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Nonlinear radial oscillations of a fluid in a parabolic basin with regard for the external action

机译:考虑外部作用的抛物线形盆地中流体的非线性径向振荡

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Within the framework of the theory of long waves, we find a class of exact analytic solutions of the problem of description of nonlinear axially symmetric oscillations of a fluid in a parabolic basin with regard for the action of stationary radial bulk forces. The radial projection of the velocity of these oscillations (seiches) is a linear function of the radial coordinate, whereas the azimuthal velocity and displacements of the free surface of the fluid are polynomials in the radial coordinate with time-dependent coefficients. The method of finding solutions is based on the exact replacement of the original problem by a system of ordinary differential and algebraic equations. The action of the bulk forces may result either in the increase in the frequency of oscillations of the fluid and in the decrease in this frequency and affect the motion of the water edge, the characteristics of waves, and the velocity field.
机译:在长波理论的框架内,我们发现一类精确的解析解,用于描述抛物线形盆地中流体的轴向轴向对称对称振动,并考虑了径向径向总力的作用。这些振荡速度(seiches)的径向投影是径向坐标的线性函数,而流体的自由表面的方位角速度和位移是径向坐标中随时间变化的系数的多项式。寻找解决方案的方法是基于使用常微分和代数方程组对原始问题的精确替换。主体力的作用可能导致流体振荡频率的增加,或者导致该频率的减小,并影响水边的运动,波的特性和速度场。

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