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Formulation and implementation of time-domain boundary conditions (TDBCs) at the surface of a reactive porous material are made challenging by the slow decay, complexity, or noncausal nature of many commonly used models of porous materials. In this paper, approaches are described that improve computational efficiency and enforce causality. One approach involves approximating the known TDBC for the modified Zwikker-Kosten impedance model as a summation of decaying exponential functions. A second approach, which can be applied to any impedance model, involves replacing the characteristic admittance with its Padé approximation. Then, approximating fractional derivatives with decaying exponentials, a causal and recursive TDBC is formulated.

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The performance bounds of a passive acoustic array operating in a turbulent medium with fluctuations described by a von Kármán spectrum are investigated. This treatment considers a single, monochromatic, plane-wave source at near-normal incidence. A line-of-sight propagation path is assumed. The primary interests are in calculating the Cramer-Rao lower bounds of the azimuthal and elevational angles of arrival and in observing how these bounds change with the introduction of additional unknowns, such as the propagation distance, turbulence parameters, and signal-to-noise ratio. In both two and three dimensions, it is found that for large values of the index-of-refraction variance, the Cramer-Rao lower bounds of the angles of arrival increase significantly at large values of the normalized propagation distance. For small values of the index-of-refraction variance and normalized propagation distance, the signal-to-noise ratio is found to be the limiting factor. In the two-dimensional treatment, it is found that the estimate of the angle of arrival will decouple from the estimates of the other parameters with the appropriate choice of array geometry. In three dimensions, again with an appropriate choice of array geometry, the estimates of the azimuth and elevation will decouple from the estimates of the other parameters, but due to the constraints of the model, will remain coupled to one another.

A general set of time-domain equations describing linear sound propagation in a rigid-frame, gas-saturated porous medium is derived. The equations, which are valid for all frequencies, are based on a relaxational model for the viscous and thermal diffusion processes occuring in the pores. The dissipative terms in the equations involve convolutions of the acoustic fields with the impulse response of the medium. It is shown that the equations reduce to previously known results in the limits of low and high frequencies. Alternative time-domain equations are also derived based on a Padé approximation.