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The effect of entrained air in violent water wave impacts

Published online by Cambridge University Press:  26 April 2006

D. H. Peregrine  and
L. Thais
D. H. Peregrine
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
L. Thais
Affiliation:
School of Mathematics, University of Bristol, Bristol BS8 1TW, UK
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Abstract

The effects of entrained air in cushioning water impact on a wall are estimated by using a flow which has many similarities to the severe flip-through impacts that have been identified for water waves hitting a vertical wall. This is a filling flow which rapidly fills a confined region, such as a crack between blocks, or the space beneath a deck projecting from the coast (Peregrine & Kalliadasis 1996). The main properties of the filling flow are easily calculated, including the high-pressure peak which corresponds to the pressure peak of a flip-through. This work extends the study of filling flows to the case where the filling liquid is an air–water mixture, thus giving explicit results for the reduction of peak pressure due to the compressibility of entrained air. The behaviour of a bubbly liquid subject to substantial pressure changes is considered. Expressions are derived for an air–water mixture treated as a compressible fluid. The reduction in pressure from the incompressible case is found to be large even for relatively small air content, and depends more on the reduction in fluid volume than any other feature of the pressure–density relation. Results are presented in such a way that they may be used to estimate compressibility corrections to both the maximum and background pressures in a flip-through wave impact if corresponding incompressible pressure values are available.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 325 , 25 October 1996 , pp. 377 - 397
Copyright
© 1996 Cambridge University Press

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References

Bagnold, R. A. 1939 Interim report on wave-pressure research. J. Inst. Civil Engng, 12, 202–226.Google Scholar
Birkhoff, G., MacDougall, D. p., Pugh, E. M. & Taylor, G. I. 1948 Explosives with lined cavities. J. Appl. Phys., 19, 563–582.Google Scholar
Cooker, M. J. & Peregrine, D. H. 1990a Computations of violent motion due to waves breaking against a wall. Proc. 22nd Intl. Conf. Coastal Engng, Delft, vol. 1, pp. 164–176. ASCE.
Cooker, M. J. & Peregrine, D. H. 1990b A model for breaking wave impact pressures. Proc. 22nd Intl. Conf. Coastal Engng, Delft. ASCE. 2, 1473–1486.
Cooker, M. J. & Peregrine, D. H. 1992 Wave impact pressure and its effect upon bodies lying on the bed. Coastal Engng, 18, 205–229.Google Scholar
Cooker, M. J. & Peregrine, D. H. 1996 Computations of water wave impact on a wall and flip-through. In preparation.
Goda, Y. 1974 A new method of wave-pressure calculation for the design of composite break-water. Proc. 14th Coastal Engng Conf. Copenhagen, vol 3, pp. 1702–1720. ASCE.
Hattori, M. & Arami, A. 1992 Impact breaking pressures on vertical walls. Proc. 21st Intl Conf. Coastal Engng, Venice, vol. 2, pp. 1785–1798. ASCE.
Hsieh, D.-Y. & Plesset, M. S. 1961 On the propagation of sound in a liquid containing gas bubbles. Phys. Fluids. 4, 970–975.Google Scholar
Korobkin, A. A. 1996 Asymptotic theory of liquid-solid impact. Proc. R. Soc. Lond. A to appear.
Leighton, T. G. 1994 The Acoustic Bubble. Academic Press.
Peregrine, D. H. 1994 Pressure on breakwaters: a forward look. Proc. Intl Workshop on Wave Barriers in Deepwaters pp. 553–573. Port & Harbour Res. Inst. Yokosuka.
Peregrine, D. H. & Kalliadasis, S. 1996 Filling flows, cliff erosion and cleaning flows. J. Fluid Mech. 310, 365–374 (referred to herein as PK).Google Scholar
Peregrine, D. H. & Topliss, M. E. 1994 The pressure field due to steep water waves incident on a vertical wall. Proc. 24th Intl Conf. Coastal Engng, Kobe. ASCE.
Ramkema, C. 1978 A model law for wave impacts on coastal structures. Proc. 16th Conf. Coastal Engng, Hamburg, vol. 3, pp. 2308–2327. ASCE.
Sangani, A. S. 1993 A pairwise interaction theory for determining the linear acoustic properties of dilute bubbly liquids. J. Fluid Mech. 232, 221–284.Google Scholar
Schmidt, R., Oumeraci, H. & Partenscky, H. W. 1992 Impact loads induced by plunging breakers on vertical structures. Proc. 23rd Intl Conf. Coastal Engng, Venice, vol. 2, pp. 1545–1558. ASCE.
Scott, J. C. 1975 The preparation of water for surface-clean fluid mechanics J. Fluid Mech. 69, 339–351Google Scholar
Topliss, M. E. 1994 Water wave impact on structures. PhD dissertation, University of Bristol.
Topliss, M. E., Cooker, M. J. & Peregrine, D. H. 1992 Pressure oscillations during wave impact on vertical walls. Proc. 23rd Intl Conf. Coastal Engng, Venice, vol. 2, pp. 1639–1650. ASCE.
Wallis, G. B. 1991 The averaged Bernoulli equation and microscopic equations of motion for the potential flow of a two phase dispersion. J. Multiphase Flow 17, 683–695.Google Scholar
Walsh, J. M., Shreffler, M. G. & Willig, F. J. 1953 Limiting conditions for jet formation in high velocity collisions. J. Appl. Phys. 24, 349–359.Google Scholar
Watanabe, M. & Prosperetti, A. 1994 Shock waves in dilute bubbly liquids. J. Fluid Mech. 274, 349–381.Google Scholar
Wijngaarden L. van 1972 One-dimensional flow of liquids containing small gas bubbles. Ann. Rev. Fluid Mech. 4, 369–395.Google Scholar
Wijngaarden L. van 1980 Sound and shock waves in bubbly liquids. In Cavitation and inhomogeneities in underwater acoustics (ed. W. Lauterborn), pp. 127–140. Springer.
Zhang, S., Yue, K. P. & Tanizawa, K. 1996 The impact of a breaking wave on a vertical wall. J. Fluid. Mech. To appear.Google Scholar