The numerical solution of acoustic propagation through dispersive moving media

As the Navy expands its dependence on underwater communication between sensors, operating in areas where turbulent turbid water layers are present; there exists a need to accurately predict prior to sensor deployment how they will operate in these environments. The benthic nepheloid layer (BNL) is an example of a moving turbid water layer in the ocean. The BNL is characterized by changing vertical thickness, concentration and speed of the suspended material. Acoustic propagation and hence acoustic communication and system performance will be affected when operating in these areas. The suspended material will alter the sound speed, density and the attenuation of the medium. Thus what was once a non-dispersive quiescent environment is now a moving dispersive environment. The numerical solution of acoustic pulse propagation through dispersive moving media requires the inclusion of attenuation and its causal companion, phase velocity. For acoustic propagation in a linear dispersive quiescent medium, Szabo [J. Acoust. Soc. Am., 96, 491-500 (1994)] introduced the concept of a convolutional propagation operator that plays the role of a casual propagation factor in the time domain. The operator has been incorporated in the linear wave equation for quiescent media. Additionally it has been used to study propagation and scattering from such widely diverse media as bubble plumes in the ocean and ultrasound propagation in human tissue. In this work, this method is extended to address acoustic propagation in dispersive moving media. The development of the modified wave equation for sound propagation in dispersive media with inhomogeneous flow will be described, along with an example. The resulting modified wave equation is solved via the method of finite differences.