A calibrated, non-invasive method for measuring the internal interface height field at high resolution in the rotating, two-layer annulus

We describe a remote sensing method for measuring the internal interface height field in a rotating, two-layer annulus laboratory experiment. The method is non-invasive, avoiding the possibility of an interaction between the flow and the measurement device. The height fields retrieved are accurate and highly resolved in both space and time. The technique is based on a flow visualization method developed by previous workers, and relies upon the optical rotation properties of the working liquids. The previous methods returned only qualitative interface maps, however. In the present study, a technique is developed for deriving quantitative maps by calibrating height against the colour fields registered by a camera which views the flow from above. We use a layer-wise torque balance analysis to determine the equilibrium interface height field analytically, in order to derive the calibration curves. With the current system, viewing an annulus of outer radius 125 mm and depth 250 mm from a distance of 2 m, the inferred height fields have horizontal, vertical and temporal resolutions of up to 0.2 mm, 1 mm and 0.04 s, respectively.

The quasi-nondispersive regimes of long extratropical baroclinic rossby waves over (slowly varying) topography

Actual energy paths of long, extratropical baroclinic Rossby waves in the ocean are difficult to describe simply because they depend on the meridional-wavenumber-to-zonal-wavenumber ratio tau, a quantity that is difficult to estimate both observationally and theoretically. This paper shows, however, that this dependence is actually weak over any interval in which the zonal phase speed varies approximately linearly with tau, in which case the propagation becomes quasi-nondispersive (QND) and describable at leading order in terms of environmental conditions (i.e., topography and stratification) alone. As an example, the purely topographic case is shown to possess three main kinds of QND ray paths. The first is a topographic regime in which the rays follow approximately the contours f/h(alpha c) = a constant (alpha(c) is a near constant fixed by the strength of the stratification, f is the Coriolis parameter, and h is the ocean depth). The second and third are, respectively, "fast" and "slow" westward regimes little affected by topography and associated with the first and second bottom-pressure-compensated normal modes studied in previous work by Tailleux and McWilliams. Idealized examples show that actual rays can often be reproduced with reasonable accuracy by replacing the actual dispersion relation by its QND approximation. The topographic regime provides an upper bound ( in general a large overestimate) of the maximum latitudinal excursions of actual rays. The method presented in this paper is interesting for enabling an optimal classification of purely azimuthally dispersive wave systems into simpler idealized QND wave regimes, which helps to rationalize previous empirical findings that the ray paths of long Rossby waves in the presence of mean flow and topography often seem to be independent of the wavenumber orientation. Two important side results are to establish that the baroclinic string function regime of Tyler and K se is only valid over a tiny range of the topographic parameter and that long baroclinic Rossby waves propagating over topography do not obey any two-dimensional potential vorticity conservation principle. Given the importance of the latter principle in geophysical fluid dynamics, the lack of it in this case makes the concept of the QND regimes all the more important, for they are probably the only alternative to provide a simple and economical description of general purely azimuthally dispersive wave systems.