Gravity-capillary water waves generated by multiple pressure distributions

Volume 6, Issue 2, pp 137--144 http://dx.doi.org/10.22436/jnsa.006.02.09

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Authors

Charlotte Page - School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, United Kingdom. Emilian I. Părău - School of Mathematics, University of East Anglia, Norwich, NR4 7TJ, United Kingdom. Scott Grandison - School of Computing Sciences, University of East Anglia, Norwich, NR4 7TJ, United Kingdom.

Abstract

Steady two-dimensional free-surface flows subjected to multiple localised pressure distributions are considered. The fluid is bounded below by a rigid bottom, and above by a free-surface, and is assumed to be inviscid and incompressible. The flow is assumed irrotational, and the effects of both gravity and surface tension are taken into account. Forced solitary wave solutions are found numerically, using boundary integral equation techniques, based on Cauchy integral formula. The integrodifferential equations are solved iteratively by Newton's method. The behaviour of the forced waves is determined by the Froude number, the Bond number, and the coefficients of the pressure forcings. Multiple families of solutions are found to exist for particular values of the Froude number; perturbations from a uniform stream, and perturbations from pure solitary waves. Elevation waves are only obtained in the case of a negatively forced pressure distribution.

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Keywords

• Nonlinear waves
• gravity-capillary waves

MSC

•  74J30
•  76B25
•  76B15

References

• [1] B. J. Binder, F. Dias, J.-M. Vanden-Broeck , Forced solitary waves and fronts past submerged obstacles, Chaos, 15 (2005), 027106.


• [2] B. J. Binder, F. Dias, J.-M. Vanden-Broeck, In uences of rapid changes in a channel bottom of free-surface flows, IMA Journal of Applied Mathematics, 73 (2008), 254-273.


• [3] F. Dias, J.-M. Vanden-Broeck , Open channel flows with submerged obstructions, Fluid Mech., 206 (1989), 155-170.


• [4] F. Dias, J.-M. Vanden-Broeck, Generalised critical free-surface flows, Journal of Engineering Mathematics, 42 (2002), 291-301.


• [5] F. Dias, J.-M. Vanden-Broeck , Trapped waves between submerged obstacles, J. Fluid Mech., 509 (2004), 93-102.


• [6] L. K. Forbes, L. W. Schwartz, Free-surface flow over a semicircular obstruction, J. Fluid Mech., 114 (1982), 299-314.


• [7] L. K. Forbes, Critical free-surface flow over a semi-circular obstruction, Journal of Engineering Mathematics, 22 (1988), 3-13.


• [8] M. Maleewong, J. Asavanant, R.Grimshaw, Free surface flow under gravity and surface tension due to an applied pressure distribtion: I Bond number greather than one-third, Theoretical and Computational Fluid Dynamics, 19 (2005), 237-252.


• [9] M. Maleewong, R. Grimshaw, J. Asavanant, Free surface flow under gravity and surface tension due to an applied pressure distribtion: II Bond number less than one-third, European Journal of Mechanics B/Fluids 24 (2005), 502-521. [10] Părău, E. and Vanden-Broeck, J.-M., Nonlinear two- and three-dimensional free surface flows due to moving pressure distributions, European Journal of Mechanics B/Fluids , 21 (2002), 643-656.


• [10] J.-M. Vanden-Broeck, F. Dias, Gravity-capillary solitary waves in water of infinite depth and related free-surface flows, J. Fluid Mech. , 240 (1992), 549-557.