1977
DOI: 10.1121/1.381417
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Attenuation of the coherent component of sound propagating in shallow water with rough boundaries

Abstract: Attenuation of the coherent component of sound propagating in shallow water with rough boundaries is studied. Normal-mode theory is used in conjunction with a boundary perturbation method. The inclusion of surface and bottom scattering cause the eigenvalues to become complex and explicit mathematical expressions for the imaginary parts of these eigenvalues are derived. These expressions correspond to the individual normal-mode attenuation coefficients due to scattering. Numerical results are presented for samp… Show more

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Cited by 54 publications
(36 citation statements)
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“…Our numerical method proceeds to obtain the integral densities u(x, k) through equation (6) in TE polarization and equation (33) in TM polarization, with coefficients v n and v n obtained from (9) and (35) respectively, and with 1% given by (25). The Taylor-Fourier expansions required in equation (12) for the functions 0+ 1 and g/<j>' + are precomputed.…”
Section: Numerical Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…Our numerical method proceeds to obtain the integral densities u(x, k) through equation (6) in TE polarization and equation (33) in TM polarization, with coefficients v n and v n obtained from (9) and (35) respectively, and with 1% given by (25). The Taylor-Fourier expansions required in equation (12) for the functions 0+ 1 and g/<j>' + are precomputed.…”
Section: Numerical Resultsmentioning
confidence: 99%
“…In detail, we obtain in Section 3 an expansion which gives I n {x, k) in terms of derivatives of u n (x) where the functions B q -t {x) are determined from the profile and incidence angle only. (We point out, however, that our algebraic treatment yields an expression for I*(x) which, although equivalent to that of (8), is different in form; see Remark 1 and equation (25).) From (7) and (8) we then find a recursion which gives u n (x) as a linear combination of derivatives of the previous coefficients i/ n _i_ g (a;)…”
Section: High-frequency Integral Equations -Te Casementioning
confidence: 99%
“…The integration is carried out over a full range of vectors~in the horizontal plane. Details of the derivations of both these results can be found in [47]. It is important to note that both contain factors that include the square of the slope of the mode shape evaluated at the surfaee.…”
Section: Dbmentioning
confidence: 99%
“…Thus, near the focus, the mean field dominates, unless scattering is strong enough to diminish the mean Green's function to such a degree that focusing is essentially destroyed. It is rather straightforward to compute the mean field in the presence of surface-wave scattering [38]. Figure 29 is an example of such a calculation using the modal propagation code, KRAKEN [39] with parameters appropriate to the 1996 Mediterranean experiment.…”
Section: Kjj>iv) =< Sg{vjv)sgl{tjv) > (69)mentioning
confidence: 99%