Some remarks on the initiation of inertial Taylor columns
Some remarks on the initiation of inertial Taylor columns
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DOI：
10.1017/s0022112075000377
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发表时间：
1975-01
影响因子：
3.7
通讯作者：
H. Huppert
中科院分区：
文献类型：
--
作者：
H. Huppert
考虑在绕垂直z轴快速旋转的两个水平面中较低平面上放置的障碍物上方的准地转流。在假设障碍物上游远处的流是均匀的，大小为V之后，在粘性消失的极限情况下计算流场。将均匀流中出现的效应与分层流中出现的效应进行比较。如果流是均匀的，当\[h_0R^{-1} > \min_r\left[r\left/\int_0^r xh(x)dx\right. \right]\]时，存在一个闭合流线区域，其中假设障碍物是圆柱对称的，由\(z = Hh_0h(r/L)\)给出，\(H\)是平面之间的距离，\(R\)是罗斯贝数\(V/(fL)\)。对于任何障碍物，（1）式的右侧大于零，因此对于出现闭合流线区域，\(h_0\)必须为正。通过一个具体例子进行论证和说明，由于（1）式涉及\(h(x)\)的积分，对于高度小于临界高度的障碍物，可以通过考虑平顶障碍物的特殊情况来获得具有代表性的流型，正如英格索尔（1969）所做的那样。如果流是具有恒定布伦特 - 维萨拉频率\(N\)的分层流，闭合流线存在的条件被证明是\[h_0R^{-1} > \min_r \left[B\int_0^{\infty}\int_0^{\infty}xt\cot h(Bt)h(x)J_0(tx)J_1(tr)\,dt\,dx \right]^{-1}\]，其中\(B = NH/fL\)。与均匀情况相反，（2）式的右侧可以为零，如果障碍物在某处是垂直的就是这种情况。这样的障碍物无论其高度多小都会产生一个闭合流线区域，因此不会导致代表光滑障碍物的流型。这是因为分层的流体柱不能在无穷小的距离上被拉伸或压缩。相反，流体柱明显弯曲，流体绕过障碍物流动。计算并讨论了一些特定障碍物的临界条件（1）和（2）。
The quasi-geostrophic flow over an obstacle placed on the lower of two horizontal planes in rapid rotation about the vertical z axis is considered. The flow field is calculated in the limit of vanishing viscosity after assuming the flow far upstream of the obstacle to be uniform, of magnitude V. The effects that occur in homogeneous flow are compared with those that occur in stratified flow. If the flow is homogeneous, there is a region of closed streamlines if \[ h_0R^{-1} > \min_r\left[r\left/\int_0^r xh(x)dx\right. \right], \] where the obstacle is assumed to be cylindrically symmetric and given by z = Hh0h(r/L), H is the distance between the planes and R is the Rossby number V/(fL). For any obstacle the right-hand side of (1) is greater than zero and hence h0 must be positive for a closed-streamline region to occur. It is argued, and illustrated by a particular example, that because (1) involves an integral of h(x) a representative flow pattern can be obtained for obstacles of less than critical height by considering the special case of a flat-topped obstacle, as is done by Ingersoll (1969). If the flow is stratified with constant Brunt-Väisälä frequency N, the condition for the existence of closed streamlines is shown to be \[ h_0R^{-1} > \min_r \left[B\int_0^{\infty}\int_0^{\infty}xt\cot h(Bt)h(x)J_0(tx)J_1(tr)\,dt\,dx \right]^{-1}, \] where B = NH/fL. In contrast to the homogeneous situation, the right-hand side of (2) can be zero and is so if the obstacle is somewhere vertical. Such obstacles will produce a closed-streamline region no matter now small their height and will hence not lead to patterns representative of smooth obstacles. This is because a stratified column of fluid cannot be stretched or compressed over an infinitesimal distance. Instead, the column bends markedly and the fluid flows around the obstacle. The critical conditions (1) and (2) for a number of specific obstacles are calculated and discussed.