Efficient Energy Distribution Research Articles

A wide-angle initial field for parabolic equation models

Numerical predictions of underwater sound propagation are routinely carried out by applying marching algorithms to solve parabolic equations. These equations require initial field data to begin marching process. For many applications, a suitably normalized Gaussian or sinc function of depth (z) is used [E. R. Robinson and D. H. Wood, J. Acoust. Soc. Am. Suppl. 1 81, S10 (1987)]. These functions, however, do not model correctly the vertical-wavenumber (kz) spectrum associated with the farfield of a point source. In this paper, a new starting field is presented that matches the proper k, variation over the full spectral aperture needed by wide-angle parabolic equation models. The new field in the z domain is obtained numerically via a discrete Fourier transform of its bandlimited spectrum. Because of this efficient distribution of energy in the kz domain, a larger step-size (Δz) can be used than that required by the Gaussian initial field [H. M. Garon, J. S. Hanna, and P. V. Rost, J. Acoust. Soc. Am. Suppl. 1 61, S12 (1977)]. Numerical examples comparing the effects of different starting fields on wide-angle parabolic equation predictions are presented.

Construction of a new source function for the parabolic equation algorithm

Present means for initializing the parabolic equation (PE) field include: (1) using a coherent sum of modes (or rays) or (2) representing the farfield of the source in terms of a Gaussian. Approaches based upon the first turn out to be far too complex, overwhelming the simple elegance of the PE algorithm. The use of a Gaussian, while simple to implement, is inefficient in terms of the distribution of energy in the vertical-wavenumber (kz) domain. We propose, instead, a new source function which appears as a low-pass filter in the kz domain, designed using existing digital filter construction techniques. As a result of this much more efficient energy distribution, a fourfold reduction in required transform size for comparable cases is obtained. The benefits also derived from this approach include: (1) a simple procedure for implementing aperture-limited sources, (2) the ability to run much higher frequencies compared to the Gaussian source for a fixed transform size, and (3) ease in normalizing the source energy distribution. A description of the algorithm as well as numerical examples will be provided.

The Value of Efficiency in Transforming and Distributing Energy

Abstract Realizing that cheaper heat and cheaper power are closely related national problems requiring engineering methods for their solution, the author in this paper gives valuable data to serve as a guide for the efficient transformation and distribution of energy. Costs of primary energy at the source, transportation or transmission costs, and costs at point of use are presented in tables and charts. Methods and costs for the preparation of a suitable working fluid for the generation of water and steam power are given, and the transformation of working-fluid energy into brake-horsepower energy is shown by means of numerous tables. Other tables give hydroelectric, steam-turbine, and Diesel oil-engine power costs. The paper concludes with an interesting summation of total costs and a comparison of economies of small and large stations.