Low-Frequency Oscillations Within the Hambantota Port During the Southwest Monsoon, 2019

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.

Offshore Breakwaters for LNG and Bulk Terminals: A Design Methodology for Determining Breakwater Layout

Over the last decades LNG and bulk terminals have been constructed in many countries. Many of these terminals have been located in sheltered sites without significant influence of swell and wind seas. As the worldwide gas market continues to grow supplying domestic, industrial and power plant projects, there is a continuous interest in new LNG terminals. With the growing gas demand LNG terminals are planned at exposed sites where the need of a breakwater is important for the ability of the facility to maintain operations and to ensure survivability of the terminal infrastructure. Studies are carried out for LNG terminal concept with the main focus on the need for a breakwater protecting the facility which will have significant impact on the CAPEX (Capital Expenditure). The mooring layout of the FSU/FSRU and LNG carrier whether perpendicular or parallel to the breakwater in addition to the planned operations determine the protection area behind the breakwater. The objective of this study is to establish design curves relating the different environmental and terminal parameters such as wave conditions, berthing facility layout, protection area and breakwater layout. These curves are derived based on the results of numerical simulations for wave transformation process of offshore waves propagating inside the terminal area. More than 700 cases are carried out in this study considering a range of wave periods, breakwater lengths, breakwater type (caisson and rubble mound), facility area dimensions and two incoming waves direction, i.e perpendicular and oblique. The simulations are carried out using the software REFONDE which is based on resolving the mild slope equation for irregular waves. The results of the study are presented in the form of curves and generalized to be used by terminal developers, designers and contractors for general guidance in future projects. Up to the authors’ knowledge, such curves for the design of marine terminals are not available at present. From this overview, a design methodology is developed to determine breakwater layouts during the early planning phase of project considering wave conditions, facility layout and terminal operations.

A new model for the three-dimensional propagation of water waves in the presence of vertically sheared, horizontally varying currents

<p>In coastal areas, steep bathymetries and strong currents are often observed. Among several causes, the presence of cliffs, rocky beds, or human structures may cause strong variations of the sea bed, while oceanic circulation, tides, wind action or wave breaking can be responsible for the generation of strong currents. For both coastal safety and engineering purposes, there are many interests in providing efficient models predicting the nonlinear, phase resolved behavior of water waves in such areas. The difficulty is known to be important, and many models achieving that goal are described in the related literature.</p><p>Recently, it was established that beneath the influence of vertically uniform currents, the vorticity involved in depth varying mean flows could have significant impact on the propagation of water waves (Rey et al. 2014). This gave rise to new derivations of equations aimed to describe this interaction. First, an extended mild slope equation was obtained (Touboul et al. 2016). Then, the now classical coupled mode theory was introduced in the system to obtain a set of coupled equations, which could be compared to the system derived by Belibassakis et al (2011) but considering currents which may present constant shear with depth (Belibassakis et al. 2017, Belibassakis et al., 2019). In these works, the currents were assumed to vary linearly with depth, presenting a constant shear. However, this approach was recently extended to more general configurations (Belibassakis & Touboul, 2019; Touboul & Belibassakis, 2019).</p><p>In this work, we extend this model to three dimensional configurations. It is emphasized that the model is able to describe rotational waves, as expected, for example, when water waves propagate with a non-zero angle with respect to the current direction (see e.g. Ellingsen, 2016).</p><p>[1] Rey, V., Charland, J., Touboul, J., Wave – current interaction in the presence of a 3d bathymetry: deep water wave focusing in opposite current conditions. Phys. Fluids 26, 096601, 2014.</p><p>[2] Touboul J., Charland J., Rey V., Belibassakis K., Extended Mild-Slope equation for surface waves interacting with a vertically sheared current, Coastal Engineering, 116, 77–88, 2016.</p><p>[3] Belibassakis, K.A., Gerostathis, Th., Athanassoulis, G.A. A coupled-mode model for water wave scattering by horizontal, non-homogeneous current in general bottom topography, Applied Ocean Res. 33, 384– 397, 2011.</p><p>[4] Belibassakis K.A., Simon B., Touboul J., Rey V., A coupled-mode model for water wave scattering by vertically sheared currents in variable bathymetry regions, Wave Motion, vol.74, 73-92, 2017.</p><p>[5] Belibassakis K., Touboul J., Laffitte E., Rey  V., A mild-slope system for Bragg scattering of water waves by sinusoidal bathymetry in the presence of vertically sheared currents,  J. Mar. Sci. Eng., Vol.7(1), 9, 2019.</p><p>[6] Belibassakis K.A., Touboul J. A nonlinear coupled-mode model for waves propagating in</p><p>vertically sheared currents in variable bathymetry-collinear waves and currents, Fluids, 4(2),</p><p>61, 2019.</p><p>[7] J. Touboul & K. Belibassakis, A novel method for water waves propagating in the presence of vortical mean flows over variable bathymetry, J. Ocean Eng. and Mar. Energy, https://doi.org/10.1007/s40722-019-00151-w, 2019.</p><p>[8] Ellingsen, S.A., Oblique waves on a vertically sheared current are rotational, Eur. J. Mech. B-Fluid 56, 156–160, 2016.</p>

Consistent nonlinear deterministic and stochastic wave evolution equations from deep water to the breaking region

Modelling the evolution of the wave field in coastal waters is a complicated task, partly due to triad nonlinear wave interactions, which are one of the dominant mechanisms in this area. Stochastic formulations already implemented into large-scale operational wave models, whilst very efficient, are one-dimensional in nature and fail to account for the majority of the physical properties of the wave field evolution. This paper presents new two-dimensional (2-D) formulations for the triad interactions source term. A quasi-two-dimensional deterministic mild slope equation is improved by including dissipation and first-order spatial derivatives in the nonlinear part of equation, significantly enhancing the accuracy in the breaking zone. The newly defined deterministic model is used to derive an updated stochastic model consistent from deep waters to the breaking region. It is localized following the approach derived in Vrecica & Toledo (J. Fluid Mech., vol. 794, 2016, pp. 310–342), to which several improvements are also presented. The model is compared to measurements of breaking and non-breaking spectral evolution, showing good agreement in both cases. Finally, the model is used to analyse several interesting 2-D properties of the shoaling wave field including the evolution of directionally spread seas.