In recent years, safety issues respecting polar ship navigation in the presence of ice have become a research hotspot. The accurate prediction of propulsion power plays an important role in ensuring safe ship navigation and evaluating ship navigation ability, and deep learning has been widely applied in the field of shipping, of which the artificial neural network (ANN) is a common method. This study combines the scientific problems of ice resistance and propulsion power for polar ship design, focusing on the design of an ANN model for predicting the propulsion power of polar ships. Reference is made to the traditional propulsion power requirements of various classification societies, as well as ship model test and full-scale test data, to select appropriate input features and a training dataset. Three prediction methods are considered: building a radial basis function–particle swarm optimization algorithm (RBF-PSO) model to directly predict the propulsion power; based on the full-scale test and model test data, calculating the propulsion power using the Finnish–Swedish Ice Class Rules (FSICR) formula; using an ice resistance artificial neural network model (ANN-IR) to predict the ice resistance and calculate the propulsion power using the FSICR formula. Prediction errors are determined, and a sensitivity analysis is carried out with respect to the relevant parameters of propulsion power based on the above methods. This study shows that the RBF-PSO model based on nine feature inputs has a reasonable generalization effect. Compared with the data of the ship model test and full-scale test, the average error is about 14%, which shows that the method has high accuracy and can be used as a propulsion power prediction tool.

We present experimental evidence of formation and persistence of localized waves, breathers, and solitons, occurring in a random sea state and uniformly traveling over non-uniform bathymetry. Recent studies suggest connections between breather dynamics and irregular sea states and between extreme wave formation and breathers, random sea states, or non-uniform bathymetry individually. In this paper, we investigate the joint connection between these phenomena, and we found that breathers and deep-water solitons can persist in more complex environments. Three different sets of significant heights have been generated within a Joint North Sea Wave Observation Project wave spectrum, and the wave heights were recorded with gauges in a wave tank. Statistical analysis was applied to the experimental data, including the space and time distribution of kurtosis, skewness, Benjamin–Feir index, moving Fourier spectra, and probability distribution of wave heights. Stable wave packages formed out of the random wave field and traveling over shoals, valleys, and slopes were compared with exact solutions of the nonlinear Schrödinger equation with a good match, demonstrating that these localized waves have the same structure as deep-water breathers. We identify the formation of rogue waves at moments and over regions where the kurtosis and skewness have local maxima. These results provide insights for understanding of the robustness of Peregrine and higher-order Akhmediev breathers, Kuznetsov–Ma solitons, and rogue waves, and their occurrence in realistic oceanic conditions, and may motivate analogous studies in other fields of physics to identify limitations of exact weakly nonlinear models in non-homogeneous media.

In this study, the propagation and evolution characteristics of internal solitary waves on slope topography in stratified fluids were investigated. A numerical model of internal solitary wave propagation based on the nonlinear potential flow theory using the multi-domain boundary element method was developed and validated. The numerical model was used to calculate the propagation process of internal solitary waves on the topography with different slope parameters, including height and angle, and the influence of slope parameters, initial amplitude, and densities jump of two-layer fluid on the evolution of internal solitary waves is discussed. It was found that the wave amplitude first increased while climbing the slope and then decreased after passing over the slope shoulder based on the calculation results, and the wave amplitude reached a maximum at the shoulder of the slope. A larger height and angle of the slope can induce larger maximum wave amplitude and more obvious tail wave characteristics. The wave amplitude gradually decreased, and a periodic tail wave was generated when propagating on the plateau after passing the slope. Both frequency and height of the tail wave were affected by the geometric parameters of the slope bottom; however, the initial amplitude of the internal solitary wave only affects the tail wave height, but not the frequency of the tail wave.

Owing to the rapid development of the offshore wind power technology and increasing capacity of wind turbines, vertical-axis wind turbines (VAWTs) have experienced a great development. Nevertheless, the VAWT wake effect, which affects the power generation efficiency and rotor fatigue life, has not been thoroughly understood. In this study, the mid-span wake measurements on a VAWT in six different configurations were conducted. This study aimed to investigate the effect of solidity on near wake instability of vertical-axis wind turbine. By using the wavelet analysis method to analyse the measured velocity (or pressure) time series signals on a multi-scale and with multi-resolution, the dynamic characteristics of the coherent vortex structures in the wake evolution process were determined. The results show that with increasing solidity, the VAWT wake develops into a bluff body wake mode. In addition, a characteristic frequency that is lower than the low-frequency large-scale vortex shedding frequency occur. The wavelet transform was used to decompose and reconstruct the measured data, and the relationship between the low-frequency large-scale vortex shedding and lower frequency pulsation was established. The results provide important data for numerical modelling and new insights into the physical mechanism of the VAWT wake evolution into a bluff body wake.

Solitary waves have been well studied in various fields, including water waves, optical communications, plasmas, and biophysics. We present experimental results that a two-dimensional solitary wave, with its crest shaped like the letter “O,” occurs around an island terrain in shallow water. We name it the O-soliton (a cylindrical-type soliton) in this paper. This is the first experimental observation of the O-soliton including both outward and inward propagation in shallow water. O-solitons are observed with stable and periodic occurrences under typical coastal conditions. A water column at its center is higher than eight times the initial mean wave height measured by six wave gauges arranged in a regular hexagon. A one-dimension solitary wave incurs a phase shift when it collides with the O-soliton. However, no phase shift is observed in the O-soliton itself. Furthermore, when it collapses to its center point, it remains in this state for a short period. This is analogous to the pausing of the wave crest during a head-on collision of solitary waves or the reflection of a solitary wave at a vertical wall. These results also enrich the general understanding of solitary waves, whose repeated occurrence suggests that they may naturally occur in the ocean, and motivate analogous studies in other fields of physics.

The wake of a vertical axis turbine is a type of unsteady flow with multi-scale coherent structures formed by a series of complex spatiotemporal evolutions of blade vortex shedding. The evolution characteristics and interaction of multi-scale coherent structures between two turbine wakes are the bases of multi-turbine optimal layout. In this study, the wake time series and turbine aerodynamic output were measured to explore the effect of solidity on the wake evolution characteristics of twin counter rotating vertical axis turbines. The dynamic evolution characteristics of multi-scale coherent structures in a wake were presented by a wavelet analysis. The results show that with the increase in solidity, the wake of the twin turbines gradually merges and is dominated by the shedding instability of the low-frequency large-scale structures. When the solidity remains unchanged and the chord length Reynolds number increases gradually, modulation mode structures appear between the low-frequency large-scale structures and rotation-induced structures. After the rotation-induced structures lose their coherence, energy transfers to a low frequency under the effect of modulation instability, forming self-organized large-scale structures.