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

9424355吴在这项研究中，我们研究了与二维起伏速度场耦合的被动标量的统计性质。实验对象是由2D Couette池驱动的自立式肥皂膜。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和表征各种流动不稳定性。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，这些涨落可以被视为一个被动标量，由于在小尺度上的急剧截止，粘性“扩散”子范围是广泛的。我们打算使用实空间成像技术来测量涨落的光谱密度作为波数的函数。此外，还将使用一种新型光纤测速仪测量速度场的时空起伏。我们希望建立具有不同程度随机分量的流动中速度场和被动厚度场的谱密度之间的关联。二维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，这一课题对气象学、海洋学和各种实验室实验都具有重要意义。这项研究的目的是为了理解被动标量，如染料或温度，这些标量是由二维上强制波动的速度分布所驱动的。我们以前的实验已经表明，独立肥皂膜的行为类似于2D流体，并且膜厚度的波动受到速度分布的时空行为的影响。一个简单的理论分析表明，如果厚度的起伏远小于平均厚度，则起伏可视为被动标量。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2D速度分布相关联。这一研究将丰富我们对二维流体动力涨落的一般认识，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. ***