Baroclinic waves in a container with sloping end walls
Baroclinic waves in a container with sloping end walls
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具有倾斜端壁的容器中的斜压波
DOI：
10.1098/rsta.1975.0032
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发表时间：
1975
期刊：
影响因子：
--
通讯作者：
Paul Mason
中科院分区：
文献类型：
--
作者：
Paul Mason
实验研究了倾斜上、下边界对差热旋转流体环隙中斜压波的影响。测量了内部温度结构、从轴对称到非轴对称流动的转变、波数和流型、漂移率和传热。倾斜边界对斜压波的影响有两种不同的方式：如果倾斜边界平行，则直接影响斜压波的能量释放机制;如果倾斜边界不平行，则引入类似于行星大气中科里奥利参数纬向变化的效应（3-效应）。为了确定从轴对称流到非轴对称流的过渡结果的基本非线性效应，波数和漂移率与Eady斜压不稳定性的线性扰动理论的适当扩展版本（Hide）进行了比较。在从轴对称流到非轴对称流的过渡的情况下，当考虑到内部温度结构的伴随变化时，得到了与线性理论惊人的良好一致性。在规则波域内，当理论预测值为1、2或3时，方位波数相当一致，但对于较高的预测波数，观测波数较小。在相对倾斜边界的情况下，观测到的相对于平均流的漂移率一般比线性理论的不稳定波的漂移率小30%。当边界以相反的方向倾斜时，也会出现另一个偏离线性理论的情况，即在足够快的旋转速率下，出现两个径向范围有限、波数和漂移速度不同的单独波列;一个波列支配着内圆柱附近的流动，另一个波列支配着外圆柱附近的流动。这一结果表明，科里奥利参数随纬度的变化可以决定斜压波的径向范围。除了其作为流体力学研究的内在兴趣之外，这项工作还涉及到β效应和大尺度地形在大气和海洋等自然系统中所起的作用。它还表明，在较高的旋转速率使用的倾斜eeoopotentials不可避免地存在于以前的实验室实验中的斜压波有重要的影响，特别是解释了以前的理论的失败，占部分的过渡的位置从轴对称到非轴对称流。
The effects of sloping upper and lower boundaries on baroclinic waves in a differentially heated rotating fluid annulus have been studied experimentally. Measurements have been made of the internal temperature structure, the transition from axisymmetric to non-axisymmetric flow, the wave numbers and flow types, the drift rates and the heat transfer. The sloping boundaries influence the baroclinic waves in two distinct ways: if they are parallel the energy releasing mechanism is directly affected, while if they are not parallel effects similar to the latitudinal variation of coriolis parameter in a planetary atmosphere (the (3-effect) are introduced. In order to identify essentially non-linear effects the results on the transition from axisymmetric to non-axisymmetric flow, the wave numbers and the drift rates have been compared with an appropriately extended version (by Hide) of Eady’s linear perturbation theory of baroclinic instability. In the case of the transition from axisymmetric to non-axisymmetric flow, when account was taken of concomitant changes in the internal temperature structure, surprisingly good agreement with linear theory was obtained. Within the regular wave regime, the azimuthal wave numbers agreed quite well when the theoretically predicted value was 1, 2 or 3 but for higher predicted wave numbers the observed wave numbers were smaller. In the case of oppositely sloping boundaries the observed drift rates relative to the mean flow were generally 30 % less than that of the unstable waves of the linear theory. Another departure from the linear theory also occurred when the boundaries sloped in opposite senses, namely the occurrence at sufficiently rapid rotation rates of two separate wave trains of limited radial extent and differing wave numbers and drift speeds; one dominated the flow near the inner cylinder and the other dominated the flow near the outer cylinder. This result suggests that the variation of coriolis parameter with latitude can determine the radial extent of the baroclinic waves. Apart from its intrinsic interest as a fluid-mechanical study this work bears on the role played by the (3-effect and large-scale topography in natural systems such as the atmosphere and oceans. It also shows that at the higher rotation rates used the sloping eeopotentials inevitably present in previous laboratory experiments on baroclinic waves have important effects, and in particular explains the failure of previous theories to account for the position of part of the transition from axisymmetric to non-axisymmetric flow.