Modelling Of Wave Propagation In The Nearshore Region Using The Mild Slope Equation With Gmres Based Iterative Solvers

Author : David R. Michalsen
Publisher :
ISBN 13 :
Total Pages : 260 pages
Book Rating : 4.:/5 (65 download)

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Download or read book An Investigation on the Modeling of Wave Field Transformation and Shoreline Morphology Near Steep Bathymetric Features written by David R. Michalsen and published by . This book was released on 2004 with total page 260 pages. Available in PDF, EPUB and Kindle. Book excerpt: Steep bathymetric anomalies in the beach profile, such as offshore borrow pits, submerged breakwaters, and nearshore canyons can significantly transform the wave climate through the effects of refraction, diffraction, and reflection. When located in the nearshore region the modified wave climate can also substantially change the location of breaking and has been observed to impact the shoreline morphology. The current study focuses on the borrow pit case and attempts to explain how limitations in existing methodologies may impact the predictions in both the wave field modification and shoreline response. Recent analytical methods by Bender (2003) have successfully explained the wave transformation near pits. However, these models are only capable of modeling bathymetries of constant depth surrounding the anomaly. Therefore in order to investigate cases without this restriction, this often requires numerical solutions following Berkhoff's (1972) mild-slope equation (MSE). However, a significant limitation of these model types is the accuracy suffers for steep bathymetric features. Booij (1983) demonstrates this for slopes larger than 1:3 (rise:run). Furthermore, these models often rely on Radder's (1979) parabolic approximation to the MSE which restricts the ability to include wave reflection which can be substantial in the case of a borrow pit. These limitations and their effects on shoreline response are investigated in the current study. By utilizing a form of the modified mild-slope equation (MMSE) originally derived by Massel (1993) the limitation of the MSE in representing steep features is removed. Additionally, a numerical model following Lee et al. (1998) is employed to investigate wave transformation around borrow pits of arbitrary depth. The formulation of the model is of hyperbolic form; therefore, the reflected waves generated by a borrow pit are included. The models accuracy is validated through a rigorous set of tests showing that the model compares well with previous analytical solutions for steep features. To estimate the importance of wave reflection, information from documented borrow sites is gathered. Using dimensionless parameters relating the incident waves and the pit geometry, an estimate of the amount of reflection generated by each borrow pit is calculated. It is shown that upward of 30% of the wave energy can be reflected by a borrow pit. Additionally, it is shown as wave frequency increases (or kh located in the intermediate depth region), the MSE's inaccuracy in predicting reflection is enhanced. Expanding on this conclusion, a parametenzation analysis is performed. The analysis describes conditions under which resonance inside the trench capable of producing large reflection is reached. The study serves as preliminary design guidance which can be used to avoid borrow pit geometries that are capable of producing a large amount of reflection. It is also of interest to describe how the effects of reflection affect the regions far shoreward of the pit. Employing a form of the MMSE model, the evolution of the wave field is analyzed. It was found that although the effects of reflection are strong near the borrow pit, as the distance leeward of the pit increases the effects of refraction and diffraction outweigh the impacts of reflection. Thus, the result using a wave model including reflection would not substantially differ from that of using a model that neglects the reflected waves when investigating the impacts on shoreline evolution. Finally, the last part of the study looks at the validity of utilizing current shoreline response models for this particular problem. Wave height and direction at breaking dictate how one-line models predict shoreline response. However, these models fail to include the effect that longshore gradients in wave height have on generating mean water level (MWL) gradients. MWL gradients in wave height are capable of producing longshore currents which can significantly alter the sediment transport trends. Coupling the MMSE wave model with a 2DH nearshore circulation model shows that MWL gradients have a significant impact on current generation. Results indicate that incipient rip currents result from the converging currents associated with the MWL gradients. The presence of these currents would thereby dictate a new sediment transport trend, possibly transporting sediment offshore instead of in the theorized salient formation predicted by one-line models.