Abstract
Two questions are asked, and answered, concerning the dynamics of vortex filaments in a three-dimensional slightly compressible fluid with constant sound speed: What is the flow (including the sound) generated by a vortex in prescribed motion? What is the response of a test vortex to an external flow? The first question is answered by a convolution of a Green’s function with a source localized at the filament; the second by a differential equation valid in the localized induction approximation. A variational principle encompassing both problems is also provided.
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