Influence of Potential Waves on Point Vortex Motion

Abstract

In this chapter we will focus on the impact of waves on the motion of point vortices. These processes are very important for fluid dynamics. Waves and vortices are two key actors whose interaction determines all hydrodynamic phenomena. The previous chapter discussed point vortices and their interaction in detail. It should be emphasized that at the present time, the properties of waves and separately of point vortices are well understood. However, in hydrodynamic media, as a rule, vortices and waves are present simultaneously. Therefore, to study the interaction between these objects is extremely important. Lighthill initiated the study of this effect in [1, 2]. He examined the generation of potential waves by vortex motion. In [3] using numerical simulation, the effect of periodic motion at point vortices was studied. The study of the inverse effect of potential waves on the evolution of a vortex began relatively recently [4, 5]. It has been found that under the influence of potential waves, the nature of the evolution of point vortices changes qualitatively. In this chapter we consider some unusual effects that appear when this interaction emerges.