Repository logo
 

Mathematical methods for fluid-solid interfaces: meandering streams and sand ripples

Simple item page
dc.contributor.authorMertens, Keith, author
dc.contributor.authorPutkaradze, Vakhtang, advisor
dc.date.accessioned2024-03-13T20:12:26Z
dc.date.available2024-03-13T20:12:26Z
dc.date.issued2008
dc.description.abstractThis thesis presents several mathematical methods for modeling free surfaces, interfaces, and fluid-solid interactions. This work is done in the context of two physical systems. In the first two sections, the focus will be to understand the the physics of streams flowing down inclined substrates. Models will be derived to investigate both steady state and dynamic meandering profiles. It will be shown that, through the right approximation techniques, many physical insights can be drawn about this system. These results include: a complete understanding of the steady states, transitions between steady states, mechanism of meandering, forces involved in meandering, and spectral scaling laws of long-time ensemble averaged meandering stream profiles. In the third section, the focus will shift to how one can model underlying physics when it becomes too complicated to address from first principles. Here, the power of symmetries and conservation laws are explored to derive an amplitude equation describing the interface between sand and water when the water is subjected to oscillatory flow. The thesis will then close by posing a novel way to study scaling laws with respect to parameters using Lie's prolongation algorithm. Through this work various tools will be combined from the fields of physics, engineering, applied and pure mathematics to develop approaches for reducing complex systems into tractable pieces which can be studied carefully.
dc.format.mediumborn digital
dc.format.mediumdoctoral dissertations
dc.identifierETDF_Mertens_2008_3321298.pdf
dc.identifier.urihttps://hdl.handle.net/10217/237874
dc.languageEnglish
dc.language.isoeng
dc.publisherColorado State University. Libraries
dc.relation.ispartof2000-2019
dc.rightsCopyright and other restrictions may apply. User is responsible for compliance with all applicable laws. For information about copyright law, please see https://libguides.colostate.edu/copyright.
dc.rights.licensePer the terms of a contractual agreement, all use of this item is limited to the non-commercial use of Colorado State University and its authorized users.
dc.subjectamplitude equations
dc.subjectbraiding patterns
dc.subjectfluid dynamics
dc.subjectfluid-solid interfaces
dc.subjectinclined plane flows
dc.subjectmeandering
dc.subjectsand ripples
dc.subjectmathematics
dc.titleMathematical methods for fluid-solid interfaces: meandering streams and sand ripples
dc.typeText
dcterms.rights.dplaThis Item is protected by copyright and/or related rights (https://rightsstatements.org/vocab/InC/1.0/). You are free to use this Item in any way that is permitted by the copyright and related rights legislation that applies to your use. For other uses you need to obtain permission from the rights-holder(s).
thesis.degree.disciplineMathematics
thesis.degree.grantorColorado State University
thesis.degree.levelDoctoral
thesis.degree.nameDoctor of Philosophy (Ph.D.)

Files

Original bundle
Now showing 1 - 1 of 1
Thumbnail Image
Name:
ETDF_Mertens_2008_3321298.pdf
Size:
1.53 MB
Format:
Adobe Portable Document Format
Download

Collections

2000-2019
Theses and Dissertations