상세정보
Export to Refworks부가기능
Selection of Quasi-Stationary States in the 2D Navier-Stokes Equation on the Torus
상세 프로파일
| 자료유형 | 학위논문 |
|---|---|
| 서명/저자사항 | Selection of Quasi-Stationary States in the 2D Navier-Stokes Equation on the Torus. |
| 개인저자 | Cooper, Eric. |
| 단체저자명 | Boston University. Mathematics & Statistics GRS. |
| 발행사항 | [S.l.]: Boston University., 2019. |
| 발행사항 | Ann Arbor: ProQuest Dissertations & Theses, 2019. |
| 형태사항 | 115 p. |
| 기본자료 저록 | Dissertations Abstracts International 81-05B. Dissertation Abstract International |
| ISBN | 9781392404317 |
| 학위논문주기 | Thesis (Ph.D.)--Boston University, 2019. |
| 일반주기 |
Source: Dissertations Abstracts International, Volume: 81-05, Section: B.
Advisor: Beck, Margaret A. |
| 이용제한사항 | This item must not be sold to any third party vendors. |
| 요약 | We consider the two-dimensional Navier-Stokes equation on the (possibly) asymmetric torus, $D_{\\delta}=[0,2\\pi\\delta]\imes[0,2\\pi]$, both with and without stochastic forcing. Absent external force, the vorticity is known to reach a rest state of zero. There exists at least three so called ``quasi-stationary states'' which attract nearby solutions at rates faster than the global decay rate. The system evolves toward one of these three qualitatively different transient states for long times while the system overall tends toward the final rest state. We develop a finite-dimensional model of the associated deterministic vorticity equation to show how the selection of the dominant quasi-stationary state depends on the aspect ratio of the domain, given by $\\delta$. This is followed by formal analysis of the problem as a perturbation from the symmetric domain. Once the selection mechanism for the deterministic model is characterized, stochastic forcing is added to the reduced system. Numerical analysis shows the dominant quasi-stationary state is consistent with what is seen in the deterministic setting. Finally through multiscale averaging methods, the leading order dynamics of the stochastically forced finite-dimensional model for $\\delta$ close to one is studied. As a result we formally obtain leading order asymptotics of statistics of interest, including the selection mechanism. |
| 일반주제명 | Mathematics. |
| 언어 | 영어 |
| 바로가기 | 
: 이 자료의 원문은 한국교육학술정보원에서 제공합니다. |
