philip L.-F. Liu ◽

Harry Yeh

Keyword(s):

Shear Stress ◽

Solitary Waves ◽

Large Scale ◽

Breaking Waves ◽

Shear Stresses ◽

Bed Shear Stress ◽

Swash Zone ◽

Flow Evolution ◽

Run Up ◽

Bed Shear Stresses

The swash of solitary waves on a plane beach is studied using large-scale experiments. Ten wave cases are examined which range from non-breaking waves to plunging breakers. The focus of this study is on the influence of breaker type on flow evolution, spatiotemporal variations of bed shear stresses and run-up. Measurements are made of the local water depths, flow velocities and bed shear stresses (using a shear plate sensor) at various locations in the swash zone. The bed shear stress is significant near the tip of the swash during uprush and in the shallow flow during the later stages of downrush. In between, the flow evolution is dominated by gravity and follows an explicit solution to the nonlinear shallow water equations, i.e. the flow due to a dam break on a slope. The controlling scale of the flow evolution is the initial velocity of the shoreline immediately following waveform collapse, which can be predicted by measurements of wave height prior to breaking, but also shows an additional dependence on breaker type. The maximum onshore-directed bed shear stress increases significantly onshore of the stillwater shoreline for non-breaking waves and onshore of the waveform collapse point for breaking waves. A new normalization for the bed shear stress which uses the initial shoreline velocity is presented. Under this normalization, the variation of the maximum magnitudes of the bed shear stress with distance along the beach, which is normalized using the run-up, follows the same trend for different breaker types. For the uprush, the maximum dimensionless bed shear stress is approximately 0.01, whereas for the downrush, it is approximately 0.002.

Download Full-text

SIMULINK MODELING FOR CIRCUIT REPRESENTATION OF GRANULAR CHAINS

Modern Physics Letters B ◽

10.1142/s0217984913500930 ◽

2013 ◽

Vol 27 (13) ◽

pp. 1350093 ◽

Cited By ~ 3

Author(s):

LOUIZA SELLAMI ◽

ROBERT W. NEWCOMB ◽

SURAJIT SEN

Keyword(s):

Solitary Waves ◽

Large Scale ◽

Vlsi Circuit ◽

Granular Chain ◽

Mathematical System ◽

Circuit Representation ◽

Granular Chains ◽

End Wall

After a review of the coupled Newton's equations for a small alignment of grains with a fixed reflecting end wall, the equations are put into block diagrams of Simulink. Simulink simulations are given for 6 grain systems for cubic and Hertz intergrain potentials. The expected granular solitary waves are seen in the simulations. The block diagrams hence convert a single impulse into a traveling energy bundle of fixed width. This work forms the necessary first step for the eventual realization of the mathematical system represented by the granular chain as a Very Large Scale Integrated (VLSI) circuit.

Download Full-text

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

10.5194/se-2020-124 ◽

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.

Download Full-text