Stationary bathtub vortices and a critical regime of liquid discharge

Article

Stepanyants, Yury and Yeoh, Guan. 2008. "Stationary bathtub vortices and a critical regime of liquid discharge." Journal of Fluid Mechanics. 604 (1), pp. 77-98. https://doi.org/10.1017/S0022112008001080

Article Title	Stationary bathtub vortices and a critical regime of liquid discharge
ERA Journal ID	1294
Article Category	Article
Authors	Stepanyants, Yury (Author) and Yeoh, Guan (Author)
Journal Title	Journal of Fluid Mechanics
Journal Citation	604 (1), pp. 77-98
Number of Pages	22
Year	2008
Publisher	Cambridge University Press
Place of Publication	Cambridge, UK
ISSN	0022-1120
	1469-7645
Digital Object Identifier (DOI)	https://doi.org/10.1017/S0022112008001080
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.
Keywords	fluid flow, bathtub vortices, whirlpools
ANZSRC Field of Research 2020	401207. Fundamental and theoretical fluid dynamics
Public Notes	File reproduced in accordance with the copyright policy of the publisher/author.
Byline Affiliations	Australian Nuclear Science and Technology Organisation

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Nikitenkova, S. P., Raj, N. and Stepanyants, Y. A.. 2015. "Nonlinear vector waves of a flexural mode in a chain model of atomic particles." Communications in Nonlinear Science and Numerical Simulation. 20 (3), pp. 731-742. https://doi.org/10.1016/j.cnsns.2014.05.031

Interaction of gaseous bubbles under the action of radiation modified Bjerknes force

Stepanyants, Yury and Yeoh, Guan. 2008. "Interaction of gaseous bubbles under the action of radiation modified Bjerknes force." 22nd International Congress of Theoretical and Applied Mechanics (IC-TAM2008). Adelaide, Australia 24 - 29 Aug 2008

Recent results on the problem of wave-current interaction including water depth, surface tension/amplitude and vorticity effects

Maissa, Philippe, Rousseaux, Germain and Stepanyants, Yury. 2013. "Recent results on the problem of wave-current interaction including water depth, surface tension/amplitude and vorticity effects." 7th International Conference on Coastal Dynamics. Arcachon, France 24 - 28 Jun 2013 Arcachon, France.

Nonlinear spectra of shallow water waves

Giovanangeli, J. -P., Kharif, C., Raj, N. and Stepanyants, Y.. 2013. "Nonlinear spectra of shallow water waves." Oceans - San Diego, 2013. San Diego, United States 23 - 26 Sep 2013 United States. IEEE (Institute of Electrical and Electronics Engineers). https://doi.org/10.23919/OCEANS.2013.6741132

Numerical study of nonlinear wave processes by means of discrete chain models

Obregon, M., Raj, N. and Stepanyants, Y.. 2012. "Numerical study of nonlinear wave processes by means of discrete chain models." Gu, Y. T. and Saha, Suvash C. (ed.) 4th International Conference on Computational Methods (ICCM 2012). Gold Coast, Australia 25 - 28 Nov 2012 Brisbane, Australia.

On numerical solution of the Gardner Ostrovsky equation

Obregon, M. A. and Stepanyants, Y. A.. 2012. "On numerical solution of the Gardner Ostrovsky equation." Mathematical Modelling of Natural Phenomena (MMNP). 7 (2), pp. 113-130. https://doi.org/10.1051/mmnp/20127210

Stationary gravity waves with the zero mean vorticity in stratified fluid

Clamond, D. and Stepanyants, Y.. 2012. "Stationary gravity waves with the zero mean vorticity in stratified fluid." Studies in Applied Mathematics. 128 (1), pp. 59-85. https://doi.org/10.1111/j.1467-9590.2011.00530.x

Measuring rate of change of oxygen concentration and intrinsic oxidation rate in a pile of material

Bennett, John, Stepanyants, Yury and Ritchie, Ian. 2004. Measuring rate of change of oxygen concentration and intrinsic oxidation rate in a pile of material. WO 2004/072636 A1

Internal solitons in laboratory experiments: Comparison with theoretical models

Ostrovsky, L A. and Stepanyants, Y. A.. 2005. "Internal solitons in laboratory experiments: Comparison with theoretical models." Chaos: an interdisciplinary journal of nonlinear science. 15. https://doi.org/10.1063/1.2107087

Measurement of hydraulic conductivity using a radioactive or activatable tracer

Waring, Christopher Leslie, Airey, Peter Lewis and Stepanyants, Yury A.. 2007. Measurement of hydraulic conductivity using a radioactive or activatable tracer. AU2007231556

Measurement of hydraulic conductivity, porosity and lithology by neutron activation borehole logging at high spatial resolution increments

Waring, C. L., Stepanyants, Y. A., Hankin, S. I., Airey, P. L. and Peterson, M. A.. 2009. "Measurement of hydraulic conductivity, porosity and lithology by neutron activation borehole logging at high spatial resolution increments." Milne-Home, William A. (ed.) IAH Groundwater in The Sydney Basin Symposium (2009). Sydney, Australia 04 - 05 Aug 2009 Sydney, NSW, Australia.

Internal solitons in the ocean and their effect on underwater sound

Apel, John R., Ostrovsky, Lev A., Stepanyants, Yury A. and Lynch, James F.. 2007. "Internal solitons in the ocean and their effect on underwater sound." The Journal of the Acoustical Society of America. 121 (2), pp. 695-722. https://doi.org/10.1121/1.2395914

Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps

Crawford, Jagoda and Stepanyants, Yury. 2005. "Influence of bottom boundary conditions for temperature on the heat distribution within oxidising heaps." Australian and New Zealand Industrial and Applied Mathematics (ANZIAM) Journal. 46, pp. C1104-C1125.

Propagation of waves in shear flows

Fabrikant, Anatoly and Stepanyants, Yury. 1998. Propagation of waves in shear flows. Singapore. World Scientific Publishing.

Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons

Stepanyants, Yury. 2005. "Dispersion of long gravity-capillary surface waves and asymptotic equations for solitons." Proceedings of the Russian Academy of Engineering Sciences Series: Applied Mathematics and Mechanics. 14, pp. 33-40.

Scalar description of three-dimensional vortex flows of incompressible fluid

Stepanyants, Yu. A. and Yakubovich, Evsey. 2011. "Scalar description of three-dimensional vortex flows of incompressible fluid." Doklady Physics. 56 (2), pp. 130-133. https://doi.org/10.1134/S1028335811020169

The inverse problem for the Gross-Pitaevskii equation

Malomed, Boris A. and Stepanyants, Yury A.. 2010. "The inverse problem for the Gross-Pitaevskii equation." Chaos: an interdisciplinary journal of nonlinear science. 20 (1). https://doi.org/10.1063/1.3367776

Dynamics of two charged particles in viscous fluid at small Reynolds numbers

Stepanyants, Y. A. and Strunin, D. V.. 2011. "Dynamics of two charged particles in viscous fluid at small Reynolds numbers." de Oliveira, Cassiano (ed.) 2011 International Conference on Mathematics and Computational Methods Applied to Nuclear Science and Enginnering (MC 2011). Rio de Janeiro, Brazil 08 - 12 May 2011 Rio de Janeiro.

Nanoparticle dynamics in a viscous fluid at small Reynolds numbers

Stepanyants, Yury A. and Yeoh, Guan H.. 2010. "Nanoparticle dynamics in a viscous fluid at small Reynolds numbers." Teh, Kian, Davies, Ian and Howard, Ian (ed.) 6th Australasian Congress on Applied Mechanics (ACAM 6). Perth, Western Australia 12 - 15 Dec 2010 Perth, Australia.

Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials

Malomed, B. A. and Stepanyants, Y. A.. 2010. "Localised nonlinear optical modes and the corresponding support structures: exact solutions to the nonlinear Schrodinger equation with external potentials." ICEAA 2010: International Conference on Electromagnetics in Advanced Applications. Sydney, Australia 20 - 24 Sep 2010 Sydney, Australia. https://doi.org/10.1109/ICEAA.2010.5651681

Lump solutions of 2D generalized Gardner equation

Stepanyants, Y. A., Ten, I. K. and Tomita, H.. 2006. "Lump solutions of 2D generalized Gardner equation." Luo, Albert C. J., Dai, Liming and Hamidzadeh, Hamid R. (ed.) Conference on Nonlinear Science and Complexity (2006). Beijing, China 07 - 12 Aug 2006 Singapore.

Internal solitons in the ocean

Apel, John R., Ostrovsky, Lev A., Stepanyants, Yury A. and Lynch, James F.. 2006. Internal solitons in the ocean. Woods Hole, MA. United States. Woods Hole Oceanographic Institution.

Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel

Caputo, Jean-Guy and Stepanyants, Y. A.. 2007. "Tsunami surge in a river: a hydraulic jump in an inhomogeneous channel." Kundu, Anjan (ed.) Tsunami and nonlinear waves. Berlin, Germany. Springer. pp. 97-112

Solutions classification to the extended reduced Ostrovsky equation

Stepanyants, Yury A.. 2008. "Solutions classification to the extended reduced Ostrovsky equation." Symmetry, Integrability and Geometry: Methods and Applications. 4. https://doi.org/10.3842/SIGMA.2008.073

Mechanisms of particle transport acceleration in porous media

Panfilov, M., Panfilova, I. and Stepanyants, Y.. 2008. "Mechanisms of particle transport acceleration in porous media." Transport in Porous Media. 74 (1), pp. 49-71. https://doi.org/10.1007/s11242-007-9201-9

Particle and bubble dynamics in a creeping flow

Stepanyants, Yury and Yeoh, Guan. 2009. "Particle and bubble dynamics in a creeping flow." European Journal of Mechanics B: Fluids. 28 (5), pp. 619-629. https://doi.org/10.1016/j.euromechflu.2009.04.004

On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons

Stepanyants, Yury. 2006. "On stationary solutions of the reduced Ostrovsky equation: periodic waves, compactons and compound solitons." Chaos, Solitons and Fractals. 28 (1), pp. 193-204. https://doi.org/10.1016/j.chaos.2005.05.020

The motion of a cylindrical body in a stratified fluid under the action of a radiation force

Kozyrev, O. R., Reznik, S. N. and Stepanyants, Yu. A.. 2009. "The motion of a cylindrical body in a stratified fluid under the action of a radiation force." Journal of Applied Mathematics and Mechanics. 73 (2), pp. 188-195. https://doi.org/10.1016/j.jappmathmech.2009.04.008

Stationary bathtub vortices and a critical regime of liquid discharge

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