Free oscillations of a balanced ball on the horizon of neutral buoyancy in a continuously stratified fluid

Abstract

Interest in the investigation of free oscillations ofneutrally buoyant bodies in stratified fluids [1, 2],which arises from the practical needs of undersea navi-gation, has increased in the past few years owing to thefact that the number of neutrally buoyant probes drift-ing in the atmosphere and hydrosphere is progressivelyincreasing [3]. The work program involves regular sur-facing of submersible vehicles in order to read the dataand their submergence back to the working horizon. Inthe analysis of the measurement results, it is assumedthat the buoys do not disturb the structure of the strati-fied medium; the amplitude-frequency characteristicsof the process of stabilization of the buoy on the hori-zons of neutral buoyancy are determined in the approx-imation of an ideal fluid [1, 2, 4, 5]. The calculationresults are noticeably different from the data of labora-tory measurements [6] and seminatural measurements[7]. In this connection, it is interesting to analyze theprocess of stabilization of buoys in full detail with dueregard for the effects of buoyancy and dissipation. Thedevelopment of the methods of symbolic and numericalcalculation makes it possible to analyze more and morecomplex models of motion of bodies in an inhomoge-neous medium. In this paper, we construct and analyzean integro-differential model of oscillations of a ball ina continuously stratified viscous fluid.Consider an exponentially stratified fluid whosedensity ρ