Direct simulation of isolated elliptic vortices and of their radiated noise

The aerodynamic evolution and the acoustic radiation of elliptic vortices with various aspect ratios and moderate Mach numbers are investigated by solving numerically the full compressible Navier–Stokes equations. Three behaviours are observed according to the aspect ratio σ = a/b where a and b are the major and minor semi-axes of the vortices. At the small aspect ratio σ = 1.2, the vortex rotates at a constant angular velocity and radiates like a rotating quadrupole. At the moderate aspect ratio σ = 5, the vortex is initially unstable. However the growth of instability waves is inhibited by the return to axisymmetry which decreases its aspect ratio. The noise level becomes lower with time and the radiation frequency increases. For vortices with larger aspect ratios σ ≥ 6, the return to axisymmetry does not occur quickly enough to stop the growth of instabilities, which splits the vortices. Various mergers are then found to occur. For instance in the case σ = 6, several successive switches between an elliptic state and a configuration of two co-rotating vortices are observed. The present results show that the initial value of the aspect ratio yields the relative weight between the return to axisymmetry which stabilizes the vortex and the growth of instabilities which tends to split it. Moreover the noise generated by the vortices is also calculated using the analytical solution derived by Howe (J. Fluid Mech. 71:625–673, 1975) and is compared with the reference solution provided by the direct computation. This solution is found to be valid for σ = 1.2. An extended solution is proposed for higher aspect ratios. Finally, the pressure field appears weakly affected by the switches between the two unstable configurations in the case σ = 6, which underlines the difficulty to detect the split or the merger of vortices from the radiated pressure. This study also shows that elliptic vortices can be used as a basic configuration of aerodynamic noise generation.