Hydrodynamic Convection of a Passive Scalar in a Two-Dimensional Couette Flow

二维库埃特流中被动标量的水动力对流

• 批准号: 9424355
• 负责人: Xiao-Lun Wu
• 金额: $ 15万
• 依托单位: University of Pittsburgh
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 1995
• 资助国家: 美国
• 起止时间: 1995-08-01 至 1999-02-28
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=9424355&HistoricalAwards=false
• 关键词: Hydrodynamic; Convection; Passive; Scalar; Two

9424355 Wu In this research we investigate statistical properties of a passive scalar coupled to a two-dimensional (2D) fluctuating velocity field. The experimental object is a free-standing soap film which is driven by a 2D Couette cell. The 2D Couette cell, which has recently been developed in our laboratory, allows precise control of hydrodynamic flow and characterization of various flow instabilities. Our early experiments have shown that a driven soap film exhibits strong spatiotemporal fluctuations in its thickness. A simple calculation suggests that these fluctuations can be treated as a passive scalar and that the viscous-"diffusion" subrange is extensive due to a sharp cutoff at small length scales. We intend to measure the spectral density of the fluctuations as a function of wavenumber using a real- space imaging technique. In addition, the spatiotemporal fluctuations of the velocity field will be measured using a novel fiber-optical velocimeter. We wish to establish correlations between the spectral densities of the velocity field and the passive thickness field in flows with different degrees of stochastic components. %%% Two-dimensional (2D) hydrodynamics and instabilities have largely remained domains for theoretical and computational analysis. However, the subject has great importance for meteorology, oceanography, and a variety of laboratory experiments. This research is geared toward an understanding of a passive scalar, such as dyes or temperature, convected by an imposed fluctuating velocity distribution in two dimensions. Our previous experiments have shown that a free-standing soap film behaves like a 2D fluid, and the fluctuations in film thickness are influenced by the spatiotemporal behavior of the velocity distribution. A simple theoretical analysis indicates that if the fluctuations in the thickness are much less than the average thickn ess, then the fluctuations can be treated as a passive scalar quantity. We will use a video imaging technique to extract statistical properties of the film thickness in space and time and correlate them with the imposed 2D velocity distribution. This research will enrich our general knowledge about hydrodynamic fluctuations in two dimensions and help to refine theoretical models. ***

9424355 Wu 在这项研究中，我们研究了与二维 (2D) 脉动速度场耦合的被动标量的统计特性。 实验对象是由二维库埃特细胞驱动的独立式肥皂膜。 我们实验室最近开发的 2D Couette 池可以精确控制流体动力流动并表征各种流动不稳定性。 我们的早期实验表明，驱动肥皂膜的厚度表现出强烈的时空波动。 简单的计算表明，这些波动可以被视为被动标量，并且由于小长度尺度上的急剧截止，粘性“扩散”子范围很广泛。 我们打算使用实空间成像技术来测量波动的谱密度作为波数的函数。 此外，速度场的时空波动将使用新型光纤速度计进行测量。 我们希望建立具有不同程度随机分量的流中速度场和被动厚度场的谱密度之间的相关性。 %%% 二维 (2D) 流体动力学和不稳定性在很大程度上仍然是理论和计算分析的领域。 然而，该学科对于气象学、海洋学和各种实验室实验非常重要。 这项研究旨在了解被动标量，例如染料或温度，通过二维施加的脉动速度分布进行对流。 我们之前的实验表明，独立式肥皂膜的行为类似于二维流体，并且膜厚度的波动受到速度分布的时空行为的影响。 简单的理论分析表明，如果厚度波动远小于平均厚度，则可以将波动视为被动标量。 我们将使用视频成像技术来提取薄膜厚度在空间和时间上的统计特性，并将它们与施加的二维速度分布相关联。 这项研究将丰富我们关于二维流体动力学波动的一般知识，并有助于完善理论模型。 ***