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The route to chaos and turbulence in annular electroconvection.

机译：环形电对流中的混沌和湍流路径。

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摘要

Convection is essential and ubiquitous in Nature. For a century, classical thermal convection, or Rayleigh-Benard convection, has been a central paradigm for laboratory studies. This thesis concerns an electrical analogue of Rayleigh-Benard convection---electroconvection in a thin fluid film. This complementary system was studied with a combination of experiment, theory, and numerical simulation. The fluid film is driven to convect by a critical applied electric potential interacting with a charge inversion, in direct analogy with the buoyancy inversion that drives thermal convection. As the imposed voltage is increased, electroconvection proceeds from steady, laminar patterns through time-dependent flows and eventually into chaotic and turbulent regimes. The experimental procedure consisted of precise measurements of current-voltage (IV) characteristics when a DC voltage was applied to an annular film between two concentric electrodes. The onset of convection was found by a change in the slope of the IV curve; unsteady flow was indicated by a large increase in current fluctuations. From the IV measurements, the corresponding dimensionless charge transport, or Nusselt number Nu, was determined as a function of the electric forcing, characterized by the dimensionless Rayleigh number R . A power-law relationship Nu ∼ Rg was observed in the turbulent convection regime when R≳ 104. The influence of the annular geometry, characterized by aspect ratio Gamma, on this scaling was investigated. A scaling theory was developed which explains the power law and its dependence on Gamma. The corresponding theory for thermal convection does not account for this Gamma dependence. In addition, a direct numerical simulation was constructed using a pseudo-spectral method, based on realistic governing equations. The simulation affords deep insights into the flow dynamics, charge distribution and electric potential of the electroconvection instability and its route to turbulence, including for the case of an externally applied shear.
机译：在自然界中，对流是必不可少的。一个世纪以来，经典的热对流或瑞利-贝纳德对流一直是实验室研究的中心范例。本文涉及流体薄膜中瑞利-贝纳德对流的电模拟---电对流。通过实验，理论和数值模拟的组合研究了这个互补系统。与驱动热对流的浮力反转直接类比，通过与电荷反转相互作用的临界施加电势驱动流体膜对流。随着施加电压的增加，电对流从稳定的层流模式开始，通过时间相关的流动，最终进入混乱和湍流状态。实验步骤包括当在两个同心电极之间的环形膜上施加直流电压时，精确测量电流-电压（IV）特性。对流的发生是通过IV曲线的斜率变化发现的。电流波动大幅度增加表明流量不稳定。从IV测量中，确定相应的无量纲电荷传输或努塞尔数Nu作为电动势的函数，以无量纲瑞利数R为特征。当R＆gsim;时，在湍流对流状态下观察到幂律关系Nu〜Rg。 104.研究了以长宽比Gamma为特征的环形几何形状对这种缩放的影响。提出了定标理论，解释了幂定律及其对伽玛的依赖性。相应的热对流理论并未解决这种伽马依赖性。此外，基于现实的控制方程，使用伪谱方法构建了直接数值模拟。该模拟对电对流不稳定性的流动动力学，电荷分布和电势及其产生湍流的途径提供了深刻的见解，包括外部施加剪切的情况。

著录项

  • 作者

    Tsai, Pei-Chun.;

  • 作者单位

    University of Toronto (Canada).;

  • 授予单位 University of Toronto (Canada).;
  • 学科 Physics Fluid and Plasma.
  • 学位 Ph.D.
  • 年度 2007
  • 页码 149 p.
  • 总页数 149
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类
  • 关键词

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