[1] G.G.Stokes,Onthetheoryofoscillatorywaves,Trans.Camb.Phil.Soc.8(1847), 441.
[2] M. J. Lighthill, Contributions to the theory of waves in nonlinear dispersive systems, J. Inst. Math. Appl. 1 (1965), 269.
[3] V. E. Zakharov, Stability of periodic waves of finite amplitude on a surface of deep fluid, J. Appl. Mech. Tech. Phys. 9 (1968), 190.
[4] T. B. Benjamin and J. E. Feir, The disintegration of wave trains on deep water, Part 1. Theory, J. Fluid Mech. 27 (1967), 417.
[5] T. B. Benjamin and J. E. Feir, The disintegration of wave trains on deep water, Part 2. Experiments (Unpublished) (1967).
[6] J. E. Feir, Some results from wave pulse experiments, Proc. Roy. Soc. A299 (1967), 54.
[7] D. L. Ross and S. G. Sajjadi, On the disintegration of oblique waves on deep water, Adv. Appl. Fluid Mech. 3 (2008), 23.
[8] S. G. Sajjadi, A note on Benjamin-Feir instability for water waves, Adv. Appl. Fluid Mech. 17(1) (2015), 17-38.
[9] W. G. Penney and A. J. Price, Finite periodic stationary gravity waves in a perfect liquid, Phil. Trans. R. Soc. Lond. A224 (1952), 254.
[10] M. S. Longuet-Higgins, The instabilities of gravity waves of finite amplitude in deep water, I. Superharmonics, Proc. Roy. Soc. A360 (1978), 471.
[11] M. S. Longuet-Higgins, The instabilities of gravity waves of finite amplitude in deep water, II. Subharmonics, Proc. Roy. Soc. A360 (1978), 489.
[12] T. B. Benjamin, Instability of periodic wavetrains in nonlinear dispersive systems, Proc. Roy. Soc. A299 (1967), 59.
[13] B. M. Lake and H. C. Yuen, A note on some nonlinear water wave experiments and the comparison of data with theory, J. Fluid Mech. 83 (1977), 75.
[14] M.-Y. Su, M. Bergin, P. Marler and R. Myrick, Experiments on nonlinear instabilities and evolution of steep gravity-wave trains, J. Fluid Mech. 124 (1982), 45.
[15] P. G. Saffman and H. C. Yuen, A new type of three-dimensional deep-water wave of permanent form, J. Fluid Mech. 101 (1980), 797.
[16] R. A. Fuchs, On the theory of short-crested oscillatory gravity waves, Natl. Bur. Standards Circ. 521 (1951), 187.
[17] J. C. Chappelear, On the description of short crested waves, Army Corps of Engrs. Tech. Memo no. 125 (1961).
[18] L. Schwartz and A. K. Whitney, A semi-analytic solution for nonlinear standing waves in deep water, J. Fluid Mech. 107 (1981), 147.
[19] P. G. Saffman and H. C. Yuen, Bifurcation and symmetry breaking in nonlinear dispersive waves, Phys. Rev. Let. 4 (1980), 1097.
[20] D. I. Meiron, P. G. Saffman and H. C. Yuen, Calculation of steady three-dimensional deep-water waves, J. Fluid Mech. 124 (1982), 109.
[21] M.-Y. Su, Three-dimensional deep-water waves. Part 1. Experimental measurement of skew and symmetric wave patterns, J. Fluid Mech. 124 (1982), 73.
[22] J. W. McLean, D. U. Martin, P. G. Saffman and H. C. Yuen, Three-dimensional instability of finite amplitude gravity waves, Phys. Rev. Let. 46 (1981), 817.
[23] D. R. Crawford, P. G. Saffman and H. C. Yuen, Evolution of a random inhomogeneous field of nonlinear deep-water gravity waves, Wave Motion 2 (1980), 1.
[24] P. G. Saffman and H. C. Yuen, Stability of a plane soliton to two-dimensional perturbations, Phys. Fluids 21 (1978), 1450.
[25] A. J. Roberts and D. H. Peregrine, Notes on long-crested water waves, J. Fluid Mechanics 135 (1983), 323-335.
[26] K. Weierstrass, Mathematische Werke, Vol. V., Johnson, New York, 1915.
[27] E. T. Whittaker and G. N. Watson, A Course of Modern Analysis, Cambridge University Press, Cambridge, 1927.
[28] M. Abramowitz and I. A. Stegun, Handbook of Mathematical Functions: With Formulas, Graphs, and Mathematical Tables, Courier Dover Publications, 1972.
[29] H. C. Yuen and B. M. Lake, Nonlinear dynamics of deep-water gravity waves, Advances in Applied Mech. 22 (1982), 67.
[30] S. G. Sajjadi, J. C. R. Hunt and F. Drullion, Asymptotic multi-layer analysis of wind over unsteady monochromatic surface waves, J. Eng. Math. 84 (2014), 73.
[31] S. G. Sajjadi, J. C. R. Hunt and F. Drullion, Dynamics of critical layer in turbulent shear flows over unsteady water waves, J. Fluid Mech. (2014), submitted.
[32] S. Leblanc, Amplification of nonlinear surface waves by wind, Phys. Fluids 19 (2007), 101.
[33] S. G. Sajjadi and H. Khanal, Interaction of Tollmien-Schlichting waves in the air with the sea surface, Adv. Appl. Fluid Mech. 5 (2008), 69.
[34] J. W. Miles, On the generation of surface waves by shear flows, J. Fluid Mech. 3 (1957), 185.
[35] T. R. Marchant and A. J. Roberts, A variational approach to the problem of deep water waves forming a circular caustic, J. Fluid Mach. 194 (1988), 581.
[36] T. R. Marchant and A. J. Roberts, Reflection of nonlinear deep-water waves incident onto a wedge of arbitrary angle, J. Austral. Math. Soc. B 32 (1990), 61.
[37] A. S. Roberts, Highly nonlinear short-crested water waves, J. Fluid Mech. 135 (1983), 301. |