Stationary bathtub vortices and a critical regime of liquid discharge

Abstract

A modified Lundgren model is applied for the description of stationary bathtub vortices in a viscous liquid with a free surface. Laminar liquid flow through the circular bottom orifice is considered in the horizontally unbounded domain. The liquid is assumed to be undisturbed at infinity and its depth is taken to be constant. Three different drainage regimes are studied: (i) subcritical, where whirlpool dents are less than the fluid depth; (ii) critical, where the whirlpool tips touch the outlet orifice; and (iii) supercritical, where surface vortices entrain air into the intake pipe. Particular attention is paid to critical vortices; the condition for their existence is determined and analysed. The influence of surface tension on subcritical whirlpools is investigated. Comparison of results with known experimental data is discussed.

Burgers–Rott vortices with surface tension

“…1). The basic set of hydrodynamic equations in cylindrical coordinate system can be presented in dimensionless form (see, e.g., [8,6,10]) as: Fig. 1.…”

“…In our recent work [10], the LABSRL-model with surface tension has been reconsidered for whirlpools in a non-rotating vessel. Basic set of equations was re-examined, derived independently, and studied numerically.…”

“…It should be noted that accounting surface tension into the model dramatically increased the complexity of the theoretical and numerical analyses. In [1,2] and [10], the influence of surface tension was numerically calculated for relatively shallow whirlpools, i.e.…”

Control of the intensity of a bathtub vortex by acting on the upstream flow

“…Stepanyants and Yeoh [1] defined three different vortex flow regimes. Subcritical vortices correspond to small dents on the free surface (Fig.…”

“…These studies, like most of the work on the bathtub vortex, focused on the subcritical and critical regimes. Only a few contributions, such as the ones by Stepanyants and Yeoh [1] or Forbes and Hocking [6], dealt with the specific case of the supercritical vortex. In the cowl box, this supercritical regime decreases the draining capabilities of the box and therefore needs to be investigated.…”