Sound generation mechanism of compressible vortex reconnection

Abstract

We study the sound generation mechanism of initially subsonic viscous vortex reconnection at vortex Reynolds number $Re~(\equiv \text {circulation}/\text {kinematic viscosity})=1500$ through decomposition of Lighthill's acoustic source term. The Laplacian of the kinetic energy, flexion product, enstrophy and deviation from the isentropic condition provide the dominant contributions to the acoustic source term. The overall (all time) extrema of the total source term and its dominant hydrodynamic components scale linearly with the reference Mach number $M_o$ ; the deviation from the isentropic condition shows a quadratic scaling. The significant sound arising from the flexion product occurs due to the coiling and uncoiling of the twisted vortex filaments wrapping around the bridges, when a rapid strain is induced on the filaments by the repulsion of the bridges. The spatial distributions of the various acoustic source terms reveal the importance of mutual cancellations among most of the terms; this also highlights the importance of symmetry breaking in the sound generation during reconnection. Compressibility acts to delay the start of the sequence of reconnection events, as long as shocklets, if formed, are sufficiently weak to not affect the reconnection. The delayed onset has direct ramifications for the sound generation by enhancing the velocity of the entrained jet between the vortices and increasing the spatial gradients of the acoustic source terms. Consistent with the near-field pressure, the overall maximum instantaneous sound pressure level in the far field has a quadratic dependence on $M_o$ . Thus, reconnection becomes an even more dominant sound-generating event at higher $M_o$ .