Schlieren visualisation and measurement of axisymmetric disturbances

Synthetic schlieren is a new technique that al- lows one easily and inexpensively to visualise density vari- ations, such as those caused by internal waves propagat- ing in a density stratified fluid. In the special case of two- dimensional internal waves (for example, those created by an oscillating cylinder), synthetic schlieren allows one to measure non-intrusively the wave amplitudes everywhere in space and time. The technique works by measuring the ap- parent displacement of points in a digitised image (such as a grid of horizontal lines), which is observed by a CCD camera through the experimental test section. Synthetic schlieren is sufficiently sensitive that it can measure sub-pixel-scale dis- turbances. In this work, we report on the first step toward measuring fully three-dimensional disturbances. We perform laboratory experiments in which internal waves are generated in a uni- formly salt-stratified fluid by a vertically oscillating sphere. Theory predicts that the resulting wave-field is in the form of two cones emanating above and below the sphere. Using inverse tomographic techniques, we exploit the axisymmetry of the wave-field to relate the apparent displacement of pix- els in an image to the wave amplitudes. tioning of the mirrors, and the sensitivity to optical imper- fections on the mirror surface and test section of the exper- iment. Furthermore, because mirrors are prone to damage traditional schlieren is prohibitively difficult to employ out- side controlled laboratory conditions. In contrast, "synthetic schlieren" is much less expensive and easier to implement: the field of view can be as large as required to visualise the