Schlieren Visualisation and Measurement of Axisymmetric Disturbances

Synthetic schlieren is a new technique that allows one easily and inexpensively to visualise density variations, such as those caused by internal waves propagating 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 nonintrusively the wave amplitudes everywhere in space and time. The technique works by measuring the apparent 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 disturbances. 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 uniformly 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 pixels in an image to the wave amplitudes.