Manifestation of scarring in a driven system with wave chaos

We consider wave propagation in a model of a deep ocean acoustic wave guide with a periodic range dependence. It is assumed that the wave field is governed by the parabolic equation. Formally the mathematical model of the wave guide coincides with that of a quantum system with time-dependent Hamiltonian. From the analysis of Floquet modes of the wave guide it is shown that there exists a "scarring" effect similar to that observed in quantum systems. It turns out that the segments of an unstable periodic ray trajectory may be distinguished in the spatial distribution of the wave field intensity at a finite wavelength. Besides the scarring effect, it is found that the so-called "stable islands" in the phase space of ray dynamics reveal themselves in the coarse-grained Wigner functions of the Floquet modes.     

Stable Components of the Wave Field in Underwater Sound Waveguides

A technique is proposed for determining which sound field components are weakly sensitive to variations in the parameters of the speed of sound field in a marine waveguide. Such components are formed by narrow ray beams, with the dispersion of their vertical coordinates on the distance to the point of observation being less than the vertical scale of the perturbation. Since these rays pass through the same inhomogeneities, their phases in the presence of perturbations acquire approximately the same increment. For a monochromatic field, such components in perturbed and unperturbed waveguides differ only by their phase factors. With a pulsed field, perturbations lead only to some additional delays of the stable components. A procedure based on decomposing the field into coherent states is proposed to select stable components from the total field. The solution to the problem of finding the location of a source using the stable components is illustrated by a simple example.     

Wave chaos and mode-medium resonances at long-range sound propagation in the ocean

We study how the chaotic ray motion manifests itself at a finite wavelength at long-range sound propagation in the ocean. The problem is investigated using a model of an underwater acoustic waveguide with a periodic range dependence. It is assumed that the sound propagation is governed by the parabolic equation, similar to the Schrodinger equation. When investigating the sound energy distribution in the time-depth plane, it has been found that the coexistence of chaotic and regular rays can cause a "focusing" of acoustic energy within a small temporal interval. It has been shown that this effect is a manifestation of the so-called stickiness, that is, the presence of such parts of the chaotic trajectory where the latter exhibit an almost regular behavior. Another issue considered in this paper is the range variation of the modal structure of the wave field. In a numerical simulation, it has been shown that the energy distribution over normal modes exhibits surprising periodicity. This occurs even for a mode formed by contributions from predominantly chaotic rays. The phenomenon is interpreted from the viewpoint of mode-medium resonance. For some modes, the following effect has been observed. Although an initially excited mode due to scattering at the inhomogeneity breaks up into a group of modes its amplitude at some range points almost restores the starting value. At these ranges, almost all acoustic energy gathers again in the initial mode and the coarse-grained Wigner function concentrates within a comparatively small area of the phase plane.     

Sensitivity of ray travel times

Ray in a waveguide can be considered as a trajectory of the corresponding Hamiltonian system, which appears to be chaotic in a nonuniform environment. From the experimental and practical viewpoints, the ray travel time is an important characteristic that, in some way, involves an information about the waveguide condition. It is shown that the ray travel time as a function of the initial momentum and propagation range in the unperturbed waveguide displays a scaling law. Some properties of the ray travel time predicted by this law still persist in periodically nonuniform waveguides with chaotic ray trajectories. As examples we consider few models with special attention to the underwater acoustic waveguide. It is demonstrated for a deep ocean propagation model that even under conditions of ray chaos the ray travel time is determined, to a considerable extent, by the coordinates of the ray endpoints and the number of turning points, i.e., by a topology of the ray path. We show how the closeness of travel times for rays with equal numbers of turning points reveals itself in ray travel time dependencies on the starting momentum and on the depth of the observation point. It has been shown that the same effect is associated with the appearance of the gap between travel times of chaotic and regular rays. The manifestation of the stickiness (the presence of such parts in a chaotic trajectory where the latter exhibits an almost regular behavior) in ray travel times is discussed. (c) 2002 American Institute of Physics.     

Reconstructing the Directivity Pattern of a Sound Source in Free Space by Measuring its Field in a Tank

Acoustical Physics - The paper discusses reconstruction of the directivity pattern of a sound source in free space from measurements of the field excited by this source in a tank. The...     

A high-power intrawell radiator of shear waves for coherent seismoacoustics

A brief review of investigations in the field of coherent seismoacoustics is presented, and the general requirements for seismoacoustic wave radiators intended for solving problems of remote sounding are formulated. The principle of operation of a novel high-power radiator created at the Institute of Applied Physics, Russian Academy of Sciences, for generating low-frequency seismic waves is described, and the results of the analytical and numerical modeling of this radiator are presented. The main element of the radiator is a piezoelectric cylinder executing bending vibrations in a well filled with water. The concept of sectioning the radiating cylinder for increasing the efficiency of excitation of various radiator modes and improving the matching the radiator with the medium is formulated. The results of the field measurements of the space-time structure of the seismic field generated by the sectioned radiator are presented. On the basis of these measurements, estimates of the power, efficiency, and quality factor of the radiator are obtained.     

Variations of mode amplitudes in a range-dependent waveguide

The ray method of calculating the mode amplitudes is used to analyze the sound fields in deep-water acoustic waveguides with two types of inhomogeneities of the refractive index: (i) weak inhomogeneities that cause small perturbations of ray trajectories and (ii) strong inhomogeneities with large spatial scales. Simple analytical relations are derived for describing the variations of the mode structure of the sound field in the presence of the aforementioned inhomogeneities. A new criterion defining the validity of the adiabatic approximation is formulated. To illustrate and test the results obtained, a numerical simulation of the sound fields is performed on the basis of the parabolic equation method.

     

Fresnel zones for modes and analysis of field fluctuations in random multimode waveguides

The notion of Fresnel zones for modes is introduced, which is analogous to the usual Fresnel zones introduced for rays. It is shown that using Fresnel zones for modes one can simplify the analysis of mode scattering at large-scale and random inhomogeneities of a medium in waveguides. Simple formulae to calculate fluctuations of mode amplitudes are obtained. They are similar to well-known formulae of geometrical optics and to those of the Rytov method used to calculate fluctuations of ray complex amplitudes. Relations deduced can be used for calculating field fluctuations both at regular waveguide points and at caustics.