THEORETICAL AND EXPERIMENTAL STUDIES OF SLENDER VORTEX FILAMENTS

We show how theoretical analysis and experimental investigation comple ment each other in the study of the dynamics of slender vortex filamen ts. The asymptotic solution of a single filament requires the initial data of the shape of the centerline and the core structure. The latter is usually not available from experimental data. When the viscous dif fusion time t(d) of the core is of the order of the duration t of the experiment, we can define the contribution of the core structure to t he filament velocity by a finite number of parameters, which can then be determined by comparing the theoretical predictions of the motion o f the centerline with the experimental data. These parameters, in turn , calibrate the single vortex generator in the experimental set up by defining the moments of the initial core structure. In the inviscid li mit, where t much less than t(d), we derive the formulas for the cont ributions of the the core structure to the filament velocity and show that they depend only on two initial data. The analytical solution can then be used to model the interaction of filaments with or without bo undaries or interfaces, and compare with the experimental data.