Numerical Models of Underwater Acoustic Propagation

Abstract

With 21 FiguresIn this chapter an attempt is made to summarize those models of propagation loss in the field of underwater acoustics which have been converted into an automated computer code capable of being executed by someone other than the originator for a wide variety of problems. No single model currently exists which is adequate for all aoplications. This is perhaps not surprising considering the diversity of the ocean environment and its boundaries, and the concomitant fact that the acoustic frequencies of interest span the regime from less than 10 Hz to greater than 100 kHz. As a result a large number of models, each with its own domain of validity which in many cases is difficult to precisely define, have been developed. Their sheer number makes an exhaustive summary impossible within these limited pages. Thus it was decided to limit consideration to those models which purport to be a solution of the wave equation found in Sect.2.2.1. Fundamentally these models consider the ocean to be a deterministic environment for which the speed of sound is only a function of the spatial coordinates. Non-deterministic effects, if accounted for at all, are included in an ad hoc fashion following the determination of the deterministic propagation loss result. Model development work for the more general problem is required and is in progress. However, this effort has not reached the point where "hands off" computer codes are available. This is due in part to a lack of available experimental! environmental data and the need for larger and faster computers.The models to be discussed can then be further segregated into range independent and range dependent categori es. The former assume that the ocean is cyl i ndri ca lly symmetrical, the speed of sound an arbitrary function of only the depth (z) coordinate, and that all boundaries are parallel with the range (r) coordinate. These models discussed, in Sect.3.1, are in a fairly complete state of development as evidenced by the concern with reducing computer execution time and memory without significantly sacrificing accuracy. The range-dependent models, taken up in Sect.3.2, allow for the speed of sound to be an arbitrary function of either 2 or 3 spatial coordinates, and the boundaries need not be parallel. Their state of development is not as complete.In general, the models which fall within these two subdivisions consider the ocean surface to be a pressure release boundary due to the large mismatch in characteristic impedance between water and air. The water column itself is treated as an ideal fluid J. A. DeSanto (ed.), Ocean Acoustics

Understanding deep-water striation patterns and predicting the waveguide invariant as a distribution depending on range and depth

“…Integral terms in Eq. (30) are small compared to S h g;m r. However, even if the waves decomposition of the eigenmode does not change much the effective group slowness, it still has a huge impact on wave dominance. Indeed, the equivalent modes (red markers) are completely different from equivalent waves (black markers).…”

“…At infinite ranges, the integral terms in Eq. (30) becomes negligible compared to S h g;m r. In this case, the four waves with the same mode number almost propagate at the same effective group slowness which is the horizontal group slowness of the mode, so that the usual definition of the travel time t m ¼ S h g;m r is appropriate and the WI as defined in Eq. (10) is a good approximation of the one defined in Eq.…”

“…7(a distance between black markers and blue dots denotes the contribution of integral terms of Eq. (30). The three equivalent waves produce three interference terms between waves w p and w q .…”

“…The WI can switch to a positive bvalue from a negative one, just because of the integral terms in Eq. (30). In other words, even if one considers refracted modes which are known to give birth to negative striation slopes, the resulting interference pattern can nevertheless exhibit positive striation slopes.…”

“…28 For a specified source/receiver configuration, visible interferences do not arise from all modes, but occur only between modes which are within those groups. This introduces the concept of "modal dominance" 3,29,30 in the calculation of E b . This feature is mentioned in the WI literature, 3,4 but as far as we know, no published investigation explicitly integrates this idea into a normal modes derivation of E b .…”