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The Geometry of Neutral Paths

机译：中性路径的几何

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Caratheodory's axiomatic development of thermodynamics is applied here to the thermohaline circulation of the ocean. The helicity of the differential form dD for the density change in an isentropic and isohaline ascent, relative to the change in the water column, does not vanish since the ratio of the thermal and haline compressibilities is a function of pressure. The form for relative density consequently lacks an integrating denominator and so there are no surfaces of constant relative density, or so-called neutral surfaces (McDougall and Jackett). As a consequence of a remarkable theorem (Caratheodory), any two points in the thermohaline state space or equivalently in the real space of the ocean are mutually accessible, in the sense that they can be joined by a neutral path. Many of the paths between any two points and possibly all may only be piecewise smooth. The theorem is supported here with analytical examples of neutral paths in state space, and a numerical example of an idealized ocean in real space, for all of which the seawater obeys a relatively simple equation of state. The existence of multiple neutral paths for pairs of close points is explicitly demonstrated. Some such neutral paths take large excursions throughout state space and throughout the ocean basin. The implications for hydrography and for ocean modeling are discussed.
机译：Caratheodory在热力学方面的公理发展被应用到海洋的热盐环流中。相对于水柱的变化，等熵线和等盐线上升中密度变化的微分形式dD的螺旋度不会消失，因为热和盐酸盐压缩率的比值是压力的函数。因此，相对密度的形式缺少积分分母，因此没有恒定相对密度的表面或所谓的中性表面（McDougall和Jackett）。由于一个非同寻常的定理（Caratheodory）的结果，在热盐状态空间中或等效地在海洋的真实空间中的任何两个点都是可以相互访问的，因为它们可以通过中性路径连接。任何两点之间的许多路径（可能全部都是路径）可能只是分段平滑的。该定理在这里得到状态空间中性路径的分析示例以及实际空间中理想化海洋的数值示例的支持，所有这些海水都服从相对简单的状态方程。明确证明了成对的闭合点有多个中性路径。一些这样的中性路径会在整个国家空间和整个海盆中进行大量游览。讨论了水文学和海洋建模的意义。

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