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The possibility of using two models to study the evolution and maximum increase in ampli tude of small distortions of sphericity of a bubble during its strong compression in a liquid is investi gated. The investigation is performed in the conditions of experiments on acoustic cavitation of deu terated acetone. The first (fully hydrodynamic) model is based on the two dimensional equations of gas dynamics. It is valid in every stage of the bubble compression. But its use takes up a lot of compu tational time. The second (simplified) model is derived by splitting the liquid and vapor motion into a spherical part and its small nonspherical perturbation. To describe the spherical component, a one dimensional version of the two dimensional model is used in this model. The advantage of the simpli fied model over the full one is its much lower consumption of computational time. At the same time, the evolution of the nonspherical perturbation in this model is described by utilizing a number of assumptions, validity of which is justified only at the initial stage of the bubble compression. It is there fore logical to apply the simplified model at the initial low speed stage of the bubble compression, while the full hydrodynamic one is applied at its final high speed stage. It has been shown that such a combination allows one to significantly reduce the computational time. It has been found that the sim plified model alone can be used to evaluate the maximum increase of the amplitude of small sphericity distortions of a bubble during its compression.

The region of application of approximate methods for describing the effect of viscosity on the decay of small distortions of a gas bubble from a spherical shape is refined by comparing solutions obtained using the approximate methods and the exact Prosperittimodel. Approximate methods corresponding to a number of limiting cases are considered. The features of the errors arising in descriptions of the evolution of the distortions using approximate methods are found in the case of a significant effect of rotational fluid flow. A new approximate method is proposed.Introduction. Until recently, in problems of bubble dynamics with small distortions from a spherical shape, the effect of fluid viscosity in relation to its effect within the framework of the Navier-Stokes equations has been taken into account approximately. In particular, this has been implemented using the solution of the problem of decay of distortions in a spherical symmetric field of mass forces [1,2]. A similar description of the viscosity effect is obtained under the assumption that the effect of fluid flow vorticity is manifested only in the surface layer [3]. Approximate methods for describing the viscosity effect are not always applicable. Their use is problematic, for example, in studies of single bubble sonoluminescence (SBSL) [4]. The SBSL phenomenon is the periodic emission of short light pulses by a gas bubble which performs radial oscillations in the current antinode of an ultrasonic standing pressure wave [4]. The discovery of the SBSL phenomenon in 1990 has stimulated research of distortions of micronsize bubbles from a spherical shape. The smaller the bubble size, the greater the viscosity effect. Therefore, in studies of SBSL, use has been made of the so-called exact method of accounting for viscosity [5] and a number of approximate method based on it [6,7]. The method of accounting for viscosity in accordance with [5] is called exact in the sense that in the case of small distortions, it is equivalent to allowing for viscosity within the framework of the Navier-Stokes equations.It is of interest to study whether the exact method of accounting for viscosity [5] can be replaced by an approximate method because the exact method is mathematical much more complicated than approximate methods [1-3, 6, 7] although it is much simpler than accounting for viscosity within the framework of the Navier-Stokes equations.The exact method of accounting for viscosity [5] was used to study the decay of oscillations of the bubble shape. Thus, Asaki and Marston [8] studied the decay of nonspherical oscillations of bubbles which were acoustically trapped in fresh water and sea water. Roberts and Wu [9] give an asymptotic solution for the magnitude of distortion for large values of the free decay time. A number of asymptotic solutions were obtained in [10] using the Laplace transformation.The goal of the present paper is to refine the region of application of the approximate methods of describing viscosity by comparing solutions obtained by approximate meth...

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