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首页> 外文期刊>Nonlinear processes in geophysics >Lagrange form of the nonlinear Schrodinger equation for low-vorticity waves in deep water
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Lagrange form of the nonlinear Schrodinger equation for low-vorticity waves in deep water

机译：深水中低涡波的非线性Schrodinger方程的拉格朗日形式

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摘要

The nonlinear Schrodinger (NLS) equation describing the propagation of weakly rotational wave packets in an infinitely deep fluid in Lagrangian coordinates has been derived. The vorticity is assumed to be an arbitrary function of Lagrangian coordinates and quadratic in the small parameter proportional to the wave steepness. The vorticity effects manifest themselves in a shift of the wave number in the carrier wave and in variation in the coefficient multiplying the nonlinear term. In the case of vorticity dependence on the vertical Lagrangian coordinate only (Gouyon waves), the shift of the wave number and the respective coefficient are constant. When the vorticity is dependent on both Lagrangian coordinates, the shift of the wave number is horizontally inhomogeneous. There are special cases (e.g., Gerstner waves) in which the vorticity is proportional to the squared wave amplitude and nonlinearity disappears, thus making the equations for wave packet dynamics linear. It is shown that the NLS solution for weakly rotational waves in the Eulerian variables may be obtained from the Lagrangian solution by simply changing the horizontal coordinates.
机译：衍生了描述利拉扬子坐标在拉格朗日坐标中无限深液中弱旋转波包的传播的非线性薛定兆（NLS）方程。假设涡度是拉格朗日坐标的任意函数，并且在与波陡本成比例的小参数中的Quadatigation。涡流效应在载波中的波数的偏移中表现出载波的偏移以及乘以非线性术语的系数乘以变化。在仅对垂直拉格朗日坐标的涡流依赖性的情况下，波数和相应系数的偏移是恒定的。当涡度取决于拉格朗日坐标时，波数的偏移是水平不均匀的。有特殊情况（例如，Gerstner Waves），其中涡度与平方波幅度成比例，非线性消失，从而使波分组动力学线性的方程。结果表明，通过简单地改变水平坐标，可以从拉格朗日解决方案获得欧拉变量中弱旋转波的NLS解决方案。

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