Heaving Signals in the Isopycnal Coordinate
Dynamical processes in the ocean are directly linked to the density field. Potential temperature (temperature hereafter, unless stated explicitly) and salinity are dynamical tracers; although they can affect the dynamical processes, such effects must go t
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Heaving Signals in the Isopycnal Coordinate
Dynamical processes in the ocean are directly linked to the density field. Potential temperature (temperature hereafter, unless stated explicitly) and salinity are dynamical tracers; although they can affect the dynamical processes, such effects must go through the link of density. In fact, the concept of heaving can be more rigorously defined in the density coordinate, or the isopycnal coordinate. Most importantly, for the largescale oceanic circulation and climate problems potential density is monotonic in the vertical direction; thus, it is an ideal alternative vertical coordinate. In this chapter we explore using potential density as the Lagrangian coordinate to identify heaving signals in the world oceans.
5.1
Introduction
Density has been used as a vertical coordinate in many previous studies in physical oceanography. There are many potential candidates, such as the in situ density, potential density, and the socalled neutral density. Depending on the specific focus, some of the desirable properties of a density used as the vertical coordinate include: (1) It is monotonic, so that a one-to-one transformation between the geopotential height coordinate and the isopycnal coordinate can be easily carried out. (2) It conserves the local vertical and horizontal stratification, so that dynamical processes can be described accurately in this coordinate.
(3) It is a conserved property, so that water parcels stay on the same coordinate surface during three-dimensional adiabatic movements in the ocean. Although it seems easy to satisfy these requirements, there is no isopycnal coordinate that can satisfy all these constraints. Searching a good isopycnal coordinate as a vertical coordinate has been a long and winding road in the history of oceanography. At first, the in situ density q ¼ qðS; T; pÞ seems a convenient choice; however, it is not a conserved quantity. In fact, the in situ density increases rapidly with pressure; a large part of this change is due to the increase of in situ pressure with depth. Increase of in situ density with pressure is mostly inert in terms of dynamics; as a result, in situ density cannot be used as a vertical coordinate. Montgomery’s (1938) pioneering work on water mass analysis was based on the rt surface. However, by definition, rt ¼ qðS; T; p ¼ 0Þ (where q is density, S is salinity, T is the in situ temperature, and p is pressure) is not a conserved quantity. Although Montgomery called his method isentropic analysis, what he used is not an isentropic surface. In fact, this density variable is no longer used in oceanography. In order to overcome problems associated with in situ density, potential density was introduced in dynamical oceanography, e.g., HellandHansen (1912). The potential density surface
© Higher Education Press and Springer Nature Singapore Pte Ltd. 2020 R. X. Huang, Heaving, Stretching and Spicing Modes, https://doi.org/10.1007/978-981-15-2941-2_5
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rp ¼ qðS; h; pr Þ (where h is potential temperature, pr is reference
