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Free Content Streamfunctions for the lateral velocity vector in a compressible ocean

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Streamfunctions are known in (i) geopotential surfaces, (ii) isobaric surfaces, (iii) surfaces of constant in situ density, , and (iv) surfaces of constant steric anomaly, . lt is desirable to map a streamfunction in a surface in which most of the mixing and movement of water-masses occurs so that the streamlines obtained in two dimensions will approximate the flow paths of the full three-dimensional flow field. These surfaces are believed to be neutral surfaces, but while a streamfunction exists in a neutral surface, we do not as yet have a closed expression for it in terms of a vertical integral of hydrographic quantities, and quite possibly we never will. An error analysis performed on the use of the Montgomery function (acceleration potential) in a neutral surface shows that the typical error at a depth of 1000 m is about 2 mm/s. To reduce the velocity error below 0.5 mm/s at 1000 m, one would need to map the Montgomery function in a surface that differed in slope from a steric anomaly surface by less than 5 × 10–6. An error analysis is also performed on the approximate Bernoulli function that is found by integrating gzi∂/∂z in the vertical, showing that errors in this Bernoulli function over a depth range of 1000 m are equivalent to a lateral velocity error of 3 mm/s. These examples demonstrate that great care must be taken in calculating a streamfunction in any surface in which an exact expression is unknown. Expressions for the relative slopes of several surfaces (surfaces of constant pressure, steric anomaly surfaces and neutral surfaces) are also derived.

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Document Type: Research Article

Publication date: May 1, 1989

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  • The Journal of Marine Research, one of the oldest journals in American marine science, publishes peer-reviewed research articles covering a broad array of topics in physical, biological and chemical oceanography. Articles that deal with processes, as well as those that report significant observations, are welcome. Biological studies involving coupling between ecological and physical processes are preferred over those that report systematics. The editors strive always to serve authors and readers in the academic oceanographic community by publishing papers vital to the marine research in the long and rich tradition of the Sears Foundation for Marine Research. We welcome you to the Journal of Marine Research.
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