Lamb Kevin G, Polukhina Oxana, Talipova Tatiana, Pelinovsky Efim, Xiao Wenting, Kurkin Andrey
Department of Applied Mathematics, University of Waterloo, Waterloo, Canada N2L 3G1.
Phys Rev E Stat Nonlin Soft Matter Phys. 2007 Apr;75(4 Pt 2):046306. doi: 10.1103/PhysRevE.75.046306. Epub 2007 Apr 19.
Nonlinear wave motion is studied in a symmetric, continuously stratified, smoothed three-layer fluid in the framework of the fully nonlinear Euler equations under the Boussinesq approximation. The weakly nonlinear limit is discussed in which the governing equations can be reduced to the fully integrable modified Korteweg-de Vries equation. For some choices of the layer thicknesses the cubic nonlinear term is positive and the modified Korteweg-de Vries equation has soliton and breather solutions. Using such a stratification, the Euler equations are solved numerically using a sign-variable, initial disturbance. Breathers were generated for several forms of the initial disturbance. The breathers have moderate amplitude and to a good approximation can be described by the modified Korteweg-de Vries equation. As far as we know this is the first presentation of a breather in numerical simulations using the full nonlinear Euler equations for a stratified fluid.
在布辛涅斯克近似下的完全非线性欧拉方程框架内，研究了对称、连续分层、平滑的三层流体中的非线性波动。讨论了弱非线性极限，在此极限下控制方程可简化为完全可积的修正科特韦格 - 德弗里斯方程。对于某些层厚度的选择，三次非线性项为正，修正科特韦格 - 德弗里斯方程具有孤子和呼吸子解。利用这种分层，使用符号变量初始扰动对欧拉方程进行数值求解。针对几种形式的初始扰动生成了呼吸子。这些呼吸子具有适度的振幅，并且在很好的近似下可以用修正科特韦格 - 德弗里斯方程来描述。据我们所知，这是在使用分层流体的完全非线性欧拉方程进行数值模拟中首次呈现呼吸子。
