Dynamics of interaction of vortices in shear turbulent flows

Abstract

The paper analyzes the results of a theoretical study of quasi-two-dimensional turbulence, two-dimensional equations of motion of which contain additional terms. The regularities of the dynamic interaction of vortex structures in shear turbulent flows of a viscous liquid are established. Based on the model of quasi-twodimensional turbulence, numerical values of the spatial scales of intermittency are determined as an alternation of large-scale and small-scale pulsations of dynamic characteristics. The experimentally observed alternation of vortex structures and the idea of their self-organization form the basis of the assumption of the existence of a geometric parameter determined by the size of the vortex core and the distance between their centers. Therefore, the main attention is paid to the theoretical calculation of the minimum spatial scales of the intermittency of vortex clusters. As a simplification, the vortex pairs are located in a reference frame, relative to which the centers of the vortices are stationary. Thus, the kinematic effect of the transfer of one vortex into the field of another is excluded from consideration. The symmetric and unsymmetric interactions of vortices, taking into account the one-sided and opposite directions of their rotation, are considered as realizable cases. A successful attempt is made to study the influence of the internal structure of vortex clusters on the numerical values of the minimum intermittency scales. The obtained results are satisfactorily confirmed by known theoretical and experimental data. Consequently, they can be used in all practical applications, without exception, where the structure of turbulence is taken into account, as well as for improving and expanding existing semi-empirical theories.