Shallow Water Channel Research Articles

A theoretical model of ambient noise in a low-loss, shallow water channel

A theoretical model of ambient noise in an isovelocity, shallow water channel with independent, randomly distributed surface sources is presented. Bottom losses in the channel are assumed to be sufficiently small for the modal energy from distant sources to predominate over the continuous radiation from nearfield sources. For frequencies at which the channel can support about ten or more modes the predicted noise field is essentially homogeneous over a large proportion of the water column away from the boundaries. This allows the vertical spatial coherence of the noise to be expressed in terms of a plane-wave directional density function. The properties of this function are shown to be characteristic of the modal structure of the noise field.

Array gain of a broadside vertical line array in shallow water

An analysis is presented of the signal gain and the noise gain of a broadside vertical line array operating in a shallow-water channel with one lossy boundary. The signal gain is derived by representing the signal field as a sum of normal modes, and is shown to lie between N and 2N provided the number of modes in the field is less than (h/2L); and a simple criterion is derived for the maximum useful aperture of the array, beyond which no significant improvement in signal gain can be achieved. The derivation of the noise gain is based on the assumption that, over the aperture of the array, the noise field can be represented as a linear superposition of plane waves. On introducing the high-N approximation it is shown that, for arbitrary anisotropy, the noise gain is the reciprocal of a series of Bernoulli polynomials, the coefficient of each being determined by the directional density function of the noise. A discussion of the noise gain in isotropic noise and in three different anisotropic noise fields illustrates the utility of the approximate method for determining the noise gain.

Use of calculated sound fields and matched-field detection to locate sound sources in shallow water

The calculated complex sound field cj for sensor j at depth zj and range rj from a sound source of frequency ω and depth z0 can be written in the normal-mode form as cj= (2π/rj)1/2 ΣmUm(z0) Um(zj) exp[i (kmrj−ωt)]. Here, km is the horizontal wavenumber of mode m and Um is the depth function of the mth mode. It is proposed that the detection factor DF=ΣJj=1 cjc*k〈 (c0jc0k*) *〉 is a reasonable measure for determination of whether a set of sound pressure measurements {c0j} for j=1,2,⋅⋅⋅,J is a good fit to calculated values of {cj} for an assumed location of the sound source. Here 〈 〉 denotes a time average and * denotes complex conjugate. Several examples are shown where a set of {c0j} are calculated for a given source location in a typical shallow water channel and values of DF are then calculated for a grid of range depth or range azimuth locations. Subject Classification: [43]60.20; [43]30.82.

La colonisation de la mangrove par Cercopithecus aethiops sabaeus au Sénégal

Cercopithecus aethiops sabaeus have been known since 1906 to inhabit the mangroves of Southern Senegal, where they are called locally «mangrove monkeys». An age-graded male troop of 33 individuals has been briefly studied in 1975 around the estuary of the Saloum river ; usually it split into smaller sub-groups or foraging parties during the day and even sometimes during the night. The troop’s home range averaged 138 ha. Territorial contests between adult males of adjacent troops have been observed ; these involved «loud barks», «chest exposure» and «penile display». The troop studied spent 80 % of its time within the mangrove and only 13 % on the mainland. Sleeping trees can be located in both habitats, but mostly in the mangrove. Though C. a. sabaeus can swim, they prefer to cross mud flats and shallow water channels at low tide, or progress through the Rhizophora stilt-roots or pass from one tree crown to the other. The time-budget of the troop is given. The monkeys were observed feeding during 8.1 % of their activity time only. In 52 % of the cases they were seen hunting fiddler crabs (Uca tangeri) and 22 % of the cases eating Rhizophora flowers, fruits, shoots and young leaves, as well as the «pith» of young stilt-roots. Two different hunting techniques for crabs are described.

Use of calculated sound fields and cross spectral matrix detection to locate sound sources in shallow water

The calculated complex sound field cj for sensor j at depth zj and range rj from a sound source of frequency ω and depth z0 can be written in the normal mode as cj = (2π/rj)1/2 ∑ m Um(z0)Um(zj) exp[(kmrj − ωt)]. Here, km is the horizontal wavenumber of mode m and Um is the depth function for the mth mode. It is proposed that the detection factor DF = ∑ j=1J ∑ k=1≠jJ cjck* 〈(cj0ck0*)*〉 is a reasonable measure for determination of whether a set of sound pressure measurements {cj0} for j = 1, 2, …, J is a good fit to calculated values of {cj} for an assumed location of the sound source. Here 〈〉 denotes a time average and * denotes complex conjugate. Several examples are shown where a set of {cj0} are calculated for a given source location in a typical shallow water channel, and values of DF are then calculated for a grid of range depth or range azimuth locations.

Propagation in a Time-Dependent Shallow-Water Channel

A ray approach is used to model transmission fluctuations for a 7-NM propagation path in the Straits of Florida. The model is based on simplifying restrictions consistent with the following assumptions: (1) Transmission fluctuations on the time scale of a few minutes and longer are attributable to time-dependent multipath interference effects. These effects are associated with variations in the channel of spatial scale larger than the source to receiver separation. (2) The bottom contributes significantly to the mean loss but insignificantly to fluctuations. For transmission loss, comparison with experiment is made on the basis of smoothed spectra, covering fluctuation periods of a few minutes to many days. The agreement is good. Time series of observed and computed phase, treated as a variable continuous over multiplets of 2π radians, also show favorable agreement. [Work supported by Acoustics Programs, Office of Naval Research.]

The Averaged Impulse Response of a Shallow-Water Channel

The averaged impulse response for sound transmission in a shallow-water channel is estimated by a theory based on ray acoustics with lossy specular reflection from the boundaries. Averaging is introduced primarily by strict averaging in depth of the square of the received pressure. Rays need be traced over but a single cycle of their paths. The impulse response contains useful and readily accessible information about environmental loss parameters. The rate of decay of the reverberant tail, which is characteristic of channels with only moderate variations in sound speed, appears to be a particularly valuable measure. Theoretical and experimental data are compared.

Refracted, Bottom-Reflected Ray Propagation in a Shallow-Water Channel with Slowly Time-Varying Stratification

The shallow-water regions of the ocean are subject to low-frequency fluctuations in stratification spacially coherent over long distances. Internal tides, which are now considered a permanent feature of many coastal areas, are an example. The present study is a preliminary investigation of the influence of these fluctuations on RBR (Refracted, Bottom-Reflected) ray propagation in a shallow water channel. The principal assumptions are that the spatial scale of the stratification fluctuations in the channel is long compared to the distance between source and receiver, and that the fluctuation time scale is long compared to the ray travel time. In addition to general relationships, a particular case with realistic channel parameters in terms of continental shelf conditions is discussed in detail. In the detailed study, it is shown that both the amplitude and phase angle of a CW signal associated with any given ray are modulated at the fluctuation frequency of the channel stratification. The amplitude modulation, however, is negligibly small so that the resultant multipath signal at the receiver is a sum of several signals nearby, constant in amplitude but phase-angle modulated.

Normal-Mode Reverberation in Channels or Ducts

Equations are derived for calculation of sonar reverberation in terms of quantities used in a normal-mode propagation calculation. The equations are suitable for moderate to long ranges and for both surface ducts and shallow water channels.

Two-Dimensional Characteristics of Shallow Water Waves

The shallow water channel is often applied to the investigation of the high speed air flow. But the behavior of the shallow water wave is not exactly the same as that of the shock wave in air. This is due to the essential difference of both properties and boundary conditions between the air and the water. This paper presents the information on the two-dimensional characteristics of shallow water waves. Assuming that the disturbance is small, the expression for wave-pattern is analyzed and the effects of the scale, the water-depth, the surface-tension and the velocity are explained. They are compared with the findings of the experiments.

A New Mathematical Journal

THE Institute for Mathematics and Mechanics of New York University, of which the director is Prof. R. Courant, has now undertaken the production of a new journal entitled Communications on Applied Mathematics, which will appear quarterly. The publishers are Interscience Publishers, New York and London, and the subscription is eight dollars a year. The first number, dated January 1948, contains 99 well-printed pages, on good paper, with several diagrams. Most of it consists of an elaborate investigation of non-linear wave propagation in shallow water and open channels by J. J. Stoker. There is also a shorter paper on free boundaries of an ideal fluid by M. Shiftman. The second number will contain other papers on water waves. It is not intended that the new journal shall deal only with hydrodynamics; later numbers will cover a great variety of topics, including quantum theory, elasticity, aerodynamics, combustion, kinetic theory of gases, and the numerical solution of non-linear partial differential equations. Most of the papers will originate from the Institute for Mathematics and Mechanics of New York University.

The formation of breakers and bores the theory of nonlinear wave propagation in shallow water and open channels

The formation of breakers and bores the theory of nonlinear wave propagation in shallow water and open channels