耗散对孤波与局地地形相互作用的影响

利用扰动法，由包括耗散和地形的准地转位涡度方程导出了强迫mKdV-Burgers方程，求得了小耗散情形下mKdV-Burgers方程的近似分析解，分析了mKdV孤波质量和能量的时间演变特性。对给定的局地地形，利用拟谱法对强迫mKdV-Burgers方程进行了数值求解。结果显示，小耗散的存在使弧波的振幅和移速随时间缓慢地减小，孤波宽度则随时间缓慢增大；在耗散和地形强迫的非线性系统中，在孤波与地形的相互作用中，耗散的存在使孤波在强迫区附近振荡传播，这有利于大振幅扰动的形成。

INFLUENCES OF DISSIPATION ON INTERACTION OF SOLITARY WAVE WITH LOCALIZED TOPOGRAPHY

By using a perturbation method, a forced mKdV-Burgers equation is derived from the geostrophic potential vorticityequation including dissipation and topography. An approximate analytic solution of the mKdV-Burgers equation is obtained for thecase with a small dissipation. The time evolution of mass and energy of the solitary waves is analyzed, and finally the numericalsolutions of the forced mKdV-Burgers equation with a small dissipation are given for a localized topographic forcing by using thepseudo-spectral method. The numerical results show that the presence of small dissipation causes a slow decrease of the amplitudeand the propagation speed of the solitary waves and slow increase of the solitary wave width. In the nonlinear system with dissipation and topographic forcing, the dissipation factor forces a moving solitary wave to oscillate in the forcing region during the interaction between the solitary wave and the topographic forcing, and it is advantageous to form large amplitude disturbances.