# Stationary bathtub vortices and a critical regime of liquid discharge

@article{Stepanyants2008StationaryBV, title={Stationary bathtub vortices and a critical regime of liquid discharge}, author={Yury A. Stepanyants and Guan Heng Yeoh}, journal={Journal of Fluid Mechanics}, year={2008}, volume={604}, pages={77 - 98} }

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…

## 37 Citations

### Burgers–Rott vortices with surface tension

- Physics, Engineering
- 2008

Abstract.A modified Lundgren’s model (the LABSRL model) accounting for the effect of surface tension is applied for the description of stationary bathtub vortices in a viscous liquid with a free…

### Study of stationary vortex with a free surface at the bottom of the orifice flow

- Physics, Engineering
- 2018

ABSTRACT Theoretical investigations are conducted to study the structure of stationary vortex with a free surface at the bottom of the orifice flow. A modified Lundgren-like model has come up to…

### Experimental study on unstable free surface vortices and gas entrainment onset conditions

- Environmental Science, Physics
- 2014

### An analytical model for vortex at vertical intakes

- Physics, EngineeringWater Supply
- 2021

In the present paper, free surface vortex formation at intakes is investigated analytically. By assuming a spiral form for vortex streamlines, continuity and momentum equations were integrated and…

### Free surface intake vortices: theoretical model and measurements

- Physics
- 2014

ABSTRACT Axially stretched free-surface vortices occur at low-head hydropower intakes under specific flow and geometric conditions. When they are sufficiently strong, they can harm performance or…

### Origin of the Bathtub Vortex and Its Formation Mechanism

- Physics
- 2012

The generation and subsequent development of the bathtub vortex appearing in a cylindrical vessel are numerically investigated in order to clarify its origin and the mechanism to determine the…

### Structure of a steady drain-hole vortex in a viscous fluid

- PhysicsJournal of Fluid Mechanics
- 2010

We use direct numerical simulations to study a steady bathtub vortex in a cylindrical tank with a central drain-hole, a flat stress-free surface and velocity prescribed at the inlet. We find that the…

### Understanding turbulent free-surface vortex flows using a Taylor-Couette flow analogy

- Physics, EngineeringScientific Reports
- 2017

Using Rayleigh’s stability criterion, it is analytically show that a wall bounded free-surface vortex can indeed become unstable due to a centrifugal driving force in a similar manner to the Taylor-Couette flow.

### Study of air-core vortical flow structure induced by a plughole vortex

- EngineeringJournal of Fluid Mechanics
- 2017

This paper describes a study of the generation of a plughole vortex and its consequences in a drainpipe during drainage of water from a stationary rectangular tank. The critical and minimum depths of…

### Scattering of surface shallow water waves on a draining bathtub vortex

- Physics, Environmental SciencePhysical Review Fluids
- 2019

In the linear approximation we study long wave scattering on an axially symmetric flow in a shallow water basin with a drain in the center. This classical problem can be considered as a model of wave…

## References

SHOWING 1-10 OF 41 REFERENCES

### Burgers–Rott vortices with surface tension

- Physics, Engineering
- 2008

Abstract.A modified Lundgren’s model (the LABSRL model) accounting for the effect of surface tension is applied for the description of stationary bathtub vortices in a viscous liquid with a free…

### The bath-plug vortex

- Engineering, PhysicsJournal of Fluid Mechanics
- 1995

Steady flow with constant circulation into a vertical drain is considered. The precise details of the outflow are simplified by assuming that the drain is equivalent to a distributed volume sink,…

### The bathtub vortex in a rotating container

- PhysicsJournal of Fluid Mechanics
- 2006

We study the time-independent free-surface flow which forms when a fluid drains out of a container, a so-called bathtub vortex. We focus on the bathtub vortex in a rotating container and describe the…

### An impulsive bathtub vortex

- Physics
- 2005

The impulsive free-surface flow due to a point sink at the bottom of a container with rotating inviscid fluid is investigated analytically by a small-time expansion. Before the sink is turned on…

### Anatomy of a bathtub vortex.

- PhysicsPhysical review letters
- 2003

The fast down-flow is found to be confined to a narrow and rapidly rotating "drainpipe" from the free surface down to the drain hole, and at the tip of the needlelike surface depression, a bubble-forming instability at high rotation rates is observed.

### Axisymmetric draining of a cylindrical tank with a free surface

- EngineeringJournal of Fluid Mechanics
- 1990

The withdrawal of layered fluids from an open tank through a hole centred on the bottom is investigated numerically under the assumption of potential flow. A fully cubic-spline nonlinear axisymmetric…

### VORTEX FORMATION AT VERTICAL PIPE INTAKES

- Engineering
- 1978

With the object of determining the similarity criterion, experimental studies on vortex formation at pipe intakes were carried out using two geometrically similar circular vortex tanks, circulation…

### Free‐Surface Air Core Vortex

- Physics
- 1986

A Rankine vortex model is used as the basis for an equation for critical submergence of intakes. The equation relates critical submergence to Froude number, circulation number, Reynolds number, and…

### A note on the bathtub vortex

- PhysicsJournal of Fluid Mechanics
- 1962

Observations were made of the vortex motion which occurs when a liquid is draining from a vessel through a hole in its bottom. It was found that, for relatively quiescent initial conditions, the…

### A Study on the Free Surface Vortex in the Pipe System

- Engineering, Physics
- 1992

During mid-loop operation of Nuclear Power Plant, to prevent the Decay Heat Removal System (DHRS) from failure due to air entrainment of free surface vortex in the piping system, a set of simulating…