Centred Splash of a Vertical Jet on a Horizontal Rotating Disc: Recent Findings and Resolving Controversies Over the Hydraulic Jump

摘要

Highlights of the asymptotic and numerical analysis of the steady axisymmetric swirl flow of a Newtonian liquid over a spinning disc and generated by a jet, impacting perpendicularly onto the latter in the direction of gravity, are presented. Ubiquitous in engineering applications and involving a myriad of disparate velocity and length scales, thus extreme aspect ratios, this flow configuration is an archetypical one for the application of dimensional reasoning and matched asymptotic expansions in fluid dynamics. Particular interest lies on the recent advances in the rigorous description of the thin developed layer relatively far from the jet, which is essentially parametrised by a suitably defined Rossby number, the influence of gravity on the thin film and its interplay with a finitely remote disc edge. The latter upstream influence explains the phenomenon of the hydraulic jump in developed flow. The clarification of long-standing and more recent controversies around this concludes the analysis.