Fluid and Solid Mechanics
Fluid and Solid Mechanics
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流体与固体力学
DOI：
10.1142/9781786340276_0001
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发表时间：
2016
期刊：
影响因子：
--
通讯作者：
Davey M
中科院分区：
文献类型：
--
作者：
Davey M
本章涉及相对于旋转参考系的大规模流体流动的数学建模，其中旋转的影响占主导地位，并且对于主导顺序，存在水平压力梯度和科里奥利力的平衡。主要应用是水平尺度为数十公里或以上、时间尺度为天或以上的海洋和大气流动。此类流动力学的一个基本方程是准地转位涡方程，这是在本章第一部分中推导的，其中分层效应以每层内密度恒定的层的形式包含在内。大尺度的类波行为以罗斯贝波的形式得到支持，并介绍了这些波的一些基本属性。简化的准地转概念模型提供了对动力学过程的理解，并描述了两个例子：海洋旋转和多重平衡。
This chapter concerns mathematical modelling of large-scale fluid flows relative to a rotating frame of reference, for which the effects of rotation are dominant and to leading order there is a balance of horizontal pressure gradients and Coriolis forces. The principal application is to oceanic and atmospheric flows with horizontal scales of tens of kilometres or more, and timescales of days or more. A fundamental equation in the dynamics of such flows is that for quasigeostrophic potential vorticity, and this is derived in the first part of the chapter, with stratification effects included in the form of layers with constant density within each layer. Large-scale wave-like behaviour is supported in the form of Rossby waves, and some basic properties of these waves are presented. Simplified conceptual quasigeostrophic models provide understanding of dynamical processes, and two examples are described: ocean spin-up and multiple equilibria.