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Models for shallow water wave processes are routinely applied in coastal, estuarine and river engineering practice, to problems such as flood waves, tidal circulation, tsunami penetration, and storm tides. Evaluation and confirmation of application codes can be facilitated by analytical solutions that may represent this wide range of physical problems, without significantly compromising the contributing flow processes. The appropriate linearized shallow water wave equations are defined, together with quite general initial and boundary conditions that will represent the expected variety of shallow water wave problems. A completely general analytical solution for both water surface elevation and flow is established, in a manner suitable for the evaluation of shallow water wave codes. The contribution of both free and forced modes is identified, together with the role of friction.

A sequence of analytical solutions explore the spectrum of response patterns expected from numerical codes for flood and tide propagation in channels. Complete analytical details of the solutions are provided, together with specific suggestions for an associated set of analytical benchmark tests. Illustrations of predicted response patterns provide the basis for a discussion of many significant physical aspects and their representation in discrete numerical codes.

With a numerical model of Northwestern Pacific region, the water movements associated with real time tides and actual storms were reproduced. Making use of reasonably representative model simulations together with data derived from the coastal observations can lead to the required estimates of extreme conditions for the purpose of coastal defense and design of offshore structure. Here, we used the model of 1/12° latitude by 1/12° longitude resolution. 75 typhoon and monsoon surge simulations were performed with specification of 8 boundary tides for real time tides. Typhoon and winter monsoon wind fields were computed from JWA/GPV data set applying Cardone's PMBL (Planetary Marine Boundary Layer) model over the whole region with embedding parameterized typhoon wind fields onto it. Present result is an updated version of papers presented earlier (Choi and Ko, 1999; Choi and Eum, 2000). Preliminary maps showing distribution of extreme sea levels of whole modeled area including coastal boundaries and surge induced extreme currents are presented in terms of recurrence intervals.

A horizontal hydrodynamic model was applied to predict the response characteristics of the Severn Estuary and Bristol Channel to regular long waves, in an effort to gain insight into the tidal behavior of this area. A boundary-fitted curvilinear mesh of high resolution was generated, covering the downstream reach of the River Severn, the Severn Estuary and the Bristol Channel, with the seaward boundary set from Milford Haven to Hartland Point to the west and the riverine boundary at Gloucester towards the east. The simulations were first calibrated against the observed tidal levels and currents at various sites, for typical spring and neap tides. Subsequently, water surface oscillations inside the domain were excited by sinusoidal long waves of different periods at the open boundary to find the fundamental mode of oscillation. The amplitude–frequency relationships were calculated at numerous sites. It was found that the primary resonant mode of oscillation in the Severn Estuary occurred at the tidal period of around 8 h. Although not exactly coinciding with this resonant mode, the M2 tide still observed a relatively high amplification factor, which helps explain why this water body experiences one of the largest tidal ranges in the world.

The tidal record on the East Coast of the United States reveals the frequent semidiurnal perturbation of the storm surge on the South Atlantic Bight. Tropical cyclones were examined to be one of the main triggers for these perturbation events. The peak of the storm surge is centered in the mid of the South Atlantic Bight, and radiating along the coast southward and northward. The process-oriented experiments were designed with parametric determination based on the historic events. The experiments were carried out in order to further discuss the various factors of tropical cyclones for their effect on the storm surge and tide interaction. The experimental analysis shows the storm surge and tide interaction is the most severe when a cyclone is moving orthogonal to the coastline, although the parallel-to-shore tropical cyclones are the most observed in history. The intensity of the semidiurnal perturbation to storm surge is positively correlated to the wind strength and the radial of the maximum wind speed of a cyclone, but negatively correlated to the translation velocity of a cyclone. For a cyclone moving parallel-to-shore, the corresponding storm surge perturbation lasts the longest and is the strongest, when the “fetch” of the alongshore wind with speed >17m/s (the criticality of the wind speed of the Tropical Storm based on the Saffir-Simpson category) reaches the maximum on the continental shelf of the mid of the South Atlantic Bight. High correlation is found between the tropical cyclone induced alongshore oceanic current and the semidiurnal perturbation to storm surge.

The storm surge residual of 2.35m was measured during Typhoon Anita in 1970 in the Tosa bay, Japan. Since the Tosa bay widely open to the Pacific Ocean, surge heights are usually small. The present study examined the reasons why the abnormal storm surge was generated due to Typhoon Anita 1970 by numerical simulations using a coupled model of surge, wave and tide with six levels computational domains of which grid sizes are from 12150m to 50m. The storm surge simulation driven by only wind and pressure fields was not able to compute the measured sea surface levels. However, when wave radiation stress terms were included in the storm surge model the computed sea surface levels showed a good agreement with the measurement data. This study clarified that the effect of wave-induced radiation stress is significant on water level rising of up to 0.5m-1.0m in the Tosa bay.

Storm surge is influenced by many factors including environmental and geographical conditions. However, laboratory experiments and filed measurements were not easy to carry due to danger and difficulties. In this study, we conducted a numerical study with a verified storm surge model. Storm surge was impacted by track, tide, water depth and sea level rise. The track of storm is related to size of storm and the range of impact could be estimated by their relationship. One of the characteristics on storm surge is that storm surge is strongly affected by water depth and surface elevation. We found that variation of storm surge could be different at each tide and depth and it makes a big difference in the western sea of Korean Peninsula whose averaged depth is about 40 m and tidal range is about 10 m. An increasing sea level rise by climate change can cause a little reduction of storm surge by its own characteristics.

Seasonal variation of residual currents in the Meghna Estuary, located at the northern part of the Bay of Bengal, has been investigated through the use of a 3D numerical model. Residual current in the Meghna Estuary appears to be strongly influenced by tidal currents and Coriolis Effect under average meteorological and hydrological conditions of four different seasons considered,. Average seasonal variation of wind speed and direction as well as fresh water inflow does not seem to have significant influence on residual current. Only under the influence of average of maximum wind speeds of different seasons, residual currents in the Meghna Estuary show their dependency on wind stress. In general, at the surface layer northward and northwestward flow is created during the pre-monsoon and monsoon periods and southwest and southeastward flow is created during the post-monsoon and winter periods.

The stratification of upper layer of coastal water can be regarded as an unused energy source in summer. In addition, the coastal water has capability to store the urban heat owing to the heat capacity difference to the atmosphere. This study assesses the usage and capacity of coastal water for heat storage. A set of numerical simulations of the urban heat release into coastal zone is performed for Osaka bay of Japan. The estimated urban heat along Osaka Bay is 1 kGJ/h within the distance from 500 m to 5000 m from the coastal line. The urban heat released within 2000 m from the coastal line had little influence on sea surface temperature of Osaka Bay.

A system is described, based on finite-difference discretisations of the governing hydrodynamic equations, which determines the three-dimensional motions in well mixed coastal seas, produced by tidal and meteorological influences. It has been thoroughly tested and has been found to be very robust and accurate.

Closure of the system of equations is achieved using forms of the Boussinesq approximation to determine the coefficients in the turbulent eddy viscosity terms. A method of calibrating the model is also described.