Inherent Properties of Two Dimension Green Function with Linear Boundary Condition of Free Water Surface

Abstract

A mathematic model of Green function is build for two dimension free water surface. The analytic expression of Green function is obtained by introducing a parameter of complex number. The intrinsic properties of Green function are discussed for the special parameter values. The real and imaginary parts of H function are shown in the paper.

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X. Wang, C. Liu, Z. Sun, M. Wu and S. Zhang, "Inherent Properties of Two Dimension Green Function with Linear Boundary Condition of Free Water Surface," Applied Mathematics, Vol. 4 No. 8A, 2013, pp. 97-99. doi: 10.4236/am.2013.48A013.

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1] W. Frank, “Oscillation of Cylinders in or below the Free Surface of Deep Fluids,” Report, No. 2375, Naval Ship Researcher and Development Center, 1967.
[2] A. Poul and W. Z. He, “On the Calculation of Two Di mensional Added Mass and Damping Coefficients by Simple Green’s Function Technique,” Ocean Engineering, Vol. 12, No. 5, 1985, pp. 425-451. doi:10.1016/0029 8018(85)90003 4
[3] J. N. Newman, “Algorithm for the Free Surface Green Function,” Journal of Engineering Mathematics, Vol. 19, No. 1, 1985, pp. 57-67. doi:10.1007/BF00055041
[4] R. Hein, M. Duran and J. C. Nedelec, “Explicit Repre sentation for the Infinite Depth Two Dimensional Free Surface Green’s Function in Linear Water Wave Theory,” AIAN: Journal on Applied Mathematics, Vol. 70, No. 7, 2010, pp. 2353-2372.
[5] Z. M. Chen, “Harmonic Function Expansion for Trans lating Green Functions and Dissipative Free Surface Waves,” Wave Motion, Vol. 50, No. 2, 2013, pp. 282-294. doi:10.1016/j.wavemoti.2012.09.005
[6] A. Poul and W. Z. He, “On the Calculation of Two Di mensional Added Mass and Damping Coefficients by Simple Green’s Function Technique,” Ocean Engineering, Vol. 12, No. 5, 1985, pp. 425-451. doi:10.1016/0029 8018(85)90003 4
[7] J. V. Wehausen and E. V. Latoine, “Surface Waves,” In: S. Flügge, Ed., Encyclopedia of Physics, Vol. IX, Sprin ger, Berlin, 1960, pp. 446-778.
[8] A. H. Clement, “An Ordinary Differential Equation for the Green Function of Time Domain Free Surface Hy drodynamics,” Journal of Engineering Mathematics, Vol. 33, No. 2, 1998, pp. 201-217. doi:10.1023/A:1004376504969
[9] R. Hein, M. Duran and J. C. Nedelec, “Explicit Repre sentation for the Infinite Depth Two Dimensional Free Surface Green’s Function in Linear Water Wave Theory,” AIAN: Journal on Applied Mathematics, Vol. 70, No. 7, 2010, pp. 2353-2372.
[10] J. N. Newman, “Algorithm for the Free Surface Green Function,” Journal of Engineering Mathematics, Vol. 19, No. 1, 1985, pp. 57-67. doi:10.1007/BF00055041

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