Hydrodynamics of natural oscillations of neutrally buoyant bodies in a layer of continuously stratified fluid (original) (raw)
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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.
Power-law decaying oscillations of neutrally buoyant spheres in continuously stratified fluid
Physics of Fluids, 2008
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.
2004
A combination of ray and Fourier methods is used to describe the linear internal wavefield generated by a horizontally moving, vertically oscillating, source in a stratified fluid. Ray theory is used to approximate the wavefield in a Fourier transform domain. The ray solutions are then superimposed by inverse Fourier transform to produce the spatial solution. This is a more practical approach than calculating the ray solution directly in the spatial domain, and it is general enough to treat background flows with depth dependent shear and stratification. The theory is compared with measurements of the internal wavefield generated in tank experiments by a towed sphere in a uniformly stratified background.
Dynamics of Atmospheres and Oceans, 2001
Experimental investigations of fine and macroscopic structures of density and velocity disturbances generated by a towing cylinder or a vertical strip in a linearly stratified liquid are carried out in a rectangular tank. A density gradient field is visualised by different Schlieren methods (direct shadow, 'slit-knife', 'slit-thread', 'natural rainbow') characterised by a high spatial resolution. Profiles of fluid velocity are visualised by density markers-wakes past a vertically descending sugar crystal or an ascending gas bubble. In a fluid at rest, the density marker acts as a vertical linear source of internal oscillations which allows us to measure buoyancy frequency over all depth by the Schlieren instrument directly or by a conductivity probe in a particular point. Sensitive methods reveal a set of high gradient interfaces inside and outside the downstream wake besides well-known large scale elements: upstream disturbances, attached internal waves and vortices. Solitary interfaces located inside the attached internal waves field have no features on their leading and trailing edges. A thickness of interfaces is defined by an appropriate diffusion coefficient and a buoyancy frequency. High gradient interfaces bound compact vortices. Vortices moving with respect to environment emit their own systems of internal waves randomising a regular pattern of attached antisymmetric internal waves. But after a rather long time a wave recurrence occurs and a regular but symmetric structure of the longest waves (similar to the pattern of initial attached internal waves) is observed again. High gradient interfaces and lines of their intersections act as collectors of a dye coming from a compact source or from a coloured liquid volume inside the tank and separate coloured and clear areas.
Flow Visualization of Internal Waves and Wakes of a Streamlined Body in a Stratified Fluid
Journal of Applied Fluid Mechanics
The wake and internal waves of a moving three dimensional (3D) airfoil body in a stratified fluid has been investigated in a large stratified tank with a finite depth using movies of shadowgraphs of the flow fields. Typical Reynolds and Froude numbers of the flow varied between 10 3 and 10 4 , and 0.3 and 2 respectively. The flows are generated often by towing the body in a uniformly stratified flow, while limited cases are carried out with body stationary and the channel was in recirculating mode. For some experiments the density profile had a stepped like shape. The wake flow is often consisted of internal waves including random and coherent ones. Distortion of density fields was also observed ahead and above the body in cases where the Froude number was subcritical. Results show that as the Froude number (Fr=U/Nh, where U is the body relative velocity, N is buoyancy frequency and h is the thickness of the body) is increased, the flow undergoes from a subcritical narrow wake (for Fr<1) to an internal waves dominated flow (for Fr~1) and then to a hydraulic jump with a turbulent wake with some mixing (for Fr>1). Typical wavelength of the exited internal waves is increased with Fr, as the theory predicts. The wake of the flow for Fr>1.4 appeared to collapse and some internal waves emission from it could be observed. Usually two types of internal waves, namely random small scale and large scale, more regular waves are observed.
Experimental and theoretical studies of oscillations of stratified fluid
IOP Conference Series: Materials Science and Engineering, 2018
This article examines the problem of small movements of liquids and the motion of a solid with a circular cylindrical cavity that is completely filled three of incompressible ideal fluids. Assuming irrotational fluid motion is formulated boundary value problem and solutions are obtained for potentials of the displacements of the particles of liquids. Using the Lagrange equations of the 2 nd kind the equations of motion of a hydromechanical system. Illustrates the difference between motion of a rigid body having a cavity with fluids from the case considered by N. E. Zhukovsky. Examines the problem of natural vibrations of liquids in a stationary tank and the motion of a rigid body fluids. Given formula, determine the natural frequencies and mode shapes. The article presents the results of an experimental study of motion of rigid body and liquids.
Doklady Physics, 2001
The pattern of attached internal waves [1] as an analogue of lee waves in the atmosphere [2] and ocean , as calculated by the source-sink method , agrees satisfactorily with observations and laboratory measurements on waves past perfectly shaped obstacles when the wake effect can be ignored. The wave field around a symmetric body dipped into a continuously stratified fluid is antisymmetric about the horizontal plane passing through the line of motion of the body center. In some flow regimes with waves interacting actively with vortices in the wake, the antisymmetric wave pattern evolves into a symmetric one at a large distance from the obstacle [6]. In a real situation, the obstacles are generally irregular in shape and, therefore, a skew in the flow can affect the field structure of radiated waves. This work is devoted to the experimental study of the internal waves generated by a vertical or inclined plate towed uniformly when not only a drag force but also a lifting force arises.
Experimental Investigations on Full Depth Buoyancy Flows in the Presenceof Surface Waves
Coastal Engineering Proceedings, 2017
The propagation of density currents in the presence of waves is experimentally investigated by considering a lock exchange schematization. In particular, we perform experiments considering the classical lock release, where the only driving force is buoyancy, as well as lock-exchange experiments with superimposed periodic surface waves, where the driving forces are both buoyancy and the wave-induced orbital motion. The application of an image processing technique is used for the detection of the main features of the front propagation (i.e depth, height, velocity etc.). All experiments are in full-depth conditions. The propagation of the waves is in intermediate water depth conditions. The presence of surface waves induces an orbital motion along the water column able to modify the dynamics of the density current propagation. Results show that the oscillation of the front advancement, as well as the oscillation of the gravity current depth observed in the presence of waves, are direct...