Concentration and depth fields

Concentration and depth fields determined by the light transmitted through a dyed solution

By CLAUDIA CENEDESE^1,2AND STUART DALZIEL¹

¹ Department of Applied Mathematics and Theoretical Physics,The University of Cambridge, Silver Street, Cambridge CB3 9EW, UK

² Physical Oceanography Department, Woods Hole Oceanographic Institution, Woods Hole, MA 02543, USA.

Abstract

In this paper we analyse a method to determine the dye concentration and the depth of a dyed solution by measuring the reduction in the intensity of light transmitted through the dyed solution, as compared to that transmitted through a clear solution. In other contexts the basis of this technique is often referred to as "optical thickness" and gives a measure of the average concentration of the dye over the whole fluid thickness h. However, for layered fluid flows, we may instead measure the depth of a layer by marking one layer with a uniform concentration of dye so that the attenuation due to the dye is confined to that layer and thus measurements of the optical thickness give the depth of the dyed layer. In this paper we present a detailed description of procedures required to derive the dye concentration (averaged along light rays) from an intensity field, and, ultimately, the thickness of the dyed layer. A number of new techniques to improve the accuracy and reliability of these measurements are also introduced. Finally the technique is illustrated with measurements of baroclinic vortices over a slope.

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