Theoretical analysis of the influence of weakly divergent beams on the formation of the spatio-temporal structure of pulse signals in the Sea of Japan

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Abstract

Using numerical modeling based on the mode theory and the geometric-acoustic approximation, it was determined that along with the classical quadruples of pulses present in the space-time field structure, the emergence of additional signals with relatively short delays is caused by the formation of weakly divergent multimode beams in the underwater sound channel of the Sea of Japan, which correspond to smooth extrema in the dependences of the spatial interference period of neighboring modes and their group velocity on the mode number. For one of the two sound speed profiles typical for the Sea of Japan, it was shown that at relatively high frequencies it is possible to receive two groups of additional signals, which correspond to weakly divergent beams formed by modes of relatively low and high orders.

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About the authors

Yu. V. Petukhov

Applied Physics Institute, Russian Academy of Sciences

Author for correspondence.
Email: yuvpetukhov@yandex.ru
Russian Federation, Nizhny Novgorod, 603950

E. L. Borodina

Applied Physics Institute, Russian Academy of Sciences

Email: borodina@appl.sci-nnov.ru
Russian Federation, Nizhny Novgorod, 603950

References

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Supplementary files

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2. Fig. 1. Dependences of the speed of sound c(z) on the depth z for two areas of the Sea of ​​Japan: the dashed line corresponds to [6], the solid line to [9].

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3. Fig. 2. The corresponding stratifications of c(z) in [6] (see Fig. 1) depend on the mode number l (a) — the spatial period of interference of neighboring modes Rl,l+1(l) (1) and (b) — their group velocity vl(l) (2) at different radiation frequencies: f = 400 Hz (curve 1), f = 700 Hz (curve 2), f = 103 Hz (curve 3).

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4. Fig. 3. Corresponding to the stratification c(z) in [6] (see Fig. 1), the dependence on the depth z of the relative propagation time τ(z) (3) of acoustic signals along the rays emerging from the source located on the channel axis zs = z0 = 150 m in the range of angles −4° ≤ χs ≤ 4°: (a) — the complete τ − z diagram and (b, c) — its characteristic fragments demonstrating the arrival of additional signals at a horizontal distance r = 200 km.

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5. Fig. 4. Dependence of the normalized excitation coefficient of modes Al(l) (4) on their number l at a radiation frequency f = 103 Hz of a source located on the axis zs = z0 = 150 m of the channel [6] (see Fig. 1).

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6. Fig. 5. The spatial distribution (over horizontal distance r and depth z) of the acoustic field intensity J0(r, z) normalized to the cylindrical divergence of the wave front, presented in the density record, obtained (a) with incoherent summation of the contributions of all refracted rays with exit angles from the source at zs = z0 = 150 m in the range −14° ≤ χs ≤ 14° and (b) using the mode theory at a radiation frequency of f = 103 Hz – for the channel in [6] (see Fig. 1).

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7. Fig. 6. The corresponding stratifications c(z) in [9] (see Fig. 1) depending on the mode number l (a) — the spatial period of interference of neighboring modes Rl,l+1(l) (1) and (b) — their group velocity vl(l) (2) at different radiation frequencies: f = 400 Hz (curve 1), f = 700 Hz (curve 2), f = 103 Hz (curve 3).

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8. Fig. 7. Corresponding to the stratification c(z) in [9] (see Fig. 1), the dependence on the depth z of the relative propagation time τ(z) (3) of acoustic signals along the rays emerging in the range of angles −4° ≤ χs ≤ 4° from a source located on the channel axis zs = z0 = 148 m: (a) — the complete τ − z diagram and (b, c) — its characteristic fragments at a horizontal distance r = 200 km.

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9. Fig. 8. Dependence of the normalized excitation coefficient of modes Al(l) (4) on their number l at a radiation frequency f = 103 Hz of a source located on the axis zs = z0 = 148 m of the channel [9] (see Fig. 1).

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10. Fig. 9. The spatial distribution (over horizontal distance r and depth z) of the acoustic field intensity J0(r, z) normalized to the cylindrical divergence of the wave front, presented in the density record, obtained (a) with incoherent summation of the contributions of all refracted rays with exit angles from the source at zs = z0 = 148 m in the range −16° ≤ χs ≤ 16° and (b) using the mode theory at a radiation frequency of f = 103 Hz for the channel in [9] (see Fig. 1).

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