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Long waves with periods greater than tens of seconds propagating into a harbor may be trapped and significantly amplified, thereby resulting in detrimental effects on port operations. The water surface elevation in the Hambantota Port, Sri Lanka, was measured to investigate the low-frequency oscillations and their forcing mechanisms. Results show that the port is protected well from short waves with periods less than 30 s; however, the protection against long waves with periods larger than 30 s is inadequate. The spectral analyses identified four dominant periods within the low-frequency wave range. Modal analysis based on the extended mild-slope equation shows that the measured spectrum density for some dominant periods is low because the measurement point is close to the corresponding modal lines. Correlation analysis shows that low-frequency oscillations inside the Hambantota Port are excited directly by the low-frequency waves contained within the incident waves. The low-frequency waves outside the Hambantota Port are generated from the higher-frequency gravity waves (swell and wind waves) due to nonlinear interactions. Empirical formula is adopted to estimate the low-frequency wave height outside the Hambantota Port.

The characteristics of wave spectrum in the swell dominated seas (i.e., the Chancay Bay on the western coast of Peru) are studied based on directional wave spectra measured using the technique of acoustic Doppler current profiler (ADCP). According to the wave rose diagram and the measured wave spectra, this sea area is mainly affected by the swell of the southwest direction and the significant wave height is between 0.7m-2.6m. Moreover, the wave spectra feature the single-peaked spectra and the double-peaked spectra. The JONSWAP spectrum model is adopted to fit single-peaked swell spectra. A close agreement could be found between the observed and fitted spectrum parameters. Hence, the JONSWAP model can be used to describe the single-peaked swell spectra in the sea area studied in this work. As for the double-peaked spectrum, Ochi-Hubble double peak spectrum model and simplified Torsethaugen double peak spectrum model are adopted to fit the wave spectra, respectively. Comparing the fitting results of two double-peaked spectrum modal, it’s possible to conclude that the measured double-peaked spectra can be well represented by the Ochi-Hubble double peak spectrum model.

Periodic undulating topographies (such as sandwaves and sandbars) are very common in coastal and estuarine areas. Normally incident water surface waves propagating from open sea to coastal areas may interact strongly with such topographies. The wave reflection by the periodic undulating topography can be significantly amplified when the surface wavelength is approximately twice the wavelength of the bottom undulations, which is often called as Bragg resonant reflection. Although the investigations on the hydrodynamic characteristics related to Bragg reflection of a region of undulating topography have been widely implemented, the effects of Bragg reflection on harbors have not yet been studied. Bragg resonant reflection can effectively reduce the incident waves. Meanwhile, however, it can also significantly hinder the wave radiation from the harbor entrance to the open sea. Whether Bragg reflection can be utilized as a potential measure to alleviate harbor oscillations is unknown. In the present study, Bragg reflection and their interactions with the harbor are simulated using a fully nonlinear Boussinesq model, FUNWAVE 2.0. For the purpose, an elongated harbor with constant depth is considered, and a series of sinusoidal bars with various amplitudes and numbers are deployed outside the harbor. The incident waves considered in this paper include regular long waves and bichromatic short wave groups. It is revealed for the first time that for both kinds of incident waves, Bragg resonant reflection can significantly alleviate harbor resonance. The influences of the number and the amplitude of sinusoidal bars on the mitigation effect of harbor resonance and on the optimal wavelength of sinusoidal bars that can achieve the best mitigation effect are comprehensively investigated, and it is found that the former two factors have remarkable influences on the latter two parameters. The present research provides a new option for the mitigation of harbor oscillations via changing the bottom profile, which is feasible as long as the navigating depth is guaranteed.

Forecasting coastal infragravity (IG) waves is crucial in preventing coastal disasters caused by IG waves. In this study, the performance of the unstructured WAVEWATCH Ⅲ (WW3) in predicting coastal IG waves is comparatively assessed using in-situ wave measurements, considering the effects of numerical schemes, time steps, and IG-source parameterization methods. The wave measurements are performed using three acoustic sensors installed at the coast of south Sri Lanka, with two being near or inside a harbor. Sensitivity analysis of the numerical schemes and time steps shows that the explicit scheme combined with a small time step leads to unexpected oscillations of the IG wave height. However, the time step has a negligible influence on the performance of the implicit scheme combined with the domain decomposition method. Generally, IG sources estimated from the empirical formula method (source M1) and the second-order spectrum method (source M2) perform similarly in reproducing the IG wave height. Regarding the IG frequency spectrum, both the IG sources properly predict the magnitude of the spectral density, but the spectral shapes are not adequately captured. M2 may provide a better directional spread of the IG wave energy. Attention is also paid to the IG waves inside the harbor. The IG waves within the harbor are underestimated, owing to the lack of some mechanisms related to IG waves in the simulation. M1 should be adopted when crudely predicting the magnitude of IG waves inside a harbor. Overall, the unstructured WW3 can effectively predict the coastal IG wave height in southern Sri Lanka, with significant correlation and acceptable errors, when compared with in-situ measurements. Finally, the IG source M1 is refined to remove the erroneous spectral gap between the IG and wind-wave frequency bands in the WW3 spectra when compared to the in-situ observed spectra.

A direct coupled method is established on the basis of the Boussinesq equations and Rankine source method to analyze the responses of floating bodies near islands and reefs. The detailed theoretical derivation, numerical solution method and the relevant calculation program THAFTS-BR are also completed. Then, the motions and connector loads of a three-module VLFS deployed near islands and reefs are investigated based on the model tests and the numerical method. Some useful conclusions are obtained, which can provide a reference for the analysis of dynamic responses, design and construction of the floating bodies near seashores and islands.

An investigation of the effects of a uniform current strength direction (following or opposing wave propagation) on the nonlinear transformation of irregular waves over a submerged trapezoidal sill is carried out using SWASH, a non-hydrostatic numerical wave model. The nonlinear parameters (i.e., asymmetry, skewness, and kurtosis) are calculated, and the empirical formulas for these parameters are presented as a function of the local Ursell number based on the present numerical data measured. In the shoaling area of the submerged sill, the nonlinear characteristics of waves are more obvious when waves propagate in the same direction as the currents than when waves propagate in the opposite direction. Whereas nonlinear parameters grow with the strengthening of the following currents over the crest, they tend to decrease as the adverse current velocity increases over the crest area of the submerged sill.

Harbor oscillations are the large fluctuations in the water surface when the frequency of long-period incident waves is equal or close to the natural frequencies of the harbor. It is one of the most frequent disasters around the world, which can cause serious damage to port infrastructures and excessive movements of moored ships inside the harbor. The research of harbor oscillations is of great significance to the water dynamic process, ship movement and water disaster prevention and assessment. Harbor oscillations are easier to occur in harbor that with more regular shape and narrow gap. There are many factors that affect the natural frequencies of harbor, including the layout shape, bathymetry and so on. In this article, the numerical model based on the modified mild slope equation is used to simulate the impact of dredging access channel on the natural frequencies and oscillation modes of the harbor. The bathymetry changes of harbor in this paper include the depth and width of the channel. For comparison, the angle of incident wave is also discussed.

Infragravity (IG) waves significantly affect the operational efficiency of ports. Therefore, an accurate prediction of IG waves inside a harbor is necessary. In this study, the accuracy of the wave-group-resolving model XBeach Surfbeat (XB-SB, Delft University of Technology, Delft, The Netherlands) in predicting the IG waves inside a harbor was assessed by comparing its results with field measurements. Field measurements were performed at Hambantota Port in southern Sri Lanka. Three acoustic waves and current sensors were used to observe the wave characteristics inside and outside the harbor. First, the model was validated against observations outside the port. Next, the performance accuracy of XB-SB in modeling the hydrodynamics in the harbor was evaluated by comparing its results with the values measured inside the port. The results of the numerical simulations indicated that both the nearshore short and IG wave heights can be accurately reproduced by XB-SB in an open domain without many obstacles. However, the short wave heights in the harbor are severely underestimated by XB-SB. The IG waves inside the harbor are overestimated most of the time. Moreover, the natural periods of Hambantota Port are well calculated by XB-SB. In general, XB-SB is a reliable tool for predicting nearshore IG waves. However, it requires further improvement to reproduce the hydrodynamics in a well-sheltered harbor, such as Hambantota Port.

For the first time, transient seismic-induced oscillations inside an actual harbor are investigated using a fully nonlinear Boussinesq-type wave model. To this end, the open-source code FUNWAVE-TVD, developed by Shi et al. (2012), is extended to include seismic effects by adding a time-dependent forcing term to the governing equations. This extension is fully validated against analytical solutions and experimental data available in the literature. Uni-directional harmonic seismic excitation is considered as an approximation in the case study of Hambantota Port. Results reveal that the natural modes of Hambantota Port with periods of O (100–1000 s) can be triggered by seismic disturbances with periods of O (1 s). Some modes that are generated immediately under the excitation are found to be those of sloshing. Thus, a possible mechanism for the seismic-induced long-period harbor oscillations is proposed using a sloshing theory. Subsequently, it is determined that the seismic direction has significant effects on the excitation of natural modes and the energy decay rate. Lastly, the seismic influence on the wave motions inside the harbor including a consideration of the incident waves from the open sea is examined.

In order to theoretically study the buckle propagation of subsea pipelines with slip-on buckle arrestors, a two-dimensional ring model was set up to represent the pipeline and a nonlinear spring model was adopted to simulate the contact between pipeline’s inner walls and between pipeline’s outer wall and slip-on buckle arrestor’s inner wall during buckle propagation. In addition, some reverse springs are added to prevent the wall of left and right sides separating from the inner wall of slip-on buckle arrestors. Considering large deformation kinematics relations and the elastic-plastic constitutive relation of material, balance equations were established with the principle of virtual work. The variation of external pressure with respect to the cross-sectional area of pipelines was analyzed, and the lower bound of the crossover pressure of slip-on buckle arrestors was calculated based on Maxwell’s energy balance method. By comparing the theoretical results with experiment and finite element numerical simulation, the theoretical method is proved to be correct and reliable.

In typhoon risk assessment and warning, a critical component is a good representation of the typhoon wind field model. In this study, a new analytical model based on the logarithmic spiral trajectory model is developed to simulate the surface wind speed distribution of a typhoon. The logarithmic spiral trajectory model could overcome the limitation of the parametric gradient wind model. A slab surface layer of constant depth is used to solving the tangential equilibrium equation, and the frictional drag at the upper boundary of the surface layer is considered correctly. Consequently, the theoretical method for determining the Holland β parameter is derived from the logarithmic spiral trajectory model. It is concluded that β increases with the surface layer depth or decreases with the radius to maximum winds. By analyzing the change in kinetic energy of the air particle, the interpretation of the relationship between β and the influencing factors is provided. The models are applied to the 17th typhoon NESAT and the 19th typhoon NALGAE of 2011. Through comparisons between the observed wind records and the simulation results, the logarithmic spiral trajectory model proposed in this study could accurately simulate the wind speeds.

The low-frequency (1/400- 1/30 Hz) oscillations within the Hambantota Port, Sri Lanka, are investigated based on the in-situ measured water surface elevations in and outside the harbor. By combining analyses of spectra derived from the in-situ measurement and modal analyses solving the extended mild-slope equation, four natural frequencies of the port are identified and their modal structures are obtained. It is found that the low-frequency oscillations within the port were dominated by its natural frequencies (i.e., the eigen oscillations) instead of the frequencies of external waves. Subsequently, the correlation analysis is carried out to determine the generation of the low-frequency oscillations. Although both the offshore low-frequency and short waves contributed to the low-frequency oscillations, the low-frequency energy spectrum within the port is found to be more significantly correlated with the offshore total low-frequency wave energy than with the offshore total short-wave energy. Moreover, the empirical formula and artificial neural network models are presented to efficiently estimate the low-frequency waves inside the harbor in terms of the offshore wave parameters. Although both methods give excellent results, the artificial neural network performs slightly better.

It is demonstrated that offshore wavenumbers of edge waves change from imaginary wavenumbers in deep water to real wavenumbers in shallow water. This finding indicates that edge waves in the offshore direction exist as evanescent waves in deep water and as propagating waves in shallow water. Since evanescent waves can stably exist in a limited region while propagating waves cannot, energy should be released from nearshore regions. In the present study, the instability region is predicted based on both the full water wave solution and the shallow-water wave approximation.

A numerical model, which can simulate wave generation and propagation is developed to simulate oscillations induced by seafloor movements inside a harbor of constant slope, and once verified and then validated through comparison with experimental results, the numerical results are used to examine the analytic solutions presented in Wang et al. (Wang, G., Dong, G., Perlin, M., Ma, X., Ma, Y., 2011. An analytic investigation of oscillations within a harbor of constant slope. Ocean Engineering 38, 479–486). Small-scale seafloor movement usually induces small longitudinal oscillations, but evident larger transverse oscillations. These transverse oscillations are sensitive to the location of the moveable seafloor. The numerical result of each transverse eigen frequency compares well with the theoretical solution; in addition the spatial structure of each mode is also well-captured by the theory. Furthermore, evident/larger longitudinal oscillations induced by large-scale seafloor movements are simulated, and the numerical resonant frequencies agree favorably with the analytical solutions. These longitudinal oscillations are sensitive to the horizontal location of the moveable seafloor.

An existing 2D time-domain method for separating irregular incident and reflected waves by wavelet transform [Ma et al., 2010. A new method for separation of 2D incident and reflected waves by the Morlet wavelet transform. Coastal Eng., 57(6):597–603] is extended to account for obliquely incident irregular waves propagating over sloping bottoms. The linear shoaling and refraction coefficients are adopted to determine the amplitude and phase changes of waves. The optimal central frequency of the Morlet wavelet is determined by the minimum Shannon wavelet entropy. Numerical tests show that the present method can accurately separate waves over horizontal depths. For waves at sloping bottoms, however, the separation errors increase as bottom slope increases and are significant for waves with incident angle larger than π /3.

In the past decades, there are numerous reports on the accidents caused by extremely large waves. A large number of papers have contributed to the study on the physical properties and the generation mechanisms of such large waves. However, most of the research has been carried out without presence of currents. In the real ocean, the waves most likely coexist with currents. In many circumstances, owing to wind force and oceanic circulation, the currents are commonly not uniform and vary with depth, which plays an important role in the evolution of gravity waves (Swan et al., 2001). Wave kinematics is a key factor in designing structures. However, experimental studies of the influence of depth-varying currents on extreme waves are mainly considered for the changing of spatial and temporal geometric characteristics (Yao and Wu, 2006). In the present study, the kinematics of extreme waves on opposing depth-varying currents will be investigated using the PIV technology.

Past studies of harbor resonance have mainly been restricted to the quasi-steady oscillations induced by steady wave conditions. This paper investigates the response of a rectangular harbor to subaerial landslide-generated impact waves based on physical models, in order to compare the oscillations induced by steady and transient waves. In response to steady incident waves, oscillations within the harbor need to experience a long process to obtain their maximum value before the input energy and the losses are balanced. Landslide-generated impact waves usually include components with solitary wave characteristics and also components with dispersive wave characteristics. Each component travels with a different celerity. Usually, solitary wave components propagate faster, and arrive in the harbor first. Oscillations attain their maximum status as soon as these components arrive. The subsequently arriving components with dispersive characteristics do not enhance the resonance oscillations. So the waves with solitary characteristics are considered to play an important role in harbor resonance. Numerical experiments, using the FUNWAVE model, were conducted in order to further verify these conclusions.

This paper proposes a new definition of groupiness factor (GF) based on the local wavelet energy density of the wave time series to describe the groupiness degree of waves. The main advantage of this new GF is that the effect of the operational definition on it is smaller than that on SIWEH-based GF or envelop-based GF. Then, the new GF is used to study the groupiness variations of mechanically generated irregular waves in a wave flume propagating on a slope of 1:45. The results of present study show that the decrease of groupiness in the coast is triggered by breaking. And energy distribution along the record time for the first harmonics of waves in the surf zone, which becomes more uniform than that out the surf zone, is the main reason causing the decrease of groupiness.