The Ertel potential vorticity theorem for stratified viscous fluids in a rotating system is analyzed herein. A set of ‘‘tracers,’’ that is, materially conserved scalar quantities, and the corresponding Ertel potential vorticities are used to obtain an absolute fluid velocity determination (including both horizontal and vertical components) that generalizes earlier formulations known in the literature within the framework of the beta-spiral method. Potential vorticity fields, respectively, of (i) density, (ii) potential temperature, (iii) salinity, and (iv) the latter’s potential vorticities ratio are analyzed in order to infer properties of steady, or quasi-steady, nonhorizontal or slightly viscous currents. For horizontal flows, general conservative properties of a large class of tracer potential vorticities are found and discussed. These ideas are then applied to various steady cases of physical interest, such as density fronts and thermohaline currents. These arguments, together with observational data, are used to obtain some interesting results, even if the values obtained are affected by large experimental errors. Using this method allows the ratio of the vertical and horizontal components of the velocity field to be estimated with greater certainty. Further insight is also gained into a purely hydrological identification of the no-motion level, a classical difficulty in hydrology.
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