An experimental study on an instability of a baroclinic flow caused by a surface cooling in a rotating fluid

通过在气象研究所大型转台上的室内实验、理论研究和数值实验，研究了半无限流体底部圆形区域在旋转框架内冷却时产生的轴对称冷岛环流及其伴随的斜压不稳定波。在室内实验中，利用水箱底部的液晶片可视化水箱底部附近的温度分布，利用PIV（Particle Image velocity meter）测量水平速度的水平分布。结果表明：当基本旋转不存在或较小时，冷岛环流保持轴对称；当它大于一个临界值时，出现周波数为2-3的扰动。随着基本转速的进一步增大，扰动波数增加，流场变得混乱。结果表明，石蒜是最适合于PIV测量的示踪粒子。进一步的理论分析表明，冷岛环流根据无量纲角速度和无量纲分层有三种不同的状态：扩散、重力流和重力波状态。唯一的非线性状态是重力电流状态，并且对于板对称情况总是不稳定的。而对于轴对称情况，当基本旋转较小且变形半径大于冷岛直径时，流动较为稳定。

An axisymmetric cool island circulation that is generated when a circular region of the bottom of a semi-infinite fluid is cooled in a rotating frame and associated baroclinic instability waves are studied by means of a laboratory experiment on the large turntable of the Meteorological Research Institute, a theoretical consideration and a numerical experiment.In the laboratory experiment, a liquid crystal sheet at the bottom of the water tank is used to visualize the temperature distribution near the bottom and PIV(Particle Image Velocimeter) is used to measure the horizontal distributions of the horizontal velocity. The following results are found : When the basic rotation is either absent or small, the cool island circulation remains axisymmetric. When it becomes larger than a critical value, disturbances with circumferential wavenumber 2-3 appear. As the basic rotation is increased further, the wavenumber of the disturbances increase and the flow field becomes chaotic. It is also found that lycopodium is the most suitable tracer particle for PIV measurement.Additional theoretical considerations reveal that the cool island circulation has three different regimes depending on the non-dimensional angular velocity and non-dimensional stratification : Diffusion, gravity current and gravity wave regimes. The only non-linear regime is the gravity current regime, and is always unstable for a slab-symmetric case. For an axisymmetric case, however, the flow is stable when the basic rotation is small and the radius of deformation is larger than the diameter of the cool island.