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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.