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大尺度浅水波方程中相互调制的非线性波

毛杰健 杨建荣

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大尺度浅水波方程中相互调制的非线性波

毛杰健, 杨建荣

Nonlinear intermodulation waves of large-scale shallow water equations

Mao Jie-Jian, Yang Jian-Rong
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  • 基于一般的浅水波方程, 根据大尺度正压大气的特点, 得到无量纲的控制大尺度大气的动力学非线性方程组. 利用多尺度法, 由无量纲的动力学方程组导出了扰动位势的非线性控制方程. 采用椭圆方程构造该扰动位势控制方程的解, 获得了扰动位势和速度的多周期波与冲击波(爆炸波) 并存的解析解. 扰动位势的解表明经向和纬向具有不同周期和波长的周期波, 且都受纬向孤波的调制; 速度的解表明大尺度大气流动存在气旋和反气旋周期性分布的现象.
    According to the general shallow water equations, the nondimensional nonlinear dynamic equations are obtained that can describe large-scale barotropic atmosphere. Using multi-scale method, a nonlinear controlling equation for disturbed height (or pressure) field is deduced. Applying elliptic equation to construct the solutions of the controlling equation, the analytic solutions of the disturbed height field and velocity are obtained, which include the multiply periodic waves and shock (explosive) waves. The solutions of the disturbed height field present periodic waves with different periodicity and wavelength along longitude and latitude, which are modulated by the solitary waves of latitude. The velocity solutions display that in the large-scale air flows exist periodic distribution phenomena of cyclone and anticyclone.
    • 基金项目: 江西省自然科学基金(批准号: 2009GZW0026)和国家自然科学基金(批准号: 10905038, 11275123)资助的课题.
    • Funds: Project supported by the Natural Science Foundation of Jiangxi Province, China (Grant No. 2009GZW0026), and the National Natural Science Foundation of China (Grant Nos. 10905038, 11275123).
    [1]

    Vincent H C 2010 J. Hydro-enviro. Res. 3 173

    [2]

    Cullen M J P 2008 Phys. D 237 1461

    [3]

    Agnes H 2008 Comput. Math. Appl. 55 2295

    [4]

    Callaghan T G, Forbes L K 2006 J. Comput. Phys. 217 845

    [5]

    Läuter M, Dörthe H, Natalja R 2007 J. Comput. Phys. 223 609

    [6]

    Frank J, Reich S 2002 J. Comput. Phys. 180 407

    [7]

    Boyd J P 1998 Dyna. Atmosph. Oceans 28 69

    [8]

    Wu J, Lee T S, Shu B 2001 Comput. Methods Appl. Mech. Engrg. 190 2099

    [9]

    Mo J Q, Lin W T 2007 Acta Phys. Sin. 56 3662 (in Chinese) [莫嘉琪, 林万涛 2007 物理学报 56 3662]

    [10]

    Lou S Y, Jia M, Tang X Y, Huang F 2007 Phys. Rev. E 75 056318

    [11]

    Lou S Y, Jia Man, Huang F, Tang X Y 2007 Internat. J. Theor. Phys. 46 C 2007

    [12]

    Yang J R, Mao J J 2009 Acta Phys. Sin. 58 3611 (in Chinese) [杨建荣, 毛杰健 2009 物理学报 58 3611]

    [13]

    Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 物理学报 56 5049]

    [14]

    Tang X Y, Shukla P K 2008 Commun. Theor. Phys. (Beijing, China) 49 229

  • [1]

    Vincent H C 2010 J. Hydro-enviro. Res. 3 173

    [2]

    Cullen M J P 2008 Phys. D 237 1461

    [3]

    Agnes H 2008 Comput. Math. Appl. 55 2295

    [4]

    Callaghan T G, Forbes L K 2006 J. Comput. Phys. 217 845

    [5]

    Läuter M, Dörthe H, Natalja R 2007 J. Comput. Phys. 223 609

    [6]

    Frank J, Reich S 2002 J. Comput. Phys. 180 407

    [7]

    Boyd J P 1998 Dyna. Atmosph. Oceans 28 69

    [8]

    Wu J, Lee T S, Shu B 2001 Comput. Methods Appl. Mech. Engrg. 190 2099

    [9]

    Mo J Q, Lin W T 2007 Acta Phys. Sin. 56 3662 (in Chinese) [莫嘉琪, 林万涛 2007 物理学报 56 3662]

    [10]

    Lou S Y, Jia M, Tang X Y, Huang F 2007 Phys. Rev. E 75 056318

    [11]

    Lou S Y, Jia Man, Huang F, Tang X Y 2007 Internat. J. Theor. Phys. 46 C 2007

    [12]

    Yang J R, Mao J J 2009 Acta Phys. Sin. 58 3611 (in Chinese) [杨建荣, 毛杰健 2009 物理学报 58 3611]

    [13]

    Mao J J, Yang J R 2007 Acta Phys. Sin. 56 5049 (in Chinese) [毛杰健, 杨建荣 2007 物理学报 56 5049]

    [14]

    Tang X Y, Shukla P K 2008 Commun. Theor. Phys. (Beijing, China) 49 229

计量
  • 文章访问数:  4742
  • PDF下载量:  690
  • 被引次数: 0
出版历程
  • 收稿日期:  2013-01-19
  • 修回日期:  2013-03-14
  • 刊出日期:  2013-07-05

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