Skip to main content Accessibility help
×
Home
Hostname: page-component-768dbb666b-9hf5z Total loading time: 0.313 Render date: 2023-02-05T07:15:14.990Z Has data issue: true Feature Flags: { "useRatesEcommerce": false } hasContentIssue true

Vortex ring bubbles

Published online by Cambridge University Press:  26 April 2006

T. S. Lundgren
Affiliation:
Department of Aerospace Engineering and Mechanics, University of Minnesota, Minneapolis, MN 55455, USA
N. N. Mansour
Affiliation:
NASA Ames Research Center, Moffett Field, CA 94035, USA

Abstract

Toroidal bubbles with circulation are studied numerically and by means of a physically motivated model equation. Two series of computations are performed by a boundary-integral method. One set shows the starting motion of an initially spherical bubble as a gravitationally driven liquid jet penetrates through the bubble from below causing a toroidal geometry to develop. The jet becomes broader as surface tension increases and fails to penetrate if surface tension is too large. The dimensionless circulation that develops is not very dependent on the surface tension. The second series of computations starts from a toroidal geometry, with circulation determined from the earlier series, and follows the motion of the rising and spreading vortex ring. Some modifications to the boundary-integral formulation were devised to handle the multiply connected geometry. The computations uncovered some unexpected rapid oscillations of the ring radius. These oscillations and the spreading of the ring are explained by the model equation which provides a more general description of vortex ring bubbles than previously available.

Type
Research Article
Copyright
© 1991 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Baker, G. R., Meiron, D. I. & Obszag, S. A., 1984 Boundary integral methods for axisymmetric and three-dimensional Rayleigh-Taylor instability problems. Physica 12D, 1931.Google Scholar
Baker, G. R. & Moore, D. W., 1989 The rise and distortion of a two-dimensional gas bubble in an inviscid liquid. Phys. Fluids A 1, 14511459.Google Scholar
Blake, J. R. & Gibson, D. C., 1987 Cavitation bubbles near boundaries. Ann. Rev. Fluid Mech. 19, 99123.Google Scholar
Cole, J. D.: 1968 Perturbation Methods in Applied Mathematics. Blaisdell.
Davies, R. M. & Taylor, G. I., 1950 The mechanics of large bubbles rising through extended liquids and through liquids in tubes. Proc. R. Soc. Land. A 200, 375390.Google Scholar
Earle, S. A. & Giddings, A., 1976 Life springs from death in Truk lagoon. Natl Geog. Mag. 149, 578603.Google Scholar
Hicks, W. M.: 1884 On the steady motion and small vibrations of a hollow vortex. Phil. Tram. R. Soc. Lond. A 175, 183.Google Scholar
Kida, S.: 1981 Motion of an elliptic vortex in a uniform shear flow. J. Phys. Soc. Japan 50, 35173520.Google Scholar
Lamb, H.: 1932 Hydrodynamics. Cambridge University Press.
Lundgren, T. S. & Ashubst, W. T., 1989 Area-varying waves on curved vortex tubes with application to vortex breakdown. J. Fluid Mech. 200, 283307.Google Scholar
Lundgben, T. S. & Mansour, N. N., 1988 Oscillations of drops in zero gravity with weak viscous effects. J. Fluid Mech. 194, 479510.Google Scholar
Moore, D. W. & Saffman, P. G., 1972 The motion of a vortex filament with axial flow. Phil. Trans. R. Soc. Lond. A 272, 407429.Google Scholar
Oguz, H. N. & Prosperetti, A., 1989 Surface-tension effects in the contact of liquid surfaces. J. Fluid Mech. 203, 149171.Google Scholar
Pedley, T. J.: 1967 The stability of rotating flows with a cylindrical free surface. J. Fluid Mech. 30, 127147.Google Scholar
Pedley, T. J.: 1968 The toroidal bubble. J. Fluid Mech. 32, 97112.Google Scholar
Ponstein, J.: 1959 Instability of rotating cylindrical jets. Appl. Sci. Res. A 8, 425456.Google Scholar
Rayleigh, Lord: 1892 On the instability of cylindrical fluid surfaces. Phil. Mag. 34, 17780.Google Scholar
Turner, J. S.: 1957 Buoyant vortex rings. Proc. R. Soc. Lond A 239, 6175.Google Scholar
Walters, J. K. & Davidson, J. F., 1962 The initial motion of a gas bubble formed in an inviscid liquid. Part 1. The two-dimensional bubble. J. Fluid Mech. 12, 408416.Google Scholar
Walters, J. K. & Davidson, J. F., 1963 The initial motion of a gas bubble formed in an inviscid liquid. Part 2. The three-dimensional bubble and the toroidal bubble. J. Fluid Mech. 17, 321336.Google Scholar
Widnall, S. & Bliss, D., 1971 Slender-body analysis of the motion and stability of a vortex filament containing an axial flow. J. Fluid Mech. 50, 335353.Google Scholar
65
Cited by

Save article to Kindle

To save this article to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Vortex ring bubbles
Available formats
×

Save article to Dropbox

To save this article to your Dropbox account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Dropbox account. Find out more about saving content to Dropbox.

Vortex ring bubbles
Available formats
×

Save article to Google Drive

To save this article to your Google Drive account, please select one or more formats and confirm that you agree to abide by our usage policies. If this is the first time you used this feature, you will be asked to authorise Cambridge Core to connect with your Google Drive account. Find out more about saving content to Google Drive.

Vortex ring bubbles
Available formats
×
×

Reply to: Submit a response

Please enter your response.

Your details

Please enter a valid email address.

Conflicting interests

Do you have any conflicting interests? *