1. Introduction
Infragravity (IG) waves are surface waves with typical periods between 30 and 300 s. More and more coastal processes have been found to be associated with IG waves since they were first observed [
1]. The typical processes include the direction of sediment transport [
2], extremely high wave runup [
3,
4,
5], dune erosion [
6,
7] and overwash [
8,
9]. Major concerns at present are the impacts of IG waves on harbor resonance [
10,
11] and the stability of the mooring vessel [
12]. IG waves can be captured and significantly amplified within a port, which can adversely affect the operations at the harbor [
13]. Knowing the wave characteristics in a harbor can help the harbor operators improve port operation schedules [
14] and reduce unwanted losses. Therefore, it is particularly necessary to accurately predict the hydrodynamics in the harbor, especially the characteristics of IG waves.
Munk [
1] was the first to observe IG waves and named them surf beat to indicate that the generation of such low-frequency waves was related to wave breaking. Tucker [
15] studied the correlation between the incident short wave group and the IG wave at various time delays and concluded that the IG wave was generated by the wave group breaking up at the coast. Longuet-Higgins and Stewart [
16] argue that a short wave group will produce a bound IG wave that travels at the same celerity as the short wave group. The bound IG wave is released at the breakpoint location and subsequently reflected at the shoreline toward deeper water as free IG waves. The field observation results of Guza [
17], List [
18], and Masselink [
19] support the hypothesis of Longuet-Higgins and Stewart. Symonds [
20] proposed an alternative mechanism for the formation of free IG waves: in the transition zone where the waves begin to break, the breakpoint location of the wave periodically moves back and forth and generates time-varying radiative stress in the region. The time-varying radiation stress produces a strong gradient, which produces waves in both the nearshore and offshore directions, thus forming free IG waves. Agnon and Sheremetfa [
21] found that at the shoaling zone, free IG waves are also the result of the nonlinear interaction of short waves before short-wave breaking.
The existing wave numerical models are mainly divided into two types: phase-resolving and phase-averaged models. Phase-resolving models consider most of the nearshore processes, such as shoaling, refraction, and reflection. Such models are capable of modeling the wave propagation process in a relatively detailed manner. However, their computational costs are high. SWASH (Delft University of Technology, Delft, The Netherlands) [
22] and FUNWAVE-TVD (Total Variation Diminishing (TVD) version of the fully nonlinear Boussinesq wave model (FUNWAVE), Center for Applied Coastal Research, University of Delaware, Newark, USA) [
23] are examples of the phase-resolving model. The phase-averaged models are based on the energy balance equation. Because the phase information of a single wave is not considered by this type of model, the computational cost of such models is significantly reduced when compared to that of the phase-resolving models. SWAN (Delft University of Technology, Delft, The Netherlands) [
24] and WAVEWATCH III (NOAA National Oceanic and Atmospheric Administration, Washington, DC, USA) [
25] (WW3, hereafter) are two examples of this model type.
Recently, both SWAN [
26] and WW3 [
27] were extended to model the IG waves through empirical formulas. However, modeling IG waves by phase-resolving models are more accurate because the wave phases of short waves are retained. The XBeach-Surf beat [
7] (XB-SB, hereafter) is a combination of phase-averaged and phase-resolving models developed for nearshore processes. XB-SB uses the wave action equation to solve the variation in the short wave envelope on the scale of wave groups. The IG waves are calculated using nonlinear shallow water equations.
XB-SB is now widely used for the study of coastal processes caused by IG waves [
28,
29,
30,
31]. However, the application of XB-SB to study hydrodynamics in harbors is rare. Because XB-SB does not consider the diffraction and reflection of short waves, it is challenging to use this model in sheltered waters such as harbors. Wong [
32] assessed the efficacy of XB-SB for modeling the wave hydrodynamics inside a harbor by comparing its performance with experimental data. However, the layout of the harbor and wave conditions used in the physical model experiment of Wong was simplistic. Therefore, the efficacy of XB-SB in modeling hydrodynamics in ports requires further validation using in situ measurements.
In this study, the accuracy of XB-SB in modeling IG waves inside a harbor was assessed using an in situ observation dataset. The observations were based on three sensors. Two of these were placed near the shoreline. In particular, one was fixed inside the port. Wave heights of the short and IG waves were the focus of this study. Furthermore, the impact of the grid resolution and computational domain scale on the simulation accuracy of XB-SB in modeling IG waves was investigated. The performance accuracy of XB-SB to model the natural periods of the harbor was also evaluated. This study provides a reference and guidance for further applications of XB-SB in coastal IG wave forecasting and harbor hydrodynamic simulations.
In the following section, a brief discussion on the field observations is provided. A numerical modeling approach is presented in
Section 3. In addition, the post-processing of data and error metrics for evaluating the accuracy of the model are discussed. In
Section 4, the model is validated using the measured data. Next, the performance of XB-SB inside the harbor is assessed, including the wave hydrodynamics and the natural periods of the port. Finally, the results of this study are discussed and the conclusions are presented.
5. Conclusions
The accuracy of the wave-group-resolving model XB-SB in modeling the IG waves in a port was assessed by comparisons with field measurements obtained at Hambantota Port located in Sri Lanka. Two computational domains of various scales (D1: 15 km × 10 km; D2: 2 km × 2.5 km) were used in the numerical simulations. The objective of D1 was to reproduce the hydrodynamics of the sea area where Hambantota Port is located. Domain D2 was used for model verification. The model was validated by comparing the simulation results of D2 with the observations at sensor G1 installed at the shoreline. An appropriate grid resolution for nearshore IG wave simulations using XB-SB was used. To investigate the impact of the use of a large range of computational domains on the accuracy of XB-SB in modeling IG waves, the model was also validated using D1 and compared with the results of D2.
Next, the accuracy of XB-SB in modeling the IG waves near and inside the harbor was assessed by comparing the model results with observations from two sensors installed in and outside Hambantota Port. The performance of the model in calculating the natural periods of the harbor was also evaluated.
The conclusions of this study are as follows:
XB-SB can accurately predict the short and IG wave heights in an open domain without obstacles. The use of a grid resolution of 20 grid points per wavelength is recommended to simulate nearshore IG waves using XB-SB.
XB-SB is capable of reproducing large-scale hydrodynamics. Because the model does not fully consider the IG waves generated by the groupiness of short waves, the IG wave height is slightly underestimated when simulations are performed using a large-scale (such as 15 km × 10 km) computational domain.
For the area near the entrance of a port like Hambantota Port, XB-SB can accurately predict the wave heights of both short and IG waves. However, a large error occurs inside the harbor. The short wave heights inside the harbor are significantly underestimated because XB-SB does not consider the diffraction and reflection of short waves. For IG waves inside the port, a correlation exists between the simulation results and observations. However, in general, XB-SB overestimates the IG wave heights. The natural periods of the Hambantota Port are well identified by XB-SB.
In general, XB-SB can be used to reproduce large-scale hydrodynamics and provide accurate predictions for nearshore IG waves. However, it is not appropriate to use it to simulate the hydrodynamics inside a harbor like Hambantota Port, which is well sheltered and where it is difficult for waves to propagate directly into the harbor basin. XB-SB is still a promising tool for predicting IG waves inside a harbor when the diffraction and reflection of short waves can be considered.