Power-law decaying oscillations of neutrally buoyant spheres in continuously stratified fluid (original) (raw)
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Oscillation and levitation of balls in continuously stratified fluids
The free motion of balls is investigated experimentally in continously stratified fluid in a finite container. The oscillation frequency is found to be very close to the local Brunt-Väisäla frequency. The effect of added mass proves to be practically negligible. The evolution of rear jets is demonstrated, and a kind of long term levitation is found. We show that the classical viscous drag would lead to a much stronger damping than observed in the experiment. This is interpreted as a consequence of the feedback from the previously excited internal waves following their reflection from the boundaries. A phenomenological equation with a modified drag term is proposed to obtain a qualitative agreement with the observations. We point out that the inclusion of a history term would lead further away from the observed data.
Damping of the free oscillations of a neutral buoyancy sphere in a viscous stratified fluid
Journal of Applied Mathematics and Mechanics, 2009
A technique is developed for calculating the oscillations of balanced spheres at neutral buoyancy levels based on the linearization of the equations of the mechanics of a viscous, continuously stratified fluid. A self-consistent system of integro-differential equations is obtained and analysed using perturbation theory methods. The results of calculations of the displacements of the centres of the spheres are reduced to a form which a permits direct comparison with a laboratory experiment and they agree with the data of measurements. A comparison is made with calculations of the free oscillations of a sphere in an ideal fluid.
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The flow patterns induced by floats of different shapes (sphere, short and long cylinders) freely sinking to the neutral-buoyancy horizon in a continuously stratified fluid are investigated using optical methods. General flow elements, both large-scale (waves, vortices, hydrodynamic wake) and fine-scale (boundary layers, extended autocumulative jets), are distinguished. For large times, the float oscillation frequencies are of the order of or greater than the buoyancy frequency of the medium. This indicates the significant effect of the induced flows on the motion of the float.
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We present an engaging levitation experiment that students can perform at home or in a simple laboratory using everyday objects. A cork, modified to be slightly denser than water, is placed in a jug containing tap water and coarse kitchen salt delivered at the bottom without stirring. The salt gradually diffuses and determines a stable density stratification of water, the bottom layers being denser than the top ones. During the dissolution of salt, the cork slowly rises at an increasing height, where at any instant its density is balanced by that of the surrounding water. If the cork is gently pushed off its temporary equilibrium position, it experiences a restoring force and starts to oscillate. Students can perform many different measurements of the phenomena involved and tackle non-trivial physical issues related to the behaviour of a macroscopic body immersed in a stratified fluid. Despite its simplicity, this experiment allows to introduce various theoretical concepts of releva...
Hydrodynamics of a sphere in a stratified fluid
Fluid Dynamics, 1989
The flow pattern around a sphere moving at constant velocity in a fluid with an exponential density distribution is investigated by optical methods. The thin density boundary layer forming the highgradient envelope of the wake is distinguished as one of the elements of the structure. The symmetry properties of the flow are investigated. The limits of applicability of the traditional approximation of weak stratification in the problem of excitation of attached internal waves are noted.
Flow-induced vibrations of a non-buoyant sphere
2008
The current study explores the behaviour of a neutrally buoyant sphere in a uniform flow using well resolved numerical simulations and water channel experiments. It is found that there exist seven different flow regimes within the range of the Reynolds number = [50, 800] according to the sphere response. Regime I (Re = [50, 205]) and Regime II (Re = [210, 260]) are characterised by steady flow structure without body movement except the loss of axisymmetry in Regime II. The sphere starts to vibrate from Regime III (Re = [270, 280]). Regime IV (Re = [300, 330]) shows suppressed body oscillation and steep decrease of off-centered distance in the plane normal to streamwise direction (yz plane). In Regime V (Re = [335, 550]), the sphere oscillates around (0,0) in yz plane. The sphere of Regime VI (Re = [600, 800]) oscillates rather irregularily. The transitions are compared with those for a fixed sphere. A series of experiments is carried out in a water channel to complement and validate the numerical findings. The experiments recorded the position of the sphere and covered the range of the Reynolds number Re = [700, 4000], extending the range of the numerical study. Within the Reynolds range = [700, 800], where the results of the simulations and experiments overlap, and corresponds to the Regime VI, it is observed that the response of the sphere is irregular. This verifies the existence of Regime VI which has been found in the numerical study. For Re ≥ 2000, it is also observed that the sphere motion reverts from highly irrgular to quasi-circular motion in the plane normal to incoming flow as the Reynolds number is increased further.
Force on a body in a continuously stratified fluid. Part 2. Sphere
Journal of Fluid Mechanics, 2003
In this paper the experimental study presented in Part 1 is extended to the threedimensional case. The in-line force coefficients (added mass and damping) of a sphere oscillating horizontally in a uniformly stratified fluid of limited depth and in a smooth pycnocline are evaluated from Fourier-transforms of the experimental records of impulse response functions. The hydrodynamic loads in the three-and two-dimensional cases are shown to be essentially different, notably in the lowfrequency limit, where the damping in the three-dimensional case is zero, while in the two-dimensional case it is maximized due to phenomena akin to blocking. The generalization of the experimental results for affinely similar geometries is discussed. It is found that, as the characteristic vertical extent of stratification decreases, the mean power of internal waves radiated by the oscillating sphere reduces and the maximum of the frequency spectrum of wave power shifts toward lower frequency, which is qualitatively similar to the effects observed in the two-dimensional case. Physically, horizontal stratified waveguides act as low-pass filters since internal waves with nearly vertical group-velocity vector cannot be effectively radiated from oscillating bodies.
Experiments on buoyant-parcel motion and the generation of internal gravity waves
Journal of Fluid Mechanics, 1978
Laboratory experiments were conducted to study the motion of miscible buoyant fluid parcels in both homogeneous and stratified media, and were complemented with numerical experiments using the model of Orlanski & Ross (1973). Parcel motion in the homogeneous case was found to be shape-preserving, in agreement with the large body of data for such motion. The stratified medium experiments were such that the parcel attained equilibrium positions. It was found that the time for the parcel to reach maximum depth was approximately 0.7 times the buoyancy period, independent of that depth. The subsequent collapse of the parcel and generation of internal gravity waves was observed. Ray-like patterns of waves propagated out from the collapse region, and wave frequencies near 0.7 times the Brunt-Vaisala frequency were predominant. The internal wave energy radiated away from the collapsed parcel was estimated and found to be 20 to 25 yo of the change in the system potential energy.
Internal waves produced by the turbulent wake of a sphere moving horizontally in a stratified fluid
Journal of Fluid Mechanics, 1993
The internal gravity wave field generated by a sphere towed in a stratified fluid was studied in the Froude number range 1.5 ≤ F ≤ 12.7, where F is defined with the radius of the sphere. The Reynolds number was sufficiently large for the wake to be turbulent (Re∈[380, 30000]). A fluorescent dye technique was used to differentiate waves generated by the sphere, called lee waves, from the internal waves, called random waves, emitted by the turbulent wake. We demonstrate that the lee waves are well predicted by linear theory and that the random waves due to the turbulence are related to the coherent structures of the wake. The Strouhal number of these structures depends on F when F [lsim ] 4.5. Locally, these waves behave like transient internal waves emitted by impulsively moving bodies.