Obregon Maria, Raj Nawin, Stepanyants Yury
E.T.S. Ingeniería Industrial, University of Malaga, Dr Ortiz Ramos s/n, 29071 Malaga, Spain.
Faculty of Health, Engineering and Sciences, University of Southern Queensland, West St., Toowoomba, Queensland 4350, Australia.
Chaos. 2018 Mar;28(3):033106. doi: 10.1063/1.5021864.
The adiabatic decay of different types of internal wave solitons caused by the Earth's rotation is studied within the framework of the Gardner-Ostrovsky equation. The governing equation describing such processes includes quadratic and cubic nonlinear terms, as well as the Boussinesq and Coriolis dispersions: (u + c u + α u u + α u u + β u) = γ u. It is shown that at the early stage of evolution solitons gradually decay under the influence of weak Earth's rotation described by the parameter γ. The characteristic decay time is derived for different types of solitons for positive and negative coefficients of cubic nonlinearity α (both signs of that parameter may occur in the oceans). The coefficient of quadratic nonlinearity α determines only a polarity of solitary wave when α < 0 or the asymmetry of solitary waves of opposite polarity when α > 0. It is found that the adiabatic theory describes well the decay of solitons having bell-shaped profiles. In contrast to that, large amplitude table-top solitons, which can exist when α is negative, are structurally unstable. Under the influence of Earth's rotation, they transfer first to the bell-shaped solitons, which decay then adiabatically. Estimates of the characteristic decay time of internal solitons are presented for the real oceanographic conditions.
在加德纳 - 奥斯特罗夫斯基方程的框架内，研究了地球自转引起的不同类型内波孤子的绝热衰减。描述此类过程的控制方程包括二次和三次非线性项，以及布辛涅斯克色散和科里奥利色散：(u + c u + α u u + α u u + β u) = γ u。结果表明，在演化的早期阶段，孤子在由参数γ描述的弱地球自转影响下逐渐衰减。针对立方非线性α的正负系数（该参数的两种符号在海洋中均可能出现），推导了不同类型孤子的特征衰减时间。二次非线性系数α仅在α < 0时决定孤立波的极性，或在α > 0时决定相反极性孤立波的不对称性。研究发现，绝热理论能很好地描述具有钟形轮廓的孤子的衰减。与此相反，当α为负时可能存在的大振幅桌面型孤子在结构上是不稳定的。在地球自转的影响下，它们首先转变为钟形孤子，然后绝热衰减。给出了实际海洋学条件下内孤子特征衰减时间的估计。
