On the refracted patterns produced by liquid vortices

A theoretical analysis of the refracted shadows produced by steady and time-decaying liquid vortices under uniform illumination from above is given in this article. An expression for the induced shadow intensity is derived and found to be a function of the vortex's free surface profile, i.e., function of the static pressure distribution. The patterns for different focusing depth are given and compared with previous visualization results from the literature. The phenomenon is examined and illustrated as a bench mark case by using both steady and time-decaying algebraic vortex models. However, this study can be extended to check the feasibility of recovering the main flow properties by analyzing the luminous image intensity of the refracted patterns. The present analysis is valid only when the swirl velocity is order of magnitude higher than the meridional flow components and the vorticity is concentrated within the core region and of intense conditions.