Konovalyuk T. Sound fields generated by interacting coherent vortex structures.

The thesis is devoted to investigations of interaction of coherent vortex structures and the sound field as the result of such interaction. Within the second-order moment model of vortex interaction and the Lighthill acoustic analogy (in Powell formulation), the interaction of several coherent vortex structures and the sound field resulted from such interaction are calculated. The two-dimensional problem in absence of boundaries is considered. The medium in which the vortices are interacting is an ideal and incompressible one; the acoustic fields are calculated with the allowance for medium compressibility. Interactions of two initial Rankine vortices of various sizes are investigated. In particularly, with the example of two initial Rankine vortices a dynamic criterion is formulated allowing the substitution of the vortex spot centres with equivalent vortex points. Various types of interaction between three point vortices with intensities of different signs are investigated. The sound field for elastic interaction between two Kirchhoff vortices is calculated. The quantitative relations between the rotation of the three point vortex system and the rotation of the directivity pattern of their generated sound field are derived. The lower part of the sound spectrum from the distributed vortex interactions is given by the large-scale vortical motions, while the higher frequencies result from the interaction or presence of internal degrees of freedom of vortices. In general case of a vortex system performing the elastic interaction, the acoustic criterion is formulated which estimates the possibility of replacement of large-scale vortical motions of distributed vortices with their point analogues. It is noted that the point vortex model cannot be used when studying sound generated by vortex patches.