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Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics.

Record Type:	Language materials, manuscript : Monograph/item
Title/Author:	Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics./
Author:	Mao, Yifeng.
Description:	1 online resource (218 pages)
Notes:	Source: Dissertations Abstracts International, Volume: 85-06, Section: B.
Contained By:	Dissertations Abstracts International85-06B.
Subject:	Applied mathematics. -
Online resource:	click for full text (PQDT)
ISBN:	9798381165340

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics.
Mao, Yifeng.

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics. - 1 online resource (218 pages)

Source: Dissertations Abstracts International, Volume: 85-06, Section: B.

Thesis (Ph.D.)--University of Colorado at Boulder, 2023.

Includes bibliographical references

Waves and their interactions are ubiquitous in nature. While linear wave equations exhibit a superposition principle, nonlinear wave equations generally do not. Previous research has delved into the mathematics of solitary waves (solitons), dispersive shock waves, and their interactions within the field of dispersive hydrodynamics. However, a more complicated class of problems, including periodic traveling waves and their interactions across multiple phases, presents a rich and physically meaningful area that motivates further investigation. Inspired by this, the primary objective of this thesis is the mathematical and experimental study of nonlinear wave interactions, starting from the generation and propagation of one-phase periodic traveling waves and extending to their two-phase interactions with solitons and with one another.The thesis focuses on multiscale nonlinear wave phenomena within a dispersive hydrodynamic framework in which waves in fluid and fluid-like systems are subject to dispersion that dominates dissipation. The research combines analytical and asymptotic techniques, numerical simulations, and experimental observations. Of particular interest in the thesis are the linear and nonlinear wave dynamics in two specific equations: the Korteweg-De Vries (KdV) equation and the conduit equation. The KdV equation is a well-known model for weakly nonlinear surface waves in shallow water. Meanwhile, the conduit equation serves as a model for nonlinear interfacial wave dynamics in a viscous two-fluid core-annular flow, where a pressure-driven core fluid is within an annulus of another miscible, heavier fluid with a small viscosity ratio between the two. The study begins with one-phase periodic traveling waves by deriving the exact dispersion relation for linear interfacial waves in the two-fluid Stokes equations and comparing them with experiments. The radiation condition for the wavemaker problem in physics that selects the unique outgoing wave is mathematically proved using a new asymptotic approach. Nonlinear periodic traveling waves in the core-annular flow system are experimentally characterized. Subsequently, experimental and theoretical investigation of nonlinear interactions between solitons and periodic traveling waves is undertaken, resulting in the emergence of traveling breathers. Special cases involving two-phase periodic wave interactions are theoretically described using an asymptotic approach called Whitham modulation theory.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2024

Mode of access: World Wide Web

ISBN: 9798381165340Subjects--Topical Terms:

1069907
Applied mathematics.
Subjects--Index Terms:

Dispersive hydrodynamicsIndex Terms--Genre/Form:

554714
Electronic books.

Two-Phase Wave Interactions and Periodic Wavemaker Problem in Dispersive Hydrodynamics.
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520 $a Waves and their interactions are ubiquitous in nature. While linear wave equations exhibit a superposition principle, nonlinear wave equations generally do not. Previous research has delved into the mathematics of solitary waves (solitons), dispersive shock waves, and their interactions within the field of dispersive hydrodynamics. However, a more complicated class of problems, including periodic traveling waves and their interactions across multiple phases, presents a rich and physically meaningful area that motivates further investigation. Inspired by this, the primary objective of this thesis is the mathematical and experimental study of nonlinear wave interactions, starting from the generation and propagation of one-phase periodic traveling waves and extending to their two-phase interactions with solitons and with one another.The thesis focuses on multiscale nonlinear wave phenomena within a dispersive hydrodynamic framework in which waves in fluid and fluid-like systems are subject to dispersion that dominates dissipation. The research combines analytical and asymptotic techniques, numerical simulations, and experimental observations. Of particular interest in the thesis are the linear and nonlinear wave dynamics in two specific equations: the Korteweg-De Vries (KdV) equation and the conduit equation. The KdV equation is a well-known model for weakly nonlinear surface waves in shallow water. Meanwhile, the conduit equation serves as a model for nonlinear interfacial wave dynamics in a viscous two-fluid core-annular flow, where a pressure-driven core fluid is within an annulus of another miscible, heavier fluid with a small viscosity ratio between the two. The study begins with one-phase periodic traveling waves by deriving the exact dispersion relation for linear interfacial waves in the two-fluid Stokes equations and comparing them with experiments. The radiation condition for the wavemaker problem in physics that selects the unique outgoing wave is mathematically proved using a new asymptotic approach. Nonlinear periodic traveling waves in the core-annular flow system are experimentally characterized. Subsequently, experimental and theoretical investigation of nonlinear interactions between solitons and periodic traveling waves is undertaken, resulting in the emergence of traveling breathers. Special cases involving two-phase periodic wave interactions are theoretically described using an asymptotic approach called Whitham modulation theory.
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