Caustic Structure of the Under Water Sound Channel

Vsevolod Petrovich Ivanov, Galina Kalenikovna Ivanova

Institute of Applied Physics, Russian Academy of Sciences, Nizhny Novgorod, Russia.

DOI: 10.4236/oja.2014.41004                

Abstract

Using the ray method, an investigation has been carried out on the structure of caustics in the wa- veguide assuming the canonical distribution of the sound velocity with depth. Monochromatic point source of sound was on the axis of the waveguide. There is considered water rays only. It is shown that the spatial part of the phase of a running sound wave does not contain the wave propagation direction and is always a positive quantity. When the trajectories are calculated, it is assumed that inversion of rays occurs at an angle of total internal reflection where the reflection coefficient is equal to unity. This eliminates the horizontal part of the trajectories. At other points, the reflection coefficient is assumed to be zero, and the passing coefficient is equal to unity. With this change in the calculation of ray’s trajectories, the basic structure of the caustics remained the same. It is shown that the boundary line of the caustic is a number of foci in which rays intersect with similar angles out of the source and have neighbour times of propagation. Structure of the sound field along the boundary line of the caustic is periodic. Its period coincides with the wavelength of the field radiated by the source.

Keywords

Rays; Running Wave; Sound Field; Caustics; Waveguide

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Brekhovskikh, L.M. (1973) Waves in Layered Spaces. M. Science, Moscow, 343.
[2]	Brekhovskikh, L.M. (1974) Ocean Acoustics. M. Science, Moscow, 693.
[3]	Zverev, V.A. and Ivanova, G.K. (2003) On the Formation of Waves Brillouin Underwater Sound Channel. Acoustical Journal, 49, 633-637.
[4]	Zverev, V.A. and Ivanova, G.K. (2005) On the Vertical Structure of the Sound Field in the Canonical Waveguide at Large Distances. Acoustical Journal, 51, 771-776.
[5]	Zverev, V.A. and Ivanova, G.K. (2007) Range Dependence of the Sound Field in the Ocean. Acoustical Physics, 53, 197-204.
[6]	Zverev, V.A. and Ivanova, G.K. (2008) The Horizontal Structure of the Sound Field in the Ocean. Acoustical Physics, 54, 356-362.
[7]	Zverev, V.A., Ivanov, V.P. and Ivanova, G.K. (2010) Calculation of the Sound Field in the Ocean in Caustic Surfaces by the Ray Method. Proceedings of the 22nd Conference of the Russian Acoustic Society, Moscow, 15-17 June 2010 191-194.
[8]	Zverev, V.A., Ivanov, V.P. and Ivanova, G.K. (2011) Caustics in Underwater Sound Channel and Their Connection with the Wave Front of the Point Source. Ocean Acoustics, Proceedings of the 13th L. M. Brekhovskikh’s Conference, Moscow, 31 May-3 June 2011, 49-52.
[9]	Ivanov, V.P. and Ivanova, G.K. (2012) One Aspect of Sound Waves Propagation in Inhomogeneous Water Space. Proceedings of the 25th Conference of the Russian Acoustic Society, Moscow, 17-20 September 2012, 338-341.
[10]	Ivanov, V.P. and Ivanova, G.K. (2013) Some Aspects of Ray Representation Running Sound Waves in Liquid Spaces. Open Journal of Acoustics, 3, 7-13.
[11]	Ivanov, V.P. and Ivanova, G.K. (2013) A New Concept of Calculation of Reflection and Passage Sound Waves on the Boundary of Liquid Spaces. Ocean Acoustics, Proceedings of the 14th L. M. Brekhovskikh’s Conference, Moscow, 17- 21 June 2013, 121-124.
[12]	Ivanov, V.P. and Ivanova, G.K. (2013) A New Concept of Calculation Coefficients of Relection and Passage Sound Waves on the Boundary of Liquid Spaces. Open Journal of Acoustica, 3, 72-79. http://dx.doi.org/10.4236/oja.2013.33012
[13]	Landau, L.D. and Lifshitz, V.M. (1988) Hydrodynamics. Publishing Nauka, Moscow.
[14]	Smirnov, V.I. (1958) Course of Higher Mathematics. State Publishing Physical and Mathematical Literature, Moscow.
[15]	Katsenelembaum, V.Z. (1966) High-Frequency Electrodynamics. Basics Mathematical Apparatus. Nauka, Moscow.
[16]	Lependin, L.F. (1978) Acoustics. Graduate School, Moscow, 448.
[17]	Physical Encyclopedic Dictionary (1966) Standing Waves. Publishing House “Soviet Encyclopedia”, Moscow.
[18]	Khaikin, S.A. (1947) Mechanics. State Publishing House of Techno-Theoretical Literature, Moscow.
[19]	Smirnov, V.I. (1958) Course of Higher Mathematics. State Publishing Physical and Mathematical Literature, Moscow.