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实验室实验、理论考虑和数值实验，研究了半无限大流体底部圆形区域在旋转坐标系中冷却时产生的轴对称冷岛环流及其相关的斜压不稳定波。在实验室实验中，水箱底部的液晶片用于显示底部附近的温度分布，PIV(粒子图像测速仪)用于测量水平速度的水平分布。结果表明：当基本自转不存在或较小时，冷岛环流仍保持轴对称；当它大于一个临界值时，出现了周向波数为2-3的扰动。随着基本旋转的进一步增加，扰动的波数增加，流场变得混沌。此外，理论分析还表明，冷岛环流有三种不同的区域，这取决于无因次角速度和无因次层结：扩散、重力流和重力波区域。唯一的非线性区域是重力流区域，并且对于板对称的情况总是不稳定的。然而，对于轴对称情况，当基本旋转较小时，变形半径大于冷岛直径时，流动是稳定的。

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.