Schlieren visualisation and measurement of axisymmetric disturbances

Abstract. 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 non-intrusively 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.