Disturbances to a Rotating Fluid with a Sphere Moving along the Axis of Rotation
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摘要: 本文用线化理论分析了整体旋转的理想流体中有一个圆球沿旋转轴作匀速运动时流体的扰动,基于旋轴对称流动的假设导出了决定运动稳定性的扰动压力方程和扰动流函数方程.用简正模法分析了扰动流函数方程,得出了非平凡中性扰动的波数与波速必须满足的约束条件,并求出了扰动的精确表达式.文中得出结论,中性扰动共有三种可能的形式.Abstract: In this paper,the disturbaces to a uniformly rotating idealfluid,with a sphere moving steadily along the axis of rotation are analysed by using linearization theory,the equations of disturbance pressure and distur bance stream function governing the stability of motion are derived based on the assumption that the flow is rotational symmetric.The equation of distur bance stream function is analysed with the method of normal modes,and the constraints on wave number and wave velocity of the nontrivial neutral disturbances are established and the exact expression of the neutral distur bances are obtained.The conclusion is drawn that there are three kinds of possible forms of ne utral disturblances.
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Key words:
- rotating fluids /
- mo tion of body /
- small disturbances /
- stability
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