The Nonlinear KdV Equation Under External Forcing With the Complete Coriolis Force

YIN Xiao-jun; YANG Lian-gui; SONG Jian; ZHANG Rui-gang; YANG Hong-li>; LIU Quan-sheng

doi:10.21656/1000-0887.370297

Volume 38 Issue 9

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2017 > 38(9): 1053-1060

YIN Xiao-jun, YANG Lian-gui, SONG Jian, ZHANG Rui-gang, YANG Hong-li>, LIU Quan-sheng. The Nonlinear KdV Equation Under External Forcing With the Complete Coriolis Force[J]. Applied Mathematics and Mechanics, 2017, 38(9): 1053-1060. doi: 10.21656/1000-0887.370297

Citation:

PDF( 362 KB)

The Nonlinear KdV Equation Under External Forcing With the Complete Coriolis Force

doi: 10.21656/1000-0887.370297

¹School of Mathematical Sciences, Inner Mongolia University, Hohhot 010021, P.R.China;²College of Science, Inner Mongolia Agricultural University, Hohhot 010018, P.R.China;³College of Science, Inner Mongolia University of Technology, Hohhot 010051, P.R.China

Funds: The National Natural Science Foundation of China(11362012)；The National Science Fund for Young Scholars of China(11202092;11301592)

Received Date: 2016-09-28
Rev Recd Date: 2016-11-08
Publish Date: 2017-09-15

Abstract

Abstract

The nonlinear KdV equation under external forcing was deduced from the potential vorticity equation involving both the vertical and the horizontal components of the Coriolis force with the perturbation method near the equatorial Rossby waves. Then the periodic solution of the model was obtained by means of the Jacobi elliptic functions. It is shown that the horizontal components of the Coriolis force play an important role in the structures of the Rossby waves.
- complete Coriolis force,
- Jacobi elliptic function,
- nonlinear Rossby wave

FullText(HTML)

References(22)

References

[1]	Long R R. Solitary waves in the Westerlies[J]. Journal of the Atmosphere Science,1964,21(3): 197-200.
[2]	Benney D J. Long nonlinear waves in fluid flows[J]. Journal of Mathematics and Physics,1966,45(1): 52-63.
[3]	Boyd J P. The effects of latitudinal shear on equatorial waves—part 1: theory and methods[J]. Journal of the Atmospheric Sciences,1978,35(12): 2236-2258.
[4]	Boyd J P. Equatorial solitary waves—part1: Rossby solitons[J]. Journal of Physical Oceanography,1980,10(11): 1699-1717.
[5]	Redekopp L G. On the theory of solitary Rossby waves[J]. Jounal of Fluid Mechanics,1977,82(4): 725-745.
[6]	Charney J G, Straus D M. Form-drag instability, multiple equilibria and propagating planetary waves in baroclinic, orographically forced, planetary wave systems[J]. Journal of the Atmospheric Sciences,1980,37(6): 1157-1176.
[7]	赵强, 刘式达, 刘式适. 切变基本纬向流中非线性赤道Rossby长波[J]. 地球物理学报, 2000,43(6): 746-753.(ZHAO Qiang, LIU Shi-da, LIU Shi-kuo. Nonlinear equatorial Rossby long waves in a shear flow[J]. Chinese Journal of Geophysics,2000,43(6): 746-753.(in Chinese))
[8]	宋健, 杨联贵, 刘全生. 正压大气模式下具有β效应与地形效应的Rossby孤立波[J]. 地球物理学进展, 2012,27(2): 393-397.(SONG Jian, YANG Lian-gui, LIU Quan-sheng. Solitary Rossby waves with beta effect and topography effect in a barotropic atmospheric model[J]. Progress in Geophysics,2012,27(2): 393-397.(in Chinese))
[9]	巢纪平, 徐昭. 热带扰动在大尺度经圈中的行为[J]. 地球物理学报, 2008,51(6): 1657-1662.(CHAO Ji-ping, XU Zhao. The behavior of tropical disturbance in large-scale meridional flow[J]. Chinese Journal of Geophysics,2008,51(6): 1657-1662.(in Chinese))
[10]	刘萍, 李子良, 楼森岳. 一类耦合非线性Schrdinger方程的Painlevé性质、严格解及其在大气重力波中的应用[J]. 应用数学和力学, 2010,31(11): 1308-1329.(LIU Ping, LI Zi-liang, LOU Sen-yue. A class of coupled nonliear Schrdinger equation: Painlevé property, exact solutions and application to atmospheric gravity waves[J]. Applied Mathematics and Mechanics,2010,31(11): 1308-1329.(in Chinese))
[11]	张永垂, 张立凤. Rossby波模型对西北太平洋海表面高度年际变异的可预测性研究[J]. 海洋与湖沼, 2013,44(6): 1409-1417.(ZHANG Yong-chui, ZHANG Li-feng. Predictability to sea level interannual variability in the northwestern pacific by first-order baroclinic Rossby waves model[J]. Oceanologia et Limnologia Sinica,2013,44(6): 1409-1417.(in Chinese))
[12]	张永利, 杨联贵. 地形效应下正压准地转模式的能量守恒[J]. 应用数学和力学, 2016,37(9): 936-944.(ZHANG Yong-li, YANG Lian-gui. Conservation of energy in a barotropic quasi-geostrophic model under orographic effects[J]. Applied Mathematics and Mechanics,2016,37(9): 936-944.(in Chinese))
[13]	汪萍, 戴新刚. 外强迫作用下正压大气非线性特征数值模拟[J]. 物理学报, 2005,54(10): 4961-4970.(WANG Ping, DAI Xin-gang. Numerial modeling of non-linear characteristics for barotropic atmosphere with external forcing[J]. Acta Physica Sinica,2005,54(10): 4961-4970.(in Chinese))
[14]	White A A, Hoskins B J, Roulstone I, et al. Consistent approximate models of the global atmosphere: shallow, deep, hydrostatic, quasi-hydrostatic and non-hydrostatic[J].Quarterly Journal of the Royal Meteorological Society,2005,131(609): 2081-2107.
[15]	Philips N A. The equations of motion for a shallow rotating atmosphere and the “traditional approximation”[J].Journal of the Atmospheric Sciences,1966,23(5): 626-628.
[16]	White A A, Bromley R A. Dynamically consistent, quasi-hydrostatic equations for global models with a complete representation of the Coriolis force[J]. Quarterly Journal of the Roynal Meteorological Society,1995,121(522): 399-418.
[17]	Burger A P. The potential vorticity equation: from planetary to small scale[J]. Tellus A,1991,43(3): 191-197.
[18]	Dellar P J, Salmon R. Shallow water equations with a complete Coriolis force and topography[J]. Physics of Fluids,2005,17(10): 106601.
[19]	Stewart A L, Dellar P J. The rle of the complete Coriolis force in cross-equatorial flow of abyssal ocean currents[J].Ocean Modelling,2011,38(3/4): 187-202.
[20]	Tort M, Dubos T. Dynamically consistent shallow-atmosphere equations with a complete Coriolis force[J]. Quarterly Journal of the Royal Meteorological Society,2014,140(684): 2388-2392.
[21]	赵强, 于鑫. 完整Coriolis力作用下非线性Rossby波的精确解[J]. 地球物理学报, 2008,51(5): 1304-1308.(ZHAO Qiang, YU Xin. Exact solutions to the nonlinear Rossby waves with a complete representation of the Coriolis force[J]. Chinese Journal of Geophysics,2008,51(5): 1304-1308.(in Chinese))
[22]	杨洁, 赵强. 有完整Coriolis力和热源影响下超长波的解析解[J]. 物理学报, 2010,59(2): 750-753.(YANG Jie, ZHAO Qiang. Analytical solutions to ultra-long waves with the complete Coriolis force and heating[J]. Acta Physica Sinica,2010,59(2): 750-753.(in Chinese))