A novel application of Curle's acoustic analogy to aeolian tones in two dimensions

A new two-dimensional formula to describe aeolian tones radiated from rigid bodies in a uniform flow at low Mach numbers is proposed as an improved approximation of Curle's dipole solution. This modified Curle's dipole is composed mainly of two simple terms; one depends on time and the other does not, which represent the acoustic propagation and the hydrodynamic mean effect, respectively. The acoustic term includes the Doppler effect by regarding the sound speed to be directional in the source-fixed frame. The formula is verified in comparison with the results by direct numerical simulations (DNS) of the two-dimensional compressible Navier-Stokes equations for sounds from a circular cylinder in low Mach number flows. The results show that the modified Curle's dipole approximates well the DNS results not only for the fluctuation pressure but also for the mean pressure in the far field. The mathematical basis of the formula is also presented in relation to the exact dipole term of the Ffowcs Williams-Hawkings equation.