## Wave processes and self-organization processes in bubbly liquids## Nail Gumerov, Galiia GilmanovaA phenomenon of bubble self-organization related self-action of the acoustic field is strongly nonlinear effect, which occurs, for example, in acoustic cavitation and sonochemical reactors. It is due to a two-way field-particle interaction, when the bubbles change their position and sizes due to the acoustic radiation and other forces and rectified diffusion; so the acoustic properties of the medium vary in space and time, which leads to restructuring of the acoustic field. So far, mathematical models of the phenomenon are studied in very simplified settings because of the complexity of the problem (especially in the three-dimensional formulation). In a weak high-frequency acoustic field bubbles "vibrate" with the frequency of the sound field, which, in fact, has no effect on this field. However, in consideration of non-linearity bubbles drift in the relatively slow time scale (due to the Bjerknes forces) and grow or collapse (due to the rectified diffusion). That is what leads to a restructuring of the field, which is quite sensitive to the presence of bubbles. Secondary effects, such as coagulation and fragmentation of bubbles, can also play an important role in the reconstruction of the field. We have developed and tested a 2D and 3D codes for simulation of bubble self-organization. Pseudospectral iterative solvers for the Helmholtz equation with spatially non-uniform wavenumber and Lagrangian methods for tracking the dynamics of |