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Asymptotic and numerical analysis of...

Berger, Kurt Michael.

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Asymptotic and numerical analysis of free surface flows: Lump solitons and wave turbulence.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Asymptotic and numerical analysis of free surface flows: Lump solitons and wave turbulence./
Author:	Berger, Kurt Michael.
Description:	95 p.
Notes:	Source: Dissertation Abstracts International, Volume: 61-08, Section: B, page: 4185.
Contained By:	Dissertation Abstracts International61-08B.
Subject:	Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9983785
ISBN:	0599901454

Asymptotic and numerical analysis of free surface flows: Lump solitons and wave turbulence.
Berger, Kurt Michael.

Asymptotic and numerical analysis of free surface flows: Lump solitons and wave turbulence. - 95 p.

Source: Dissertation Abstracts International, Volume: 61-08, Section: B, page: 4185.

Thesis (Ph.D.)--The University of Wisconsin - Madison, 2000.

Three-dimensional solitary waves or lump solitons are known to be solutions to the Kadomtsev-Petviashvili I (KP-I) equation, which models small-amplitude shallow-water waves when the Bond number is greater than &frac13;. Recently, Pego and Quintero presented a proof of the existence of such waves for the Benney-Luke equation with surface tension. Here we establish an explicit connection between the lump solitons of these two equations and numerically compute the Benney-Luke lump solitons and their speed-amplitude relation. Furthermore, we numerically collide two Benney-Luke lump solitons to illustrate their soliton wave character. Finally, we study the flow over an obstacle near the linear shallow-water speed and show that three-dimensional lump solitons are periodically generated.

ISBN: 0599901454Subjects--Topical Terms:

515831
Mathematics.

Asymptotic and numerical analysis of free surface flows: Lump solitons and wave turbulence.
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020 $a 0599901454
035 $a (UnM)AAI9983785
035 $a AAI9983785
040 $a UnM $c UnM
100 1 $a Berger, Kurt Michael. $3 1908401
245 1 0 $a Asymptotic and numerical analysis of free surface flows: Lump solitons and wave turbulence.
300 $a 95 p.
500 $a Source: Dissertation Abstracts International, Volume: 61-08, Section: B, page: 4185.
500 $a Supervisor: Paul A. Milewski.
502 $a Thesis (Ph.D.)--The University of Wisconsin - Madison, 2000.
520 $a Three-dimensional solitary waves or lump solitons are known to be solutions to the Kadomtsev-Petviashvili I (KP-I) equation, which models small-amplitude shallow-water waves when the Bond number is greater than &frac13;. Recently, Pego and Quintero presented a proof of the existence of such waves for the Benney-Luke equation with surface tension. Here we establish an explicit connection between the lump solitons of these two equations and numerically compute the Benney-Luke lump solitons and their speed-amplitude relation. Furthermore, we numerically collide two Benney-Luke lump solitons to illustrate their soliton wave character. Finally, we study the flow over an obstacle near the linear shallow-water speed and show that three-dimensional lump solitons are periodically generated.
520 $a In the second part of this dissertation, our goal is to study, numerically, the statistics of a large number of interacting finite-depth gravity surface waves. The weak- or wave-turbulence problem consists of finding statistical states with constant flux of energy in wavenumber space. These states are obtained by forcing and dissipating the conservative water wave problem at disparate scales and predicting the spectrum, often as a Kolmogorov-like power law, at intermediate scales. Majda, McLaughlin, and Tabak started the numerical investigation of the predictions of weak turbulence theory using a nonlinear dispersive NLS model equation. Here we investigate wave turbulence in a manner similar to Majda et al, but for an equation modeling gravity water waves, which is the original context in which the problem was posed. We perform long time computations on the one-dimensional, finite-depth Benney-Luke equation and compute various statistical quantities of interest. To validate this model, we first show, analytically and numerically, that Benney-Luke equations correctly predict the main deterministic aspects of resonant gravity wave interactions: resonant quartets, Benjamin-Feir type wave-packet stability, and wave-mean flow interactions.
590 $a School code: 0262.
650 4 $a Mathematics. $3 515831
650 4 $a Physics, Fluid and Plasma. $3 1018402
690 $a 0405
690 $a 0759
710 2 0 $a The University of Wisconsin - Madison. $3 626640
773 0 $t Dissertation Abstracts International $g 61-08B.
790 1 0 $a Milewski, Paul A., $e advisor
790 $a 0262
791 $a Ph.D.
792 $a 2000
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=9983785