Investigation of vortex structure dynamics in angular domain and near the surface with deepening (Q2711653)

The paper deals with numerical simulation of formation of large two-dimensional stationary vortices in a near-wall flow of angular domain or deepening (circular lune). Considering the ideal incompressible fluid, the complex potential of the flow is determined by a conformal mapping of the physical domain onto the upper half-plane. The strength and coordinates of the stationary vortices are obtained as functions of its geometric parameters. The stationary vortex is shown to possess own eigenfrequency, which corresponds to the frequency of the vortex precession around the stationary point under the small disturbance of its position in stream. The presence of such an eigenfrequency develops the selective response of the stationary vortex and local separation zone generated by this vortex to small periodic disturbances of incoming flow. These external disturbances deviate the vortex with respect to its stationary position. As a result, the vortex moves periodically along a closed trajectory of finite amplitude. Moreover, the dependence of the maximum deviation over period on the external disturbance frequency is of resonan character. A sharp increasing amplitude of the disturbed vortex motion, when the disturbance frequency approaches the vortex eigenfrequency, leads to the intensification of mixing and chaotic flow regime in local separate zones which are formed by standing vortices.