Force on a Body Exerted by Vortex Motion

Abstract

Based on the theory of aerodynamic sound in the presence of a solid body, it is found that the force on the body exerted by a system of loop vortices is represented by a linear combination of an individual integral for each vortex, and that the integral is reduced to the time derivative of a volume flux J (through the vortex loop) of a hypothetical potential flow around the body. The second time derivative of J gives the amplitude of the dipolar sound wave excited by the vortex motion.