The oscillations of buoyant bodies in stratified fluids are deduced from the variations of their added mass. Three configurations are considered: a body displaced from its neutral level then released; a Cartesian diver set into oscillation by a modulation of the hydrostatic pressure, then released; and a body attached to a pendulum to which an impulse is applied. The first configuration is related to the dynamics of Lagrangian floats in the ocean. Two particular bodies are considered: an elliptic cylinder of horizontal axis, typical of two-dimensional bodies; and a spheroid of vertical axis, typical of three-dimensional bodies. The ultimate motion of the body consists of oscillations at the buoyancy frequency with an amplitude decaying algebraically with time. Before that, the resonant response of the system is observed, either aperiodic exponential decay when the system has no intrinsic dynamics, or exponentially damped oscillation otherwise. Comparison with available measurements demonstrates the need to include viscous dissipation in the analysis. At high Stokes number, dissipation comes from the Basset–Boussinesq memory force and is affected negligibly by the stratification; at low Stokes number, dissipation comes from Stokes resistance and exhibits a significant effect of the stratification.

中文翻译：

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浮力振荡

分层流体中浮体的振荡是根据其附加质量的变化推导出来的。考虑三种配置： 物体从中性水平位移然后释放；笛卡尔潜水员通过调节静水压力开始振荡，然后释放；和一个连接到钟摆上的物体，向其施加脉冲。第一种配置与海洋中拉格朗日浮子的动力学有关。考虑两个特定的物体：水平轴的椭圆柱，典型的二维物体；以及一个垂直轴的椭球体，这是典型的三维物体。身体的最终运动由浮力频率的振荡组成，其振幅随时间代数衰减。在此之前，观察系统的谐振响应，当系统没有内在动力学时，要么是非周期性指数衰减，要么是指数阻尼振荡。与现有测量结果的比较表明需要在分析中包括粘性耗散。在高斯托克斯数下，耗散来自 Basset-Boussinesq 记忆力，并且受分层的影响可以忽略不计；在低斯托克斯数下，耗散来自斯托克斯阻力，并且表现出显着的分层效应。