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Parametric Forcing of Confined and S...

Yalim, Jason.

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Parametric Forcing of Confined and Stratified Flows.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Parametric Forcing of Confined and Stratified Flows./
Author:	Yalim, Jason.
Published:	Ann Arbor : ProQuest Dissertations & Theses, : 2019,
Description:	193 p.
Notes:	Source: Dissertations Abstracts International, Volume: 80-11, Section: B.
Contained By:	Dissertations Abstracts International80-11B.
Subject:	Applied Mathematics. -
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13860192
ISBN:	9781392136904

Parametric Forcing of Confined and Stratified Flows.
Yalim, Jason.

Parametric Forcing of Confined and Stratified Flows. - Ann Arbor : ProQuest Dissertations & Theses, 2019 - 193 p.

Source: Dissertations Abstracts International, Volume: 80-11, Section: B.

Thesis (Ph.D.)--Arizona State University, 2019.

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

A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations.The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.

ISBN: 9781392136904Subjects--Topical Terms:

1669109
Applied Mathematics.
Subjects--Index Terms:

Bifurcation

Parametric Forcing of Confined and Stratified Flows.
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100 1 $a Yalim, Jason. $3 3545192
245 1 0 $a Parametric Forcing of Confined and Stratified Flows.
260 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 193 p.
500 $a Source: Dissertations Abstracts International, Volume: 80-11, Section: B.
500 $a Publisher info.: Dissertation/Thesis.
500 $a Includes supplementary digital materials.
500 $a Advisor: Welfert, Bruno D.;Lopez, Juan M.
502 $a Thesis (Ph.D.)--Arizona State University, 2019.
506 $a This item must not be sold to any third party vendors.
520 $a A continuously and stably stratified fluid contained in a square cavity subjected to harmonic body forcing is studied numerically by solving the Navier-Stokes equations under the Boussinesq approximation. Complex dynamics are observed near the onset of instability of the basic state, which is a flow configuration that is always an exact analytical solution of the governing equations. The instability of the basic state to perturbations is first studied with linear stability analysis (Floquet analysis), revealing a multitude of intersecting synchronous and subharmonic resonance tongues in parameter space. A modal reduction method for determining the locus of basic state instability is also shown, greatly simplifying the computational overhead normally required by a Floquet study. Then, a study of the nonlinear governing equations determines the criticality of the basic state's instability, and ultimately characterizes the dynamics of the lowest order spatial mode by the three discovered codimension-two bifurcation points within the resonance tongue. The rich dynamics include a homoclinic doubling cascade that resembles the logistic map and a multitude of gluing bifurcations.The numerical techniques and methodologies are first demonstrated on a homogeneous fluid contained within a three-dimensional lid-driven cavity. The edge state technique and linear stability analysis through Arnoldi iteration are used to resolve the complex dynamics of the canonical shear-driven benchmark problem. The techniques here lead to a dynamical description of an instability mechanism, and the work serves as a basis for the remainder of the dissertation.
590 $a School code: 0010.
650 4 $a Applied Mathematics. $3 1669109
650 4 $a Mathematics. $3 515831
653 $a Bifurcation
653 $a Computational mathematics
653 $a Dynamical systems
653 $a Fluid dynamics
653 $a Parametric resonance
653 $a Stratified flows
690 $a 0364
690 $a 0405
710 2 $a Arizona State University. $b Mathematics. $3 3433211
773 0 $t Dissertations Abstracts International $g 80-11B.
790 $a 0010
791 $a Ph.D.
792 $a 2019
793 $a English
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=13860192