The paper deals with a non-linear problem of long water waves approaching a sloping beach. In order to describe the phenomenon we apply the Lagrange’s system of material variables. With these variables it is much easier to solve boundary conditions, especially conditions on a shoreline. The formulation is based on the fundamental assumption for long waves propagating in shallow water of constant depth that vertical material lines of fluid particles remain vertical during entire motion of the fluid. The analysis is confined to one – dimensional case of unsteady water motion within a ’triangular’ body of fluid. The partial differential equations of fluid motion, obtained by means of a variational procedure, are then substituted by a system of equations resulting from a perturbation scheme with the second order expansion with respect to a small parameter. In this way the original problem has been reduced to a system of linear partial differential equations with variable coefficients. The latter equations are, in turn, substituted by a system of difference equations, which are then integrated in a discrete time space by means of the Wilson-µ method. The procedure developed in this paper may be a convenient tool in analysing non-breaking waves propagating in coastal zones of seas. Moreover, the model can also deliver useful results for cases when breaking of waves near a shoreline may be expected.

In this paper, a 2D numerical modeling of sound wave propagation in a shallow water medium that acts as a waveguide, are presented. This modeling is based on the method of characteristic which is not constrained by the Courant–Friedrichs–Lewy (CFL) condition. Using this method, the Euler time-dependent equations have been solved under adiabatic conditions inside of a shallow water waveguide which is consists of one homogeneous environment of water over a rigid bed. In this work, the stability and precision of the method of characteristics (MOC) technique for sound wave propagation in a waveguide were illustrated when it was applied with the semi-Lagrange method. The results show a significant advantage of the method of characteristics over the finite difference time domain (FDTD) method.

In the article the equations have been worked making it possible to model the motion of freerunning grain mixture flow on a flat sloping vibrating sieve within the framework of shallow water theory. Free-running grain mixture is considered as a heterogeneous system consisting of two phases, one of which represents solid particles and the other one gas. The mixture is brought into a state of fluidity by means of high-frequency vibration imposition. Coefficients of internal and external friction and dynamic-viscosity decrease by exponential law as the fluctuation intensity is increased. When considering grain mixture dynamics, the following assumptions are put forward: we ignore the air presence in space between particles, we consider the density of particles to be constant, the free-running mixture is similar to Newtonian liquid. The basic system of equations of grain mixture dynamics is due to the laws of continuum mechanics. The equation of continuity is issued from the law of conservation of mass, and the dynamic equations are issued from the law of variation of momentum. The stress tensor equals to the sum of the equilibrium tensor and the dissipative tensor. The equilibrium part of the stress tensor is represented by the spherical tensor, which is found to conform to Pascal law for liquids, and the dissipative part, which is responsible for viscous force effect and defined by Navier-Stokes law. Boundary conditions on the surfaces (restricting the capacity of the free-running grain mixture) have been researched. The distributions of apparent density and velocity field are assigned at the inlet and outlet flow sections of the mixture. The normal velocity component of the grain mixture on the side frames and on the sieve becomes zero, which meets the no-fluid-loss condition of the medium through the frame. Beyond that point at this time we satisfy dynamic conditions, which characterize the mixture sliding down the hard frame, motion flow resistance force is represented as average velocity linear dependence. A kinematic condition and two dynamic ones are stipulated on the free surface layer. One of the conditions states mass flow continuity across the free surface, the other one states the stress continuity while passing through the free surface. The basic premise of planned motion equations is the condition of small size of flow depth in comparison with its width. With the use of shallow water theory the basic principles of the equations of flow dynamics are simplified and for their solving a Cauchy problem can be set.

The shipping noise near channels and ports is an important contribution to the ambient noise level, and the depth of these sites is often less than 100 m. However less attention has been paid to the measurement in shallow water environments (Brooker, Humphrey, 2016). This paper presents extensive measurements made on the URN (underwater radiated noise) of a small fishing boat in the South China Sea with 87 m depth. The URN data showed that the noise below 30 Hz was dominated by the background noise. The transmission loss (TL) was modelled with FEM (finite element method) and ray tracing according to the realistic environmental parameters in situ. The discrepancy between the modelled results and the results using simple law demonstrates both sea surface and bottom have significant effect on TL for the shallow water, especially at low frequencies. Inspired by the modelling methodology in AQUO (Achieve QUieter Oceans) project (Audoly et al., 2015), a predicted model applied to a typical fishing boat was built, which showed that the URN at frequencies below and above 100 Hz was dominated by non-cavitation propeller noise and mechanical noise, respectively. The agreement between predicted results and measured results also demonstrates that this modelling methodology is effective to some extent.

Passive source localization in shallow water has always been an important and challenging problem. Implementing scientific research, surveying, and monitoring using a short, less than ten meter long, horizontal linear array has received considerable attention in the recent years. The short array can be conveniently placed on autonomous underwater vehicles and deployed for adaptive spatial sampling. However, it is usually difficult to obtain a sufficient spatial gain for localizing long-range sources due to its limited physical size. To address this problem, a localization approach is proposed which is based on matched-field processing of the likelihood of the passive source localization in shallow water, as well as inter-position processing for the improved localization performance and the enhanced stability of the estimation process. The ability of the proposed approach is examined through the two-dimensional synthetic test cases which involves ocean environmental mismatch and position errors of the short array. The presented results illustrate the localization performance for various source locations at different signal- to-noise ratios and demonstrate the build up over time of the positional parameters of the estimated source as the short array moves at a low speed along a straight line at a certain depth.

The impact of the noise radiated from merchant ships on marine life has become an active area of research. In this paper, a methodology integrating observation at a single location and modelling the whole noise field in shallow waters is presented. Specifically, underwater radiated noise data of opportunistic merchant ships in the waters of Zhoushan Archipelago were collected at least one day in each month from January 2015 to November 2016. The noise data were analyzed and a modified empirical spectral source level (SSL) model of merchant ships was proposed inspired by the RANDI-3 model (Research Ambient Noise Directionality) methodology. Then combining the modified model with the realistic geoacoustic parameters and AIS data of observed merchant ships, the noise mappings in this area were performed with N×2D of Normal Mode calculations, in which the SSL of each ship was estimated using the modified model. The sound propagation at different receiving positions is different due to the shielding effect of islands and bottom topography. The methodology proposed in this paper may provide a reference for modelling shipping noise in shallow waters with islands and reefs.

The underwater acoustic communication (UAC) operating in very shallow-water should ensure reliable transmission in conditions of strong multipath propagation, significantly disturbing the received signal. One of the techniques to achieve this goal is the direct sequence spread spectrum (DSSS) technique, which consists in binary phase shift keying (BPSK) according to a pseudo-random spreading sequence.
This paper describes the DSSS data transmission tests in the simulation and experimental environment, using different types of pseudo-noise sequences: m-sequences and Kasami codes of the order 6 and 8. The transmitted signals are of different bandwidth and the detection at the receiver side was performed using two detection methods: non-differential and differential.
The performed experiments allowed to draw important conclusions for the designing of a physical layer of the shallow-water UAC system. Both, m-sequences and Kasami codes allow to achieve a similar bit error rate, which at best was less than 10 ⁻³. At the same time, the 6th order sequences are not long enough to achieve an acceptable BER under strong multipath conditions. In the case of transmission of wideband signals the differential detection algorithm allows to achieve a significantly better BER (less than 10 ⁻²) than nondifferential one (BER not less than 10 ⁻¹). In the case of narrowband signals the simulation tests have shown that the non-differential algorithm gives a better BER, but experimental tests under conditions of strong multipath propagation did not confirm it. The differential algorithm allowed to achieve a BER less than 10 ⁻² in experimental tests, while the second algorithm allowed to obtain, at best, a BER less than 10 ⁻¹. In addition, two indicators have been proposed for a rough assessment which of the detection algorithms under current propagation conditions in the channel will allow to obtain a better BER.