Runup of nonlinearly deformed waves on a coast

Didenkulova, Ira; Zahibo, Narcisse; Kurkin, A. A.; Левин, Б. В.; Pelinovsky, Efim; Soomere, Tarmo

doi:10.1134/s1028334x06080186

Cited by 42 publications

(36 citation statements)

References 4 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In the nonlinear theory the same effects can be found for a particular case of the linearly inclined bay with a parabolic cross-section m = 2 ). The solution of the nonlinear problem in this case can be obtained with the use of the Legendre (hodograph) transformation, which has been very popular for long wave runup on a plane beach (Carrier and Greenspan, 1958;Pedersen and Gjevik, 1983;Synolakis, 1987;Tadepalli and Synolakis, 1996;Li, 2000;Li and Raichlen, 2001;Carrier et al, 2003;Kânoğlu, 2004;Tinti and Tonini, 2005;Kânoğlu and Synolakis, 2006;Didenkulova et al, 2006;2008a;Antuono and Brocchini, 2007;Pritchard and Dickinson, 2007) and is valid for non-breaking waves. In this case the nonlinear system (3) can be reduced to the linear equation (Choi et al, 2008; …”

Section: Traveling Waves In U-shaped Bays With a Arbitrary Varying Dementioning

confidence: 99%

Runup of Tsunami Waves in U-Shaped Bays

Didenkulova

Pelinovsky

2010

Pure Appl. Geophys.

View full text Add to dashboard Cite

The problem of tsunami wave shoaling and runup in U-shaped bays (such as fjords) and underwater canyons is studied in the framework of shallow water theory. The wave shoaling in bays, when the depth varies smoothly along the channel axis, is studied with the use of asymptotic approach. In this case a weak reflection provides significant shoaling effects. The existence of traveling (progressive) waves, propagating in bays, when the water depth changes significantly along the channel axis, is studied. It is shown that traveling waves do exist for certain bay bathymetry configurations and may propagate over large distances without reflection.The tsunami runup in such bays is significantly larger than for a plane beach.

show abstract

Section: Traveling Waves In U-shaped Bays With a Arbitrary Varying Dementioning

confidence: 99%

Runup of Tsunami Waves in U-Shaped Bays

Didenkulova

Pelinovsky

2010

Pure Appl. Geophys.

View full text Add to dashboard Cite

show abstract

“…In particular, we especially note in the context of this paper the analyses using the nonlinear shallow water equations by Didenkulova (2009), Didenkulova et al (2006Didenkulova et al ( , 2007, and Pelinovsky (2006) which demonstrate the role of initial nonlinear steepness in increasing the eventual runup height, and that by Didenkulova et al (2014) who found that this nonlinear steepness effect was enhanced when the initial wave was one of depression. However, although these models have proved valuable and insightful, they are non-dispersive and hence do not capture the effects of wavenumber dispersion as the tsunami waves develop shorter length scales in their propagation shoreward.…”

Section: Introductionmentioning

confidence: 99%

Changing forms and sudden smooth transitions of tsunami waves

Grimshaw

Hunt

Chow

2014

J. Ocean Eng. Mar. Energy

View full text Add to dashboard Cite

In some tsunami waves travelling over the ocean, such as the one approaching the eastern coast of Japan in 2011, the sea surface of the ocean is depressed by a small metre-scale displacement over a multi-kilometre horizontal length scale, lying in front of a positive elevation of comparable magnitude and length, which together constitute a down-up wave. Shallow water theory shows that the latter travels faster than the former, leading to an interaction, whose description is the issue addressed in this paper, using model equations of the Korteweg-de Vries type. First, we re-examine the undular bore solutions of the Korteweg-de Vries equation which describe how an initial depression wave deforms into a depression rarefaction wave followed by an undular bore of large elevation waves riding on this depression. Then we develop a new extended Korteweg-de Vries equation some of whose solutions can be used to describe the interaction of an elevation wave chasing a depression wave. These show that the two waves coincide at a given position and time producing a maximum elevation. Typically this amplitude is larger than the initial displacement magnitude by a factor which can be as large as two, which may explain anomalous elevations of tsunamis at particular positions along their trajectories. It is physically significant that for these small amplitude waves, no wave breaking occurs and there is no excess dissipation. Then, following the transition, the elevation wave moves ahead of the depression wave and the distance between them increases either linearly or

show abstract

“…In particular, studies by Didenkulova (2009), Didenkulova et al (2006Didenkulova et al ( , 2007 and Pelinovsky (2006) using the nonlinear shallow water equations have elucidated the role of initial steepness in increasing the eventual run-up height, and we especially note that Didenkulova et al (2014) found that this nonlinear steepness effect was enhanced when the initial wave was one of depression.…”

Section: Introductionmentioning

confidence: 99%

Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation

Grimshaw

Yuan

2016

Nat Hazards

View full text Add to dashboard Cite

Although tsunamis in the deep ocean are very long waves of quite small amplitudes, as they propagate shorewards into shallow water, nonlinearity becomes important and the structure of the leading waves depends on the polarity of the incident wave from the deep ocean. In this paper, we use a variable-coefficient Korteweg-de Vries equation to examine this issue, for an initial wave which is either elevation, or depression, or a combination of each. We show that the leading waves can be described by a reduction of the Whitham modulation theory to a solitary wave train. We find that for an initial elevation, the leading waves are elevation solitary waves with an amplitude which varies inversely with the depth, with a pre-factor which is twice the maximum amplitude in the initial wave. By contrast, for an initial depression, the leading wave is a depression rarefaction wave, followed by a solitary wave train whose maximum amplitude of the leading wave is determined by the square root of the mass in the initial wave.

show abstract

Runup of nonlinearly deformed waves on a coast

Cited by 42 publications

References 4 publications

Runup of Tsunami Waves in U-Shaped Bays

Runup of Tsunami Waves in U-Shaped Bays

Changing forms and sudden smooth transitions of tsunami waves

Depression and elevation tsunami waves in the framework of the Korteweg–de Vries equation

Contact Info

Product

Resources

About