Solitary waves in a finite depth fluid

Joseph, R. I.

doi:10.1088/0305-4470/10/12/002

Cited by 262 publications

(183 citation statements)

References 4 publications

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“…At the time of their study, the wave amplitudes, associated wave velocities, distance traveled, and lifetimes were among the largest ever observed. Good agreement was found between the observed wave characteristics and modal solutions to a finite-depth version of the KdV equation [38], [39]. The South China Sea waves were actually larger and propagated farther than the Sulu Sea waves.…”

Section: E Internal Wavesmentioning

confidence: 60%

Internal Solitons in the Northeastern South China Sea Part I: Sources and Deep Water Propagation

Ramp

Tang²,

Duda³

et al. 2004

IEEE J. Oceanic Eng.

344

321

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Abstract-A moored array of current, temperature, conductivity, and pressure sensors was deployed across the Chinese continental shelf and slope in support of the Asian Seas International Acoustics Experiment. The goal of the observations was to quantify the water column variability in order to understand the along-and across-shore low-frequency acoustic propagation in shallow water. The moorings were deployed from April 21-May 19, 2001 and sampled at 1-5 min intervals to capture the full range of temporal variability without aliasing the internal wave field. The dominant oceanographic signal by far was in fact the highly nonlinear internal waves (or solitons) which were generated near the Batan Islands in the Luzon Strait and propagated 485 km across deep water to the observation region. Dubbed trans-basin waves, to distinguish them from other, smaller nonlinear waves generated locally near the shelf break, these waves had amplitudes ranging from 29 to greater than 140 m and were among the largest such waves ever observed in the world's oceans. The waves arrived at the most offshore mooring in two clusters lasting 7-8 days each separated by five days when no waves were observed. Within each cluster, two types of waves arrived which have been named type-a and type-b. The type-a waves had greater amplitude than the type-b waves and arrived with remarkable regularity at the same time each day, 24 h apart. The type-b waves were weaker than the type-a waves, arrived an hour later each day, and generally consisted of a single soliton growing out of the center of the wave packet. Comparison with modeled barotropic tides from the generation region revealed that: 1) The two clusters were generated around the time of the spring tides in the Luzon strait; and 2) The type-a waves were generated on the strong side of the diurnal inequality while the type-b waves were generated on the weaker beat. The position of the Kuroshio intrusion into the Luzon Strait may modulate the strength of the waves being produced. As the waves shoaled, the huge lead solitons first split into two solitons then merged together into a broad region of thermocline depression at depths less than 120 m. Elevation waves sprang up behind them as they continued to propagate onshore. The elevation waves also grew out of regions where the locally-generated internal tide forced the main thermocline down near the bottom. The "critical T. Y. Tang is with the Institute of Oceanography, National Taiwan University, Taipei, ROC.H. point" where the upper and lower layers were equal was a good indicator of when the depression or elevation waves would form, however this was not a static point, but rather varied in both space and time according to the presence or absence of the internal tides and the incoming trans-basin waves themselves.

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Section: E Internal Wavesmentioning

confidence: 60%

Internal Solitons in the Northeastern South China Sea Part I: Sources and Deep Water Propagation

Ramp

Tang²,

Duda³

et al. 2004

IEEE J. Oceanic Eng.

344

321

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“…The famous integrable Boussinesq equation [52] u tt = u xxxx + (u 2 ) xx (48) belongs to this class. Recently all integrable equations of the form…”

Section: Integrable Boussinesq Type Equationsmentioning

confidence: 99%

Symbolic representation and classification of integrable systems

Михайлов

Новиков

Wang

2008

Algebraic Theory of Differential Equations

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“…Internal waveforms that have positive displacements can not generate solitons in this situation. Another method of generating internal solitons, as discussed by Joseph [1977] and Djordjevic and Redekopp [1978], involves a process called fissioning. Fissioning is the process by which an initial solitary wave breaks into a packet of smaller internal solitons as it propagates into shallower water (provided hi remains less than h 2 ).…”

Section: Instrumentmentioning

confidence: 99%

A characterization of internal solitons in the SWARM region of the New York bight

Racine¹

1996

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A field experiment was undertaken during July and August of 1995 aimed at understanding the interaction of acoustic signals with the internal wave field off the coast of New Jersey. As part of SWARM (Shallow Water Acoustics in a Random Medium), physical data were collected in 75 m of water near 390 15.34' N, 720 56.59' W with three thermistor strings, a bottom-mounted ADCP, and yo-yo CTDs. These data spanned a two-week period of the month-long study. With the exception of a time following a storm event, during which the generation mechanism near the shelf break was effectively switched off, large-amplitude (up to 20 meters), rank-ordered groups of internal solitons were observed traveling through the region approximately every 12.4 hours. These groups of solitons progressed across the shelf with phase speeds of 61.8 ± 14.9 cm/s with a heading of 280 ± 310 T. Two-layer finite-depth theory was tested on this data and shown to consistently overpredict the phase speed of the internal solitons within each group.Predictions of horizontal scale, particle velocities, and displacements were in qualitative agreement with two-layer finite-depth dynamics. standing by me even when I make it next to impossible, I have you to love. I only hope the rest of our life together continues to grow and strengthen the way it has so far. Acknowledgments

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Solitary waves in a finite depth fluid

Cited by 262 publications

References 4 publications

Internal Solitons in the Northeastern South China Sea Part I: Sources and Deep Water Propagation

Internal Solitons in the Northeastern South China Sea Part I: Sources and Deep Water Propagation

Symbolic representation and classification of integrable systems

A characterization of internal solitons in the SWARM region of the New York bight

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