Aircraft Vortex Wake Dynamics

Sound scattering by a vortex: case of exponentially decaying velocity

“…It follows that in case PWPV and, more broadly speaking, in the case of a uniform plane wave (1.3) scattering by an arbitrary flow with non-zero total circulation the RP is ill-posed. There is no contradiction because the total kinetic energy of an unbounded incompressible flow with as is hence it cannot exist, as noted by Reinschke et al (1997) and Gaifullin (2015, § III.1). In an unbounded three-dimensional fluid, only vortical structures with zero total circulation over any cross-section can emerge, such as the wake vortex behind an aeroplane with a high-aspect-ratio wing, which consists of two vortex tubes with opposite circulation, or the helicopter vortex ring.…”

“…In the case of low Mach numbers , the solution is reduced to one in an incompressible fluid. The flow is the difference between the irrotational vortex and the Lamb–Oseen (1912) vortex outside (Gaifullin 2015, § III.1), and a solid-body rotation inside. The circulation distribution is where is kinematic viscosity of the unperturbed fluid.…”