The effect of noise and sampling size on vorticity measurements in rotating fluids

This paper describes a new technique for presenting information based on given flow images. Using a multistep first order differentiation technique, we are able to map in two dimensions, vorticity of fluid within a region of investigation. We can then present the distribution of this property in space by means of a color intensity map. In particular, the state of fluid rotation can be displayed using maps of vorticity flow values. The framework that is implemented can also be used to quantify the vortices using statistical properties which can be derived from such vorticity flow maps. To test our methodology, we have devised artificial vortical flow fields using an analytical formulation of a single vortex. Reliability of vorticity measurement from our results shows that the size of flow vector sampling and noise in flow field affect the generation of vorticity maps. Based on histograms of these maps, we are able to establish an optimised configuration that computes vorticity fields to approximate the ideal vortex statistically. The novel concept outlined in this study can be used to reduce fluctuations of noise in a vorticity calculation based on imperfect flow information without excessive loss of its features, and thereby improves the effectiveness of flow.