A theory of viscous evolution and selection of symmetric two-dimensional dipoles is suggested, based on a combination of numerical simulations and an asymptotic analysis, where the slow time scale associated with the vorticity diffusion due to viscosity is incorporated. It is shown that viscosity first brings a dipole to an intermediate asymptotic state, which is independent of the initial conditions, and then slowly takes the dipole away from this state. We demonstrate that, among the variety of possible ideal-fluid dipole solutions, viscosity going to zero selects a unique solution, which is described to high accuracy by the elliptical dipole solution with a separatrix aspect ratio of 1.037.

Linear and nonlinear mechanisms of sound generation in subsonic jets are investigated by numerical simulations of the compressible Navier–Stokes equations. The main goal is to demonstrate that low-frequency waves resulting from nonlinear interaction between primary, highly amplified, instability waves can be efficient sound radiators in subsonic jets. The current approach allows linear, weakly nonlinear and highly nonlinear mechanisms to be distinguished. It is demonstrated that low-frequency waves resulting from nonlinear interaction are more efficient in radiating sound when compared to linear instability waves radiating directly at the same frequencies. The results show that low-frequency sound radiated predominantly in the downstream direction and characterized by a broadband spectral peak near St = 0.2 can be observed in the simulations and described in terms of the nonlinear interaction model. It is also shown that coherent low-frequency sound radiated at higher angles to the jet axis (θ = 60°–707°) is likely to come from the interaction between two helical modes with azimuthal wavenumbers n = ±1. High-frequency noise in both downstream and side-line directions seems to originate from the breakdown of the jet into smaller structures.