Journal of Waterway, Port, Coastal, and Ocean Engineering

This study presents a methodology for applying the three-dimensional actuator disk-RANS technique in modeling tidal energy converters within a regional-scale simulation. Of particular interest are the robustness of the applied momentum source term and its effectiveness in modeling an array of full-sized tidal turbines under realistic hydrodynamic and operational conditions. The Inner Sound region, which is the site of commercial-scale deployment projects of the Pentland Firth in Scotland, is chosen as the study area. While the actuator disk approach had been used in past studies to parameterize the far-wake region of horizontal-axis tidal turbines, details of its three-dimensional implementation have not been thoroughly discussed. Criteria adopted in deciding the array location are presented in this study, along with the actuator disks’ detailed setup and constraints. The models are subjected to one operational characteristic that is similar to commercial devices in service to examine the accuracy of the imposed source term under complex flow conditions. The results demonstrate that the thickness of the disk imposed in the source term has a pronounced influence on the model outputs. In addition to accurately modeling flow propagation and wake interactions, the models are also able to replicate the observed asymmetrical tidal currents in the region. Because there is currently limited published material on the detailed application of the actuator disk approach in ocean-scale models, this study is hoped to fill the research gap and provide evidence, guidance, and examples of best practices for future studies.

The Morison equation is extensively employed to consider viscous effects in hydrodynamic investigations of diverse wave energy converters using the boundary element method (BEM). Nonetheless, linearizing the nonlinear drag component in frequency-domain analysis and determining the appropriate drag coefficients present a challenge. This paper proposes a simple method using the completely linear form of the artificial damping torque equation to consider the energy dissipation due to viscosity in the frequency-domain BEM analysis of bottom-hinged oscillating surge wave energy converters (OSWECs) under regular waves. Similar to the drag coefficient, a constant artificial damping ratio demonstrates applicability across various wave periods for a given OSWEC, with its most pronounced effects observed near the natural periods. Through scanning different values, the fittest artificial damping ratio is determined by minimizing the deviation between the BEM responses and the experimental or high-fidelity computational fluid dynamics data. In contrast to the widely varying drag coefficients, the fittest artificial damping ratios for three OSWECs with different dimensions fall within a narrow range. Hence, a recommended artificial damping ratio is proposed for the rapid approximate estimation of responses, particularly in the absence of validation data during the initial design phase.

In the context of actual surface wave conditions, the wave field is represented as a set of complex fluctuations that randomly change in both time and space, commonly known as “random waves.” These random waves can be expressed mathematically as a combination of multiple monochromatic waves, each having unique phases, directions, and amplitudes. Frequency-domain phase-resolving wave models have been shown to be robust predictors of random wave propagation provided the dispersive characteristics are valid for the range of water depths considered. Recently, a new dispersive nonlinear mild-slope equation model was developed by establishing a closer correspondence between the scaling of nonlinearity, horizontal depth variation, and modulation scale during the derivation process. In this work, this new model is augmented with a wave-breaking dissipation model using frequency-squared dissipation weighting over the wave spectrum. The new model and previous models are compared with laboratory data for accuracy in modeling the evolution of the random wave spectrum. Overall, the new model demonstrates improved agreement with results compared with the previously derived models. The additional nonlinear terms of the model, indicating the interaction effects between amplitude and amplitude change, correct the overprediction of wave spectral energy from prior models, especially at the lower frequencies of the shallowest gauges. Furthermore, the predictions of free surface elevation by the newly derived model are in excellent agreement with the observations at the shallowest gauge, primarily due to the alleviation of phase mismatch caused by the additional terms. Lastly, we provide the nonlinear modification to linear wavenumber on the basis of the additional nonlinearity.

Abstract

Montrose Bay’s coastline in Scotland is experiencing the most severe erosions, especially in its southern section, interfacing with the Montrose Tidal Inlet System. This inlet system could induce a distinct ebb tidal jet and eddy when ebbing, influenced by its high-angle half-delta, and the understanding of jet and eddy formation at this type of inlet is still limited. This paper presents the results of a numerical modeling study conducted using Delft3D FM to characterize tidal hydrodynamics at the Montrose Tidal Inlet System, emphasizing the flow features at its seaward side. Acoustic Doppler current profiler measurements captured an asymmetry between peak ebb and flood flow induced by the interaction between the residual of an ebb jet and the alongshore tidal current, which later was successfully replicated by the model, especially after a satellite-derived topography was applied to the Montrose Basin. The observed jet and eddy formation at the Montrose System is unique compared to what has appeared at other inlets with different delta shapes. At spring tides, the jet develops a pair of main and frontal bodies that extend more than 2 km from the inlet and experiences a sharp deflection after interacting with cross current. This jet is accompanied by only one transient eddy with about 1 km diameter at the landward side of the jet frontal. Analysis of residual flow revealed a strong residual going toward the harbor channel at adjacent beaches, which could be contributing to the ongoing sedimentation at the channel.

Practical Applications

This study is about a unique coastal current formation at the southern end of Montrose Bay, Scotland, United Kingdom, visualized through numerical modeling. The main feature of this current is a strong outflow, known as the ebb (tidal) jet, which forms during the ebbing phase. This ebb jet expands in the offshore direction before being strongly deflected to the North by the ambient current and simultaneously forming a counter-clockwise eddy within a region between the ebb jet and the beach. This unique coastal current formation is strongly influenced by the configuration between shoreline features, inlet positioning, and the ambient tidal current. This study further explores the potential relevance of this ebb jet and eddy to the ongoing erosion and sedimentation in and around the inlet. Furthermore, this research provides insights into various ebb jet and eddy formations observed at other inlets around the world and highlights the value of utilizing satellite-derived topography data for numerical modeling.

Sparse borehole data and unreasonable sampling strategies pose challenges in accurately constructing geological profiles, resulting in inaccurate soil distribution information and impacting the design of implementation plans for dredging engineering. Therefore, an automatic construction and uncertainty analysis approach to the geological profile of dredging engineering is proposed using multiple-point geostatistics. The approach uses a training image instead of the variogram function, considering the spatial variability of the soil and adapting to learn high-order spatial information. This enables the characterization of spatial relationships and distribution patterns between multiple points. Subsequently, statistical uncertainty analysis is conducted based on the results obtained from stochastic simulations. The effects of neighboring cell numbers, threshold, and borehole spacings on the performance of our approach are systematically investigated and the optimal simulation parameters are determined. Additionally, the simulated geological profiles are categorized into three areas (high, medium, and low) based on the level of uncertainty, quantifying the uncertainty of the proposed approach. The equidistant method is then used for comparison and verification. When applied to a dredging engineering case in the Lianyungang Channel, the approach achieved a prediction accuracy of over 93.7% and successfully quantified boundary areas with high uncertainty in soil layers. This shows the enhanced capacity of the approach to capture characteristics of soil distribution. The approach reduces the area of high uncertainty by 11.4%, demonstrating advancements in selecting drilling locations. The study will provide decision support for geological surveys in dredging engineering and provide reliable soil information for subsequent construction.