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

小行星9424355 在这项研究中，我们调查的统计特性的被动标量耦合到一个二维（2D）的脉动速度场。 实验对象是一个独立的肥皂膜，这是由一个二维库埃特细胞驱动。 二维库埃特细胞，这是最近在我们的实验室开发的，可以精确控制流体动力学流动和各种流动不稳定性的表征。 我们早期的实验表明，驱动肥皂膜在其厚度上表现出强烈的时空波动。 一个简单的计算表明，这些波动可以被视为一个被动标量和粘性“扩散”的子范围是广泛的，由于在小的长度尺度急剧截止。 我们打算使用真实的空间成像技术测量波动的谱密度作为波数的函数。 此外，时空波动的速度场将使用一种新型的光纤测速仪测量。 我们希望在具有不同程度随机分量的流动中建立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，这门学科对气象学、海洋学和各种实验室实验都很重要。 这项研究是面向一个被动标量的理解，如染料或温度，对流施加的波动速度分布在两个维度。 我们以前的实验已经表明，一个独立的肥皂膜的行为像一个二维流体，和膜厚度的波动的时空行为的速度分布的影响。 一个简单的理论分析表明，如果厚度的波动远远小于平均厚度，那么波动可以被视为被动标量。 我们将使用视频成像技术， 提取膜厚度在空间和时间上的统计特性，并将它们与所施加的2D速度分布相关联。 本研究 将丰富我们对 二维流体动力学波动，并有助于完善理论模型。 ***

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. ***