NUMERICAL STUDY OF SOUND EMISSION BY 2D REGULAR AND CHAOTIC VORTEX CONFIGURATIONS

The far-field noise generated by a system of three Gaussian vortices l ying over a flat boundary is numerically investigated using a two-dime nsional vortex element method. The method is based on the discretizati on of the vorticity field into a finite number of smoothed vortex elem ents of spherical overlapping cores. The elements are convected in a L agrangian reference along particle trajectories using the local veloci ty vector, given in terms of a desingularized Biot-Savart law. The ini tial structure of the vortex system is triangular; a one-dimensional f amily of initial configurations is constructed by keeping one side of the triangle fixed and vertical, and varying the abscissa of the centr oid of the remaining vortex. The inviscid dynamics of this vortex conf iguration are first investigated using non-deformable vortices. Depend ing on the aspect ratio of the initial system, regular or chaotic moti on occurs. Due to wall-related symmetries, the far-field sound always exhibits a time-independent quadrupolar directivity with maxima parall el and perpendicular to the wall. When regular motion prevails, the no ise spectrum is dominated by discrete frequencies which correspond to the fundamental system frequency and its superharmonics. For chaotic m otion, a broadband spectrum is obtained; computed soundlevels are subs tantially higher than in non-chaotic systems. A more sophisticated ana lysis is then performed which accounts for vortex core dynamics. Resul ts show that the vortex cores are susceptible to inviscid instability which leads to violent vorticity reorganization within the core. This phenomenon has little effect on the large-scale features of the motion of the system or on low frequency sound emission. However, it leads t o the generation of a high-frequency noise band in the acoustic pressu re spectrum. The latter is observed in both regular and chaotic system simulations. (C) 1995 Academic Press, Inc.