Cathy Ann Clark

Acoustic wave propagation in horizontally variable media

An overview of the multipath expansion method of solving the Helmholtz wave equation to describe the underwater sound field for a fixed point source in a plane multilayered medium is presented. The approach is then extended to account for horizontal variations in bottom depth, bottom type, and sound speed in the stationary phase approximation. Comparisons of model results to a limited number of measured data sets and standard propagation codes are presented.

An Efficient Normal Mode Solution to Wave Propagation Prediction

In this paper, an overview of a normal mode method of solving the Helmholtz wave equation to describe the underwater sound field for a fixed-point source in a plane multilayered medium is presented. The mode functions are well-defined at all depths of the medium as they are continuous across turning points of the separated depth-dependent differential equation. Comparisons of model results to a limited number of measured data sets and benchmark propagation codes are presented.

A normal mode inner product to account for acoustic propagation over horizontally variable bathymetry

This talk will consider the conversion of normal mode functions over local variations in bathymetry. Mode conversions are accomplished through an inner product, which enables the modes compromising the field at each range-dependent step to be written as a function of those in the preceding step. The efficiency of the method results from maintaining a stable number of modes throughout the calculation of the acoustic field. A verification of the inner product is presented by comparing results from its implementation in a simple mode model to that of a closed-form solution for the acoustic wedge environment. A solution to the more general problem of variable bottom slope, which involves a decomposition of bathymetric profiles into a sequence of wedge environments, will also be discussed. The overall goal of this research is the development and implementation of a rigorous shallow water acoustic propagation solution which executes in a time window to support tactical applications.

Mode coupling due to bathymetric variation

In shallow water the assumption of range independence fails in conditions of rapidly-varying bathymetry and/or horizontal sound speed. In these environments, the modes of vibration of the acoustic wave equation become coupled, with a transfer of energy between adjacent modes occurring upon traversing a horizontal change of environment. In this talk, we will consider some simple applications of mode conversions due to variable bathymetry. Results will be compared to closed form propagation solutions in constant-slope wedge environments. The ultimate goal of this research is the development of a fully non-adiabatic range-dependent mode solution which retains analytical integrity while executing in a time window that is tactically useful for warfare applications.

Normal mode coupling through horizontally variable sound speed

In conjunction with construction of a normal mode model specifically designed to compute acoustic propagation in shallow water environments, the coupling associated with horizontally variable sound speed is predicted using a closed form solution in a modified Pekeris wave guide with a hard bottom. The code enables analysis of the correspondence between mode summation and the corresponding wave propagation as represented by ray propagation. The closed form solution is being used to provide insights into horizontal mode coupling and as a benchmark for verification of coupling in the shallow water normal mode solution.In conjunction with construction of a normal mode model specifically designed to compute acoustic propagation in shallow water environments, the coupling associated with horizontally variable sound speed is predicted using a closed form solution in a modified Pekeris wave guide with a hard bottom. The code enables analysis of the correspondence between mode summation and the corresponding wave propagation as represented by ray propagation. The closed form solution is being used to provide insights into horizontal mode coupling and as a benchmark for verification of coupling in the shallow water normal mode solution.

Acoustic wave propagation in horizontally variable shallow water

A unique normal mode solution which approximates sound speed variation with depth by a sequence of isovelocity layers is verified for a sample of range independent environments. Within each layer, two closed-form fundamental solutions which satisfy the separated depth-dependent wave equation are formulated with complex analogues to be used in evanescent regions. Piecewise-continuous potential mode solutions are constructed by satisfying an upper boundary condition and extending through isovelocity layers to the bottom. The value of the Wronskian for the Green’s function thus obtained is used to locate the eigenvalues of the normal modes comprising the propagating field. A closed form solution in a modified two-layer Pekeris waveguide with step-wise changes in the upper layer sound speed with range is used to study horizontal mode coupling through a series of such environments and to predict propagation loss as a function of range.

The Sound Lab at Fort Trumbull, New London, Connecticut, 1945–1996

The Navy Underwater Sound Laboratory was formed in 1945 when the U.S. Navy merged on-going efforts of Columbia and Harvard Universities to combat the German U-boat threat in the North Atlantic. Prior to that time, the Division of War Research of Columbia, housed in a single building at Fort Trumbull, was sponsored by the National Defense Research Committee (NDRC) while the Harvard Underwater Sound Laboratory was doing similar work in Cambridge, Massachusetts. For the next 50 years, until it was formally closed in 1996, the “Sound Lab” continued to support virtually all aspects of Naval Warfare technology. This talk will attempt to describe the rich scientific culture and technological contributions of the New London Sound Lab.

In memory of Bill Carey

Bill Carey has been a strong and influential mentor to many young and not-so-young acousticians and engineers. He had a profound effect on my career, encouraging me to publish my work and to attend Acoustical Society Meetings. His work in bottom acoustics, noise directionality, and surface effects, in particular, provided significant input to my research. He was also instrumental in nominating me for Fellowship in the Acoustical Society. I am deeply grateful and appreciate having an opportunity to remember him in this session.

A range recursive algorithm for random sum acoustic propagation loss prediction

The work of P. W. Smith, Jr. includes prediction of the averaged impulse response for sound transmission in a shallow-water channel. His predictions are most applicable in situations for which cycle mixing with range results in randomization of phase interference between modes. In this talk, a calculation of random summation propagation loss for these types of conditions is presented. An integral expression approximating the normal mode sum is reformulated through a change of variable to an integral with respect to cycle number. The resultant formulation leads to a recursive relation in the range variable which enables calculations to be simplified significantly. The integral formulation is shown to successfully reproduce propagation loss with range by comparison to measurements in a number of environments.

Wave propagation prediction over a thin elastic sediment and rock basement

In this paper, a model which computes both compressional-and shear-wave transmissions and reflections through a sediment layer is utilized to formulate a single bottom reflection coefficient which is shown to successfully predict resonance effects due to shear-wave conversion in various types of sediment. Comparisons of model results to published bottom loss curves are presented. Propagation results obtained by implementing the bottom loss calculations in a normal mode model are compared to other model results and measured data sets over a variety of bottom types.