On the sound field from a moving source in a viscous medium.
Based on a one-dimensional model, a wave-theoretic analysis of the sound field from a moving, harmonic source in a viscous medium is developed. When the source is inbound to the receiver, the field consists of an attenuated propagating wave with Doppler up-shifted frequency. A similar wave is present when the source is outbound from the receiver but with down-shifted frequency. Also present on the outbound run is an evanescent wave that appears at the instant the source passes the receiver. The evanescent wave is very highly attenuated and exists only in the presence of both source motion and dissipation. Expressions are formulated for the frequency and attenuation coefficient of the two propagating waves and the evanescent wave. The attenuation of the propagating waves scales with the square of the frequency, which is a characteristic of viscous dissipation; and the attenuation is strongly asymmetrical, being significantly higher on approach than departure. The asymmetry in the attenuation arises partly from the upward and downward Doppler shifts in the frequency on approach and departure, respectively. In addition, the attenuation is skewed by the factor (1 +/- beta)(-1), where the lower (upper) sign applies on approach (departure) and beta is the Mach number of the source. At a Mach number of 0.85, the ratio of the inbound to outbound attenuation is 2000.
Buckingham
Michael J
MJ
Marine Physical Laboratory, Scripps Institution of Oceanography, University of California, San Diego, 9500 Gilman Drive, La Jolla, California 92093-0238, USA. mjb@mpl.ucsd.edu