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Traveling Waves in an Inclined Chann...

Yang, Zhao.

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Traveling Waves in an Inclined Channel and Their Stability.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Traveling Waves in an Inclined Channel and Their Stability./
作者:	Yang, Zhao.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
面頁冊數:	222 p.
附註:	Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
Contained By:	Dissertations Abstracts International80-12B.
標題:	Fluid mechanics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13864388
ISBN:	9781392168547

Traveling Waves in an Inclined Channel and Their Stability.
Yang, Zhao.

Traveling Waves in an Inclined Channel and Their Stability. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 222 p.

Source: Dissertations Abstracts International, Volume: 80-12, Section: B.

Thesis (Ph.D.)--Indiana University, 2019.

This item must not be sold to any third party vendors.

The inviscid Saint-Venant equations are commonly used to model fluid flow in an inclined dam or spillway. Several traveling wave solutions are known to the equations. They are for F > 2 the inviscid Dressler roll waves and for F < 2 the hydraulic shock profiles with or without subshocks. This dissertation merges the existence and stability results of these traveling waves obtained by the author and his collaborators in [JNR+18, YZ18, SYZ18]. Chapter one first reviews the construction of these traveling waves. Next, the stability of the inviscid Dressler roll waves is studied in Chapter two where we develop the periodic Evans-Lopatinsky determinant, i.e. a stability function which conveniently addresses the spectral stability study of periodic traveling waves with discontinuous shocks, and a numerical hybrid method to calculate the stability function. With these developments, a complete stability diagram is obtained. The stability of the hydraulic shock profiles is studied in Chapter three where we establish nonlinear H2 ∩ L1 → H2 orbital stability with sharp rates of decay in Lp, p ≥ 2, of hydraulic shock profiles with/ without subshocks under the assumption of spectral stability. Instead of verifying the assumption conventionally by numerical methods, we prove spectral stability by reducing the eigenvalue problem to a generalized Sturm-Liouville eigenvalue problem and investigating the spectra of the generalized eigenvalue problem. The last chapter is a miscellaneous report on the numerics, which includes efficiency of the solver for periodic Evans-Lopatinsky determinant, spectral curves, numerical simulation of the Saint-Venant equations, etc.

ISBN: 9781392168547Subjects--Topical Terms:

528155
Fluid mechanics.
Subjects--Index Terms:

Fluid mechanics

Traveling Waves in an Inclined Channel and Their Stability.
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245 1 0 $a Traveling Waves in an Inclined Channel and Their Stability.
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300 $a 222 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-12, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Advisor: Zumbrun, Kevin.
502 $a Thesis (Ph.D.)--Indiana University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a The inviscid Saint-Venant equations are commonly used to model fluid flow in an inclined dam or spillway. Several traveling wave solutions are known to the equations. They are for F > 2 the inviscid Dressler roll waves and for F < 2 the hydraulic shock profiles with or without subshocks. This dissertation merges the existence and stability results of these traveling waves obtained by the author and his collaborators in [JNR+18, YZ18, SYZ18]. Chapter one first reviews the construction of these traveling waves. Next, the stability of the inviscid Dressler roll waves is studied in Chapter two where we develop the periodic Evans-Lopatinsky determinant, i.e. a stability function which conveniently addresses the spectral stability study of periodic traveling waves with discontinuous shocks, and a numerical hybrid method to calculate the stability function. With these developments, a complete stability diagram is obtained. The stability of the hydraulic shock profiles is studied in Chapter three where we establish nonlinear H2 ∩ L1 → H2 orbital stability with sharp rates of decay in Lp, p ≥ 2, of hydraulic shock profiles with/ without subshocks under the assumption of spectral stability. Instead of verifying the assumption conventionally by numerical methods, we prove spectral stability by reducing the eigenvalue problem to a generalized Sturm-Liouville eigenvalue problem and investigating the spectra of the generalized eigenvalue problem. The last chapter is a miscellaneous report on the numerics, which includes efficiency of the solver for periodic Evans-Lopatinsky determinant, spectral curves, numerical simulation of the Saint-Venant equations, etc.
590 $a School code: 0093.
650 4 $a Fluid mechanics. $3 528155
650 4 $a Mathematics. $3 515831
653 $a Fluid mechanics
653 $a Roll waves
653 $a Shallow water flow
653 $a Stability
653 $a Subshock
653 $a Traveling waves
690 $a 0204
690 $a 0405
710 2 $a Indiana University. $b Mathematics. $3 1036206
773 0 $t Dissertations Abstracts International $g 80-12B.
790 $a 0093
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13864388