Rotating annulus experiments to study the beta-effect in atmospheric dynamics

在旋转环形实验中，我们研究了锥形底地形的β效应，发现当锥形底坡度为0.4时，波数为2的气流按准地转位涡方程传播到层结层中，其漂移速度比平底时低。在这项研究中，我们追求在波数为1和轴对称流中获得更明显的β效应，因为理论上已知波数越低，垂直波传播越强。由于很难产生波数为1的流动，我们研究了轴对称流动。为了测量纬向速度的垂直依赖性，这里发现了一个非常有用的方法：一个绿色激光片垂直地投射在环的中半径处，并从侧面拍摄垂直片的视频图像。因此，我们可以得到比波数2流动更好的β效应。为了直接观察垂直流动，我们还向水中注入几滴铀溶液，并将卤素光片垂直地和水平地投射，我们可以得到铀的曲线图，以表示流动的拉格朗日轨迹。从观察到的线的形状，我们可以理解，在圆锥形底部中的锥形流的向上垂直分量明显比在平的底部中强。为了进行这项研究，我们访问了几个研究所，如埃因霍温的技术大学，给他们讲我们的实验，并看到他们的实验。在那里，我们可以得到有用的信息，特别是在技术方面，激光片可用于拍摄PIV分析的视频图像：墨水等染料非常有助于可视化非常缓慢的流动，并且在理论方面，它们支持我们的想法，即使在斜压层中，圆锥形底部也会引起地形β效应。

In the rotating annulus experiments, we have studied the topographic beta-effect with the use of a conical bottom and found so far that when the slope of the conical bottom is set 0.4, the wavenumber-2 flow propagates into the stratified layer according to the quasi-geostrophic potential vorticity equation and has a lower drift velocity than in the case of the flat bottom. In this research, we pursued to get more evident beta-effect in the wavenumber-1 and axisymmetric flows because the vertical wave propagations are theoretically known to be stronger as wavenumber is lower. Because it was found very difficult to produce the wavenumber-1 flow, we studied the axisymmetric flow. To measure the vertical dependence of the zonal velocities, here was found a very useful method: a green laser light sheet is projected vertically at the mid-radius of the annulus and video pictures of the vertical sheet are taken from the side. Thus, we could get a dearer beta-effect than in the wavenumber-2 flows. To see directly the vertical flow, furthermore, injecting several drops of uranine solution into the water and projected the halogen light-sheet vertically and meridionally, we could obtain pictures of curved lines of uranine to represent the Lagrangian trajectories of the flow. From the shapes of the observed lines, we could understand that the upward vertical component of the meridional flow is clearly stronger in the conical bottom than in the flat one.To proceed this study, we visited several institutes such as University of Technology at Eindhoven to give them a talk of our experiments and see their experiments. There we could get useful information, especially that in the technical points, a laser light sheet is available for taking the video pictures of PIV analysis: dye such as ink is very helpful to visualize very slow flows and in the theoretical points, they supported our idea that even in the baroclinic layer the conical bottom would cause the topographic beta-effect.