Acoustic particle velocities can provide additional energy flow information of the sound field; thus, the vector acoustic model is attracting increasing attention. In the current study, a vector wavenumber integration (VWI) model was established to provide benchmark solutions of ocean acoustic propagation. The depth-separated wave equation was solved using finite difference (FD) methods with second- and fourth-order accuracy, and the sound source singularity in this equation was treated using the matched interface and boundary method. Moreover, the particle velocity was calculated using the wavenumber integration method, consistent with the calculation of the sound pressure. Furthermore, the VWI model was verified using acoustic test cases of the free acoustic field, the ideal fluid waveguide, the Bucker waveguide, and the Munk waveguide by comparing the solutions of the VWI model, the analytical formula, and the image method. In the free acoustic field case, the errors of the second- and fourth-order FD schemes for solving the depth-separated equation were calculated, and the actual orders of accuracy of the FD schemes were tested. Moreover, the time-averaged sound intensity (TASI) was calculated using the pressure and particle velocity, and the TASI streamlines were traced to visualize the time-independent energy flow in the acoustic field and better understand the distribution of the acoustic transmission loss.

Convergence-zone (CZ) sound propagation is one of the most important hydro-acoustic phenomena in the deep ocean, which allows the acoustic signals with high intensity and low distortion to realize the long-range transmission. Accurate prediction and identification of CZ is of great significance in implementing remote detection or communication, but there is still no standard definition in the sense of mathematical physics for convergence zone. Especially for the issue of systematic error of computation introduced by the earth curvature, there is no exact propagation model. The curvature-correction methods always lead to the imprecision of the ray phase. In previous research work, we realized that the Riemannian geometric meaning of the caustics phenomena caused by ray convergence is that the caustic points are equivalent to the conjugate points, which form on geodesics with positive section curvature. In this work, we present a spherical layered acoustic ray propagation model for CZ based on the Riemannian geometric theory. With direct computation in the curved manifolds of the earth , a Riemannian geometric description of CZ is provided for the first time, on the basis of comprehensive analysis about its characteristics. And it shows that the mathematical expression of section curvature adds an additional item \begin{document}${{\hat c(l){{\hat c}^\prime }(l)}}/{l}$\end{document} after considering the earth curvature, which reflects the influence of the earth curvature on the ray topology and CZ. By means of Jacobi field theory of Riemannian geometry, computational rule and method of the location and distance of CZ in deep water are proposed. Taking the typical Munk sound velocity profile for example, the new Riemannian geometric model of CZ is compared with the normal mode and curvature-correction method. Simulation and analysis show that the Riemannian geometric model of CZ given in this paper is a mathematical form naturally considering the earth curvature with theoretical accuracy, which lays more solid scientific foundations for the study of convergence zone. Moreover, we find that the location of CZ moves towards sound source when the earth curvature is considered, and the width of CZ near the sea surface first increases and then decreases with sound propagation proceeding. The maximum width is about 20 km and the minimum is about 4 km.

In this study, the stable dynamics of a kind of high-order cellular neural networks accompanying $ D $ operators and mixed delays are analyzed. The global existence of bounded positive solutions is substantiated by applying some novel differential inequality analyses. Meanwhile, by exploiting Lyapunov function method, some sufficient criteria are gained to validate the positiveness and globally exponential stability of pseudo almost periodic solutions on the addressed networks. In addition, computer simulations are produced to test the derived analytical findings.

Experimental data from the SACLANTCEN 1993 Mediterranean Experiment are reviewed to assess the reduction of the search space for the localization and tracking of an acoustic source in a three-dimensional environment. Key to this goal is the availability of an initial estimate of source range and depth (called the 2D initial guess); an ambiguous estimate of source bearing can be obtained from the 2D initial guess through Environmental Signal Processing, and the ambiguity can be removed by searching for the source only in the range/bearing regions where bearing estimates are higher. This search provides a new estimate of source range and a single bearing, which together with the estimate for source depth constitute the center of the reduced search space for source localization and tracking. The suggested approach is tested on experimental data from the SACLANTCEN experiment considering different frequencies, as well as a stationary and a moving source.

Orbital angular momentum (OAM) provides a new physical dimension for enhancing the capacity of underwater acoustic communication. However, in complex propagation environments, acoustic OAM signals are often affected by factors such as multipath reflections, leading to distortion of their phase maps and increasing the difficulty of recognition. This paper proposes an Angular-Spectrum-Compensation Residual Network for intelligent and robust recognition of acoustic OAM in complex marine propagation environments. The method uses ResNet18 as its backbone. Based on the extraction of spatial texture features, it constructs a polar coordinate system centered on the prediction point, obtains angular harmonic spectral features via FFT, and finally compensates for the backbone recognition results using a residual correction approach. Furthermore, this study established a small-water-tank experimental platform to acquire experimental acoustic OAM phase data and developed a structured acoustic OAM simulator and a simulation-to-tank evaluation configuration to generate a more realistic simulation dataset. The experiments focused on 9 types of single-mode OAM and 28 types of composite OAM, and were compared with traditional neural network methods. The 28-class composite-OAM study is simulation-only.The results indicate that the proposed method exhibits faster convergence and higher validation accuracy; furthermore, it demonstrates stronger generalization capabilities. Additionally, the feature extraction capability of the angular-spectrum branch was validated through experiments. The research results show that this model can improve the accuracy and robustness of acoustic OAM pattern recognition under complex propagation conditions.