Pearson, A.; Cox, E.; Blake, J. R.; Otto, S. R. Bubble interactions near a free surface. (English) Zbl 1070.76040 Eng. Anal. Bound. Elem. 28, No. 4, 295-313 (2004). Summary: A boundary integral method is used to calculate the highly nonlinear motion of both one and a vertical column of two bubbles beneath a free surface, although the theory is developed for a finite number of bubbles. Cubic splines are used to represent the surface of the bubble and the infinite free surface. A nonlinear distribution of nodes is employed on the free surface in order to more accurately capture the motion of free surface spike, which experiments show to be narrow and pronounced when bubbles are generated close to the boundary. Calculations show excellent agreement with experiments in both the one- and two-bubble cases.© Elsevier Science Ltd Cited in 16 Documents MSC: 76M15 Boundary element methods applied to problems in fluid mechanics 76B10 Jets and cavities, cavitation, free-streamline theory, water-entry problems, airfoil and hydrofoil theory, sloshing Keywords:cubic spline; boundary integral method; free surface spike × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Best JP. The dynamics of underwater explosions. PhD Thesis, The University of Wollongong; 1991. [2] Best, J. P., The rebound of toroidal bubbles, 405-412 [3] Blake, J. R., The Kelvin impulse: application to cavitation bubble dynamics, J Aust Math Soc B, 30, 127-146, 1988 · Zbl 0661.76105 [4] Blake, J. R.; Cerone, P., A note on the impulse due to a vapour bubble near a boundary, J Aust Math Soc B, 23, 383-393, 1982 · Zbl 0491.76019 [5] Blake, J. R.; Gibson, D. C., Growth and collapse of a vapour cavity near a free surface, J Fluid Mech, 111, 123-140, 1981 [6] Blake, J. R.; Robinson, P. B.; Shima, A.; Tomita, Y., Interaction of two cavitation bubbles with a rigid boundary, J Fluid Mech, 255, 707-721, 1993 [7] Blake, J. R.; Taib, B. B.; Doherty, G., Transient cavities near boundaries. Part 1. Rigid boundary, J Fluid Mech, 170, 479-497, 1986 · Zbl 0606.76050 [8] Blake, J. R.; Taib, B. B.; Doherty, G., Transient cavities near boundaries. Part 2. Free surface, J Fluid Mech, 181, 197-212, 1987 [9] Brebbia, C. A., The boundary element method for engineers, 1980, Pentech Press: Pentech Press London, Second revised edition [10] Chahine, G. L., Experimental and asymptotic study of non-spherical bubbles in non-uniform flow fields, Appl Sci Res, 38, 187-197, 1982 [11] Cox E. The source signature due to the close interaction of marine seismic airguns. PhD Thesis, The University of Birmingham; 2003. [12] Herring, C., Theory of the pulsations of the gas bubble produced by an underwater explosion [13] Kucera, A.; Blake, J. R., Approximate methods for modelling cavitation bubbles near boundaries, Bull Aust Math Soc, 41, 1-44, 1990 · Zbl 0673.76017 [14] Lenoir, M., Calcul numérique de l’implosion d’une bulle de cavitation au voisinage d’une paroi ou d’une surface libre, J Méc, 15, 5, 725-751, 1976 · Zbl 0352.76010 [15] Longuet-Higgins, M. S., Bubbles, breaking waves and hyperbolic jets at a free surface, J Fluid Mech, 127, 103-124, 1983 · Zbl 0517.76103 [16] Longuet-Higgins, M. S.; Cokelet, E. D., The deformation of steep surface waves on water. I. A numerical method of computation, Proc R Soc Lond A, 350, 1-26, 1976 · Zbl 0346.76006 [17] Lundgren, T. S.; Mansour, N. N., Oscillations of drops in zero gravity with weak viscous effects, J Fluid Mech, 194, 479-510, 1988 · Zbl 0645.76110 [18] Pearson A. Hydrodynamics of jet impact in a collapsing bubble. PhD Thesis, The University of Birmingham; 2002. [19] Robinson, P. B.; Blake, J. R.; Kodama, T.; Shima, A.; Tomita, Y., Interaction of cavitation bubbles with a free surface, J Appl Phys, 89, 12, 8225-8237, 2001 [20] Rogers, J. C.W.; Szymczak, W. G., Computations of violent surface motions: comparisons with theory and experiment, Phil Trans R Soc Lond A, 355, 649-663, 1997 · Zbl 0884.76078 [21] Taylor, G. I., Vertical motion of a spherical bubble and the pressure surrounding it [22] Tomita, Y.; Kodama, T., Some aspects of the motion of two laser-produced cavitation babbles near a free surface, 303-310 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.