A unified linear theory of homogeneous and stratified rotating fluids
A unified linear theory of homogeneous and stratified rotating fluids
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均匀和分层旋转流体的统一线性理论
DOI：
10.1017/s0022112067001053
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发表时间：
1967
影响因子：
3.7
通讯作者：
J. Pedlosky
中科院分区：
文献类型：
--
作者：
V. Barcilon;J. Pedlosky
给出了给定任意分层下旋转流体线性动力学的统一图像。研究了均质流体理论$\sigma S < E^{\frac{2}{3}}$和强分层流体理论σS > E 1 / 2的有效范围以外的分层范围，其中σS = vαgΔT/κΩ2L, E =v/ΩL2。通过对中间区域E2/3 < σS < e1 / 2的详细研究，阐明了从一种动力学向另一种动力学的转变。结果表明，在这一中间分层范围内，除了存在埃克曼层的水平边界附近外，动力学与两种极端情况不同。特别是侧壁边界层呈现三重结构，由(i)厚度为(σS)−1/4 e1 / 2的浮力亚层（其中粘性力和浮力平衡），（ii）厚度为（σS） 1/ 2的中间流体静力斜压层和（iii）类似于均匀流体中的外层e1 /4层组成。内部动力主要受ekman层吸力控制，但表现出混合动力特征；特别地，动力场可以分解为满足泰勒-普罗德曼定理的“齐次分量”和满足热风关系的斜压“分层分量”。在所有区域中都详细显示了流的结构。
A unified picture of the linear dynamics of rotating fluids with given arbitrary stratification is presented. The range of stratification which lies outside the region of validity of both the theories of homogeneous fluids, $\sigma S < E^{\frac{2}{3}}$ and the strongly stratified fluids, σS > E½, is studied, where σS = vαgΔT/κΩ2L and E =v/ΩL2. The transition from one dynamics to the other is elucidated by a detailed study of the intermediate region E2/3 < σS < E½. It is shown that, within this intermediate stratification range, the dynamics differs from that of either extreme case, except in the neighbourhood of horizontal boundaries where Ekman layers are present. In particular the side wall boundary layer exhibits a triple structure and is made up of (i) a buoyancy sublayer of thickness (σS)−1/4 E½ in which the viscous and buoyancy forces balance, (ii) an intermediate hydrostatic, baroclinic layer of thickness (σS)½ and (iii) an outer E¼-layer which is analogous to the one occurring in a homogeneous fluid. In the interior, the dynamics is mainly controlled by Ekman-layer suction, but displays hybrid features; in particular the dynamical fields can be decomposed into a ‘homogeneous component’ which satisfies the Taylor-Proudman theorem, and into a ‘stratified component’ which is baroclinic and which satisfies a thermal wind relation. In all regions the structure of the flow is displayed in detail.