American Journal of Geophysics, Geochemistry and Geosystems
Articles Information
American Journal of Geophysics, Geochemistry and Geosystems, Vol.6, No.2, Jun. 2020, Pub. Date: Jun. 29, 2020
Nonlinear Evolution of Gravity Waves on the Surface Deep-water Under the Action of Viscosity and Surfactant
Pages: 50-57 Views: 63 Downloads: 23
[01] Augustin Daïka, Laboratory of Earth’s Atmosphere Physics, Faculty of Science, University of Yaoundé 1, Yaoundé, Cameroon; Department of Meteorology, Climatology, Hydrology and Pedology, National Advanced School of Engineering, University of Maroua, Maroua, Cameroon.
[02] Cesar Mbané Biouélé, Laboratory of Earth’s Atmosphere Physics, Faculty of Science, University of Yaoundé 1, Yaoundé, Cameroon.
This paper presents a nonlinear evolution of gravity waves on the surface deep-water under the effects of viscosity and surfactant in terms of their space and time evolution, that is, their motion and also in terms of mechanical transformations that these systems may suffer in their dealings with other systems. We give a formal derivation of evolution equations, obtained from the modified nonlinear Schrödinger equation, for viscous capillary-gravity waves with surfactants in water of infinite depth. To fully simulate the non-linear evolution of the wave train in the presence of viscosity and surfactant, a new numerical model, based on the Bogning-Djeumen Tchaho-Kofane method (BDKm) and the Peregrine model, is developed. On the basis of these different approaches, the role of viscosity and surfactant on gravity waves in water of infinite depth is analyzed. The results show the effect of viscosity and surfactants on the nonlinear evolution of gravity waves on the surface deep-water. Naturally, they affect the remote images strongly in radar and lidar remote sensing of the sea surface.
Gravity Waves, Surface Deep-water, Presence of Viscosity and Surfactant, Bdk Method and Peregrine Model
[01] Miles, J. W. (1988), The evolution of a weakly nonlinear, weakly damped, capillary-gravity wave packet. J. Fluid Mech., vol. 187, pp. 141-154.
[02] Lapham, G. S., Dowling, D. R. and Schultz, W. W. (2001), Linear and nonlinear gravity-capillary water waves with a soluble surfactant, Experiments in Fluids 30, pp. 448-457, Springer-verlag 2001.
[03] Miles, J. W. (1967), Surface wave damping in closed basins. Proc. R. SOC. Lond. A 297, pp. 459-475.
[04] Bogning, J. R. (2013), Pulse Soliton Solutions of the Modified KdV and Born-Infeld Equations, International Journal of Modern Nonlinear Theory and Application, 2, pp. 135-140,
[05] Djeumen, T. C. T., Bogning, J. R. and Kofané, T. C. (2012), Modulated Soliton Solution of the Modified Kuramoto- Sivashinsky’s Equation, American Journal of Computational and Applied Mathematics, Vol. 2, No. 5, pp. 218-224. doi: 10.5923/j.ajcam.20120205.03.
[06] Bogning, J. R., Djeumen, T. C. T. and Kofané, T. C. (2012), Generalization of the Bogning-Djeumen Tchaho-Kofane Method for the Construction of the Solitary Waves and the Survey of the Instabilities”, Far East Journal of Dynamical Systems, Vol. 20, No. 2, pp. 101-119.
[07] Daika., A. and Mbané B. C. (2015), Relationship between Sea Surface Single Carrier Waves and Decreasing Pressures of Atmosphere Lower Boundary. Open Journal of Marine Science, 5, pp. 45-54.
[08] Daika, A. (2018), Etude des instabilités modulationnelles des ondes de gravité générées par les interactions atmosphère-Nappe d’eau étendue et profonde: le cas des vagues scélérates ou meurtrières, PhD Thesis, University of Yaounde 1, pp. 203.
[09] Daïka, A., Nkoa, T. N. and Mbané B. C. (2014) Application of Stationnary Phase Method to Wind Stress and Breaking Impacts on Ocean Relatively High Waves. Open Journal of Marine Sciences, 4, 18-24.
[10] JOO, S. W., Messiter, A. F. and Schultz, W. W. (1991), Evolution of weakly nonlinear water waves in the presence of viscosity and surfactant, J. Fluid Mech., vol. 229, pp. 135-158.
[11] Chabchoub, A., Hoffmann, N. and Akhmediev, N. (2011), Rogue wave observation in a water wave tank, Physical Review Letters, 106 (20), 204502.
[12] Kibler, B., Fatome, J., Finot, C, Millot, G., Dias, F., Genty, G., Akhmediev, N. and Dudley, J. (2010), The Peregrine soliton in nonlinear fiber optics, Nature Physics, 6 (10), pp. 790–795.
[13] Bailung, H., Sharma, S. K and Nakamura, Y. (2011), Observation of Peregrine solitons in a multi component plasma with negative ions, Physical Review Letters, 107, 255005.
MA 02210, USA
AIS is an academia-oriented and non-commercial institute aiming at providing users with a way to quickly and easily get the academic and scientific information.
Copyright © 2014 - American Institute of Science except certain content provided by third parties.