Acoustic Emission by a Vortex Ring Passing near a Sharp Wedge
Abstract
The acoustic field is analysed for a vortex ring passing near a sharp wedge of span angle φ _{0} at low Mach numbers. This includes the halfplane as a special case (φ _{0} = 0), which has received detailed consideration in the literature. Let U be the ring's velocity, c the sound speed, and L the shortest distance of the vortex ring from the edge of the wedge. The sound pressure at large distances x is found to be proportional to c^{π /φ 1}U^{π /φ 1+2}L^{2}x^{1}, while the time history of the wave profile is in the form of fractional derivative D_{hat{t}}^{π /φ 1} g(hat{t}) with φ _{1} = 2π  φ _{0}, where hat{t} is dimensionless time and g(hat{t}) is a smooth function of hat{t}. The directivity of the radiated sound is found to be given by cos ((π /φ _{1})φ _{i}) (sin θ _{i})^{π /φ 1}, where (θ _{i}, φ _{i}) denotes the direction of observation. An additional factor, appearing as (sin θ _{p})^{π /φ 1+2}, characterizes the effect of the angle θ _{p}, formed between the path of the vortex ring and the edge of the sharp wedge.
 Publication:

Proceedings of the Royal Society of London Series A
 Pub Date:
 April 1994
 DOI:
 10.1098/rspa.1994.0053
 Bibcode:
 1994RSPSA.445..141C