• 主题
高级搜索  >
历史搜索 清空历史
首页> 外文学位 >Studies in hydrodynamic stability: Double-diffusive oscillations and explosive gravitational instability of interpenetrating fluids.
【24h】

Studies in hydrodynamic stability: Double-diffusive oscillations and explosive gravitational instability of interpenetrating fluids.

机译：水动力稳定性研究：互穿流体的双扩散振动和爆炸重力失稳。

获取原文
获取原文并翻译 | 示例
页面导航
  • 摘要
  • 著录项
  • 相似文献
  • 相关主题

摘要

This work explores two problems in hydrodynamic stability theory whose primary mathematical distinction is the manner in which unstable equilibria relax to a stable state. The first problem involves a dissipative fluid for which the diffusive relaxation of a linear instability is the primary saturation mechanism. The second problem arises from a conservative system where the relaxation is governed either by linear instabilities or nonlinear interactions among linearly stable modes.; The dissipative problem considers thermohaline convection and the diffusive relaxation of two-dimensional, convectively unstable rolls. For this situation, the disparate diffusion rates of the heat and salt play a crucial role not only in triggering an instability, but also in dictating the nature of the saturation. We study these issues in two particular contexts. In the first case the effect of a nonlinear, basic state salt profile on the bifurcation to instability is examined, and some of the possible patterns in the weakly nonlinear regime are discussed. The second case explores the dynamics of a salt field diffusing so slowly that it does not have time to redistribute itself on the timescale over which the weakly unstable pattern develops. This necessitates a mathematical description that differs from the amplitude equations traditionally employed to capture the nonlinear saturation.; The conservative system comes from astrophysics and cosmology. Motivated by the coexistence of dark and luminous matter in the cosmos, we investigate the instabilities of two interpenetrating fluids that interact only through the gravitational field. The result of primary importance is that negative energy modes may exist if the relative motion is substantial. This fact can have dramatic consequences on the nonlinear stability of the system if linearly stable waves of different energy signature conspire to resonate. In the absence of dissipative forces, the nature of the saturation must be a nonlinear one, and therefore fundamentally differs from the diffusive relaxation involved in the thermohaline problem.; The possible nonlinear dynamics are elucidated within the context of the free-energy principle, the validity of which hinges on the existence of a conserved Hamiltonian functional whose definiteness or indefiniteness reveals the crucial stability information. When the Hamiltonian is indefinite, both positive and negative energy modes can coexist, and a triad of resonant waves may experience explosive instability. The implication of this for structure formation is briefly discussed.; The influence of dissipation on the negative energy modes is also examined. Of primary concern is the condition under which dissipation may render a previously stable system unstable by feeding more negative energy to a negative energy wave. Criteria are presented that describe whether dissipation of various types projects onto the negative energy modes to promote instability, or whether the dissipation in some sense “misses” the negative energy modes and induces their decay by feeding them positive energy.
机译：这项工作探讨了流体动力稳定性理论中的两个问题，它们的主要数学区别是不稳定平衡松弛到稳定状态的方式。第一个问题涉及耗散流体，线性不稳定性的扩散弛豫是其主要的饱和机理。第二个问题来自于一个保守的系统，在该系统中，松弛是由线性不稳定性或线性稳定模式之间的非线性相互作用控制的。耗散问题考虑了热盐对流和二维对流不稳定辊的扩散松弛。对于这种情况，热量和盐的不同扩散速率不仅在引发不稳定性方面起着至关重要的作用，而且在决定饱和度的性质方面也起着至关重要的作用。我们在两种特定情况下研究这些问题。在第一种情况下，检查了非线性基本状态盐分布对分叉至不稳定性的影响，并讨论了弱非线性状态中的一些可能模式。第二种情况探讨了盐场扩散的动力学，它是如此缓慢，以至于它没有时间在弱不稳定模式发展的时间尺度上重新分配自己。这就需要一个不同于传统上用来捕获非线性饱和度的振幅方程的数学描述。保守的系统来自天体物理学和宇宙学。受宇宙中暗物质和发光物质共存的影响，我们研究了仅通过重力场相互作用的两种互穿流体的不稳定性。最重要的结果是，如果相对运动很大，则可能存在负能量模式。如果具有不同能量特征的线性稳定波共鸣，则该事实可能会对系统的非线性稳定性产生重大影响。在没有耗散力的情况下，饱和度的性质必须是非线性的，因此与热盐碱问题所涉及的扩散弛豫从根本上是不同的。在自由能原理的背景下阐明了可能的非线性动力学，其有效性取决于保守的哈密顿函数的存在，该函数的确定性或不确定性揭示了关键的稳定性信息。当哈密顿量是不确定的时，正能量模式和负能量模式都可以共存，并且三振共振波可能会经历爆炸不稳定性。简要讨论了这对于结构形成的意义。还检查了耗散对负能量模式的影响。首先要考虑的情况是，在这种情况下，通过向负能量波提供更多的负能量，耗散可能会使先前稳定的系统不稳定。提出了描述各种类型的耗散是否投射到负能量模式上以促进不稳定性的标准，或者描述了在某种意义上的耗散是否“错过”了负能量模式并通过向它们提供正能量来诱导其衰减的标准。

著录项

  • 作者

    Casti, Alexander Robert Richard.;

  • 作者单位

    Columbia University.;

  • 授予单位 Columbia University.;
  • 学科 Mathematics.; Physics Astronomy and Astrophysics.; Physics Fluid and Plasma.
  • 学位 Ph.D.
  • 年度 1999
  • 页码 144 p.
  • 总页数 144
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 数学;天文学;等离子体物理学;
  • 关键词

相似文献

  • 外文文献
  • 中文文献
  • 专利
获取原文

客服邮箱：kefu@zhangqiaokeyan.com

京公网安备：11010802029741号 ICP备案号：京ICP备15016152号-6 六维联合信息科技 (北京) 有限公司©版权所有

  • 客服微信

  • 服务号