## 4 Discussion  
In this paper, we considered the influence of Gaussian and non-Gaussian fluctuations in the speed of sound in acoustic waveguides of the shallow sea. The laws governing the decay of the average intensity of a low-frequency sound signal with distance were investigated. It is shown that the effect of attenuation of transmission losses in a random waveguide with absorbing and penetrable bottom, established in previous works for Gaussian fluctuations, in the presence of non-Gaussian ones is not only preserved in the considered examples, but also may manifests itself more clearly. At the same time, the main parameters providing the effect of attenuation of sound signal losses are characteristic scales of longitudinal fluctuations (horizontal radius of the correlation of inhomogeneities) and characteristic scales of sound attenuation associated with bottom penetrability and absorption, which form one or another modal attenuation coefficient. If the characteristic scale of attenuation of sound in a waveguide is comparable to the scale of longitudinal fluctuations, the effect of slowing down the decay of the average intensity is measured in tens of decibels already at relatively close distances from the source. If the attenuation of sound in the waveguide is small (a rather \"rigid\" bottom boundary, or vice versa, it is very \"soft\"), so that the characteristic attenuation scale significantly exceeds the scale of longitudinal fluctuations, then the effect of slowing down the decay of the average intensity becomes hardly noticeable at distances (up to 50 km) that are of interest in studying shallow-water waveguides of the sea shelf. It is obvious that the studied statistical regularities of transmission losses during signal propagation should be observed in any waveguides (optical, ionospheric, electrodynamic, etc.) with fluctuations and lossy boundaries, if the wave processes within these waveguides are described by similar equations. The obvious direction of deepening and expanding on the research performed is to consider the effect of random inhomogeneities of the waveguide boundaries (surface and bottom in the sea), which, along with fluctuations in the speed of sound in the water column, will lead to changes in transmission losses of the acoustic signal. The approach (1), (2), (9) developed in this work without fundamental changes allows us to investigate such a more general problem. The ratio of the scales of  
Figure 8: Transmission loss for a waveguide with Gaussian fluctuations \(\varepsilon\) (thin curves) and with fluctuations \(\varepsilon_{2}(r)\) having log-normal probability distribution (bold curves); \(L_{z}\) = 20 m, \(L_{r}\) = 4 km. Parameters of the bottom: \(c_{1}\) = 1530 m/s, (\(\rho_{1}\)/\(\rho_{0}\)) = 1.5, \(\beta_{1}\) = 0.01. \(H\)-\(z_{0}\) = 42 m. Blue curves: \(H\)-\(z\) = 42 m, red curves: \(H\)-\(z\) = 26 m.  
random inhomogeneities and attenuation of sound in a waveguide will also play a fundamental role in this case.  
F. Z.(Data curation, Writing-original draft); O.E.G. (Formal analysis, Validation, Writing--review and editing); I.O.Y. (Investigation, Software, Project administration).  
This research was funded by the National Natural Science Foundation of China, Grant No. 41406041. The research was carried out as a part of the Russian State program \"The study of the fundamental foundations of the appearance, development, transformation and interaction of hydroacoustic, hydrophysical and geophysical fields in the conditions of the deep and shallow sea\" (No. 0271-2018-0011).  
The authors declare no conflict of interest.