Buoyancy oscillations

Abstract

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.

A Cartesian diver to study oscillations and internal gravity waves in a stratified fluid

“…We can exploit the results of this first experiment and immerse a Cartesian diver in an analogously obtained stratified liquid, with the great advantage that the density of the diver ρ t (p) can be finely tuned by changing the external pressure p applied to the container [20,21]. For any pressure, the diver will be in stable equilibrium at a depth z 0 of the layered fluid such that ρ t (p(z 0 )) = ρ(z 0 ) = ρ 0 , where ρ(z) is the density of the solution of salt and water.…”

“…In the following we will outline a simple frictionless linear model able to describe the oscillations of a density matched body immersed in a stably stratified fluid. For a recent exhaustive treatise including the effects of viscous dissipation see [21].…”

“…The interest of this research topic is also witnessed by some recently published research papers, where the fundamental aspects of the dynamical behavior of a Cartesian diver in a stratified fluid are studied both experimentally and theoretically [20,21]. The experimental work by Le Gal et al investigates the dynamics of a Cartesian diver forced to oscillate in a stably stratified fluid in a rectangular narrow container [20].…”

“…Inspired by the seminal work of Couder and coworkers on the wave-particle duality of droplets bouncing at the free surface of a vibrated fluid bath [22], the authors investigate the possibility of finding hydrodynamical quantum analogs determined by the association between the diver and the internal gravity waves generated by its oscillations. The very recent theoretical work by Voisin [21], provides an accurate modelling of the oscillations of buoyant bodies in stratified fluids, taking into account both the effect of friction and the one of the fluid inertia, which acts as a virtual added mass. Both papers are extremely interesting and report new research results.…”

Numerical simulation of the 2D trajectory of a non-buoyant fluid parcel under the influence of inertial oscillation

“…Inertial oscillations, arising from the intricate interplay between the Earth's rotation and fluid motions, exert a profound influence on the behavior of these fluid parcels [1]. Accurately predicting the transport and dispersion of tracers such as pollutants, nutrients, and biological organisms in the oceans and atmosphere hinges on a comprehensive understanding of the trajectories of non-buoyant particles subjected to such oscillating flows [2].…”