Coastal Engineering Journal

The 2011 Great East Japan Earthquake and Tsunami caused devastation all along the coast of eastern Japan. Ishinomaki City was one of the most severely damaged municipalities, though the height of the tsunami in this city was smaller than that in Iwate and northern Miyagi. A large difference in the extent of building damage was found comparing two areas of Ishinomaki: one not protected by breakwaters, and the other behind the breakwaters of a large Fishery port. In this paper, the authors perform numerical simulations to determine whether these general breakwaters, which were designed not to block tsunamis but wind waves, reduced the tsunami's energy and contributed to a reduction in inundation of the areas behind the port. Before assessing the effectiveness of breakwaters against tsunamis, simulated inundation heights in each of these two areas were compared with heights measured by The 2011 Tohoku Earthquake Tsunami Joint Survey Group. It was found that a simulation with larger Manning's n value (n = 0.30) can evaluate inundation more precisely than when this value is small (n = 0.06), as often used by Japanese coastal engineers. Comparing the region protected by breakwaters with the unsheltered area, the results of a 2D shallow water equation model do not show a significant difference in inundation mainly because the tsunami intrudes through the openings in the breakwater and fills up the port basin with seawater in a very short time. Therefore, the effectiveness of general breakwaters in reducing tsunami impact should not be overestimated. However, a hypothetical study shows that water levels could be greatly reduced if the port were fully enclosed by breakwaters. This implies that a port could substantially reduce tsunami inundation if the breakwater openings were equipped to be closed before tsunami arrival. The authors also demonstrate that the difference in the extent of building damage in the two areas of Ishinomaki considered can be explained by the difference in drag forces due to the topography as well as the difference in land use, rather than by the presence of breakwaters.

The C coefficients in the now well-known parabolic bay shape equation (PBSE) are the most important parameters for verifying the bay beach stability or designing a headland bay beach in static equilibrium. These coefficients are revised specifically for bays in static and dynamic conditions in Thailand. Three techniques, namely Least Square (LS), Genetic Algorithms (GA), and Differential Evolution (DE) are used to determine the alternative coefficients. The newly derived C coefficients for static equilibrium bays (SEB) differ slightly from the original coefficients. Dynamic equilibrium bays (DEBs) with sediment within the embayment are analyzed to obtain a new set of C coefficients, which are a function not only of wave obliquity but also sediment supply ratio (SSR), which is a new parameter representing the ratio between the rate of sediment supplied from a river source to the bay and the longshore sediment transport rate. The resulting new C coefficients for DEBs vary uniformly and systematically, similar to those for the SEBs, and are expected to be applicable to DEBs elsewhere for coastal management.

Developing an accurate and reliable time-averaged beach profile evolution model under storm and nonstorm conditions is a challenging task. Over the last few decades, a number of beach deformation models have been developed under limited experimental conditions and uncertainties, and sometimes they required a long computation time. It is quite evident that a large amount of wave, current, sediment and beach profile data is available today. The present study leads to the development of a simple two-dimensional beach profile evolution model with on–offshore sand bar formation under nonstorm and storm conditions based on the time-averaged suspended sediment concentration models of Jayaratne and Shibayama [Jayaratne, M. P. R. and Shibayama, T. [2007] "Suspended sediment concentration on beaches under three different mechanisms," Coastal Eng. J., JSCE49(4), 357–392.] and Jayaratne et al. [Jayaratne, M. P. R., Sritharan, S. and Shibayama, T. [2011] "Examination of the suspended sediment concentration formulae using full-scale rippled bed and sheet flow data," Coastal Eng. J., JSCE53(4), 451–489.]. These models were formulated for computing sediment concentration in and outside the surf zone under three different mechanisms: (1) suspension due to turbulent motion over sand ripples, (2) suspension from sheet flow layer and (3) suspension due to turbulent motion under breaking waves. The suspended load is calculated by the product of time-averaged sediment concentration and undertow velocity from edge of the wave boundary layer to wave trough and mass transport velocity from wave trough to crest (bore-like wave region). Sediment transport in wave boundary layer is computed from the modified Watanabe [Watanabe, A. [1982] "Numerical model of nearshore currents and beach deformation model," Coastal Eng. Jpn., JSCE25, 147–161.] model. Rattanapitikon and Shibayama [Rattanapitikon, W. and Shibayama, T. [1998] "Energy dissipation model for regular and irregular breaking waves," Coastal Eng. J., JSCE40(4), 327–346.] wave model is used to calculate the average rate of energy dissipation due to wave breaking. The beach deformation is calculated from the conservation of sediment mass while the avalanching concept of Larson and Kraus [Larson, M. and Kraus, N. C. [1989] SBEACH: Numerical model for simulating storm induced beach change, Report 1, Technical Report CERC-89-9, US Army Eng. Water. Exp. Station.] is used to re-distribute the sediment mass in neighboring grids for a steady solution. Published field-scale experimental and natural beach profiles from five high-quality data sources from 1983–2009 [Kajima et al., 1983; Kraus and Larson, 1988; Port and Airport Research Institute, Japan, 2005, 2009; Hasan and Takewaka, 2007, 2009; Ruessink et al., 2007] are used to verify the performance of the proposed numerical model. The key feature in this process-based model is that it takes about a couple of minutes to simulate beach profiles of a 2–3 days storm qualitatively at a fairly satisfactory level using a standard personal computer. It is found that the present numerical predictions are not better than the null hypothesis as the model is in a stage of ongoing development. Therefore, it is believed that the final model is often of more value to a practical coastal engineer than a very detailed study of hydrodynamics and sediment transport study, however an incorporation of swash dynamics, more precise evaluation of offshore sand bar formation and continuation to a longer time scale with precise beach deformation are recommended as the next stage of the model.

The attenuation of shallow-water waves over stratified seabed mud is investigated. A two-layer viscoelastic mud model is introduced, in which the upper layer of fluid mud is described by the Maxwell model and the lower layer of deformable mud bed is described by the Kelvin–Voigt model. Based on the perturbation analysis and the Laplace transformation, a set of Boussinesq-type equations for wave attenuation is established. The Boussinesq-type equations are consistent with literature results when the mud model degenerates to single-layer models. Based on the Boussinesq-type equations, the damping rate of linear long waves and the evolution formula of solitary-wave amplitude are obtained. In the case of linear sinusoidal waves, the wave energy is mainly dissipated by shear motions within the upper mud layer. When resonance occurs, the wave damping is significantly enhanced. In the case of a solitary wave, the loss of wave energy is due to the viscous dissipation within the upper mud layer as well as the elastic absorbing within the lower mud layer. The viscosity of the lower mud layer has little influence on the damping of solitary waves. Modal analysis shows that the mud motion is always dominated by the first mode.