Narrow Results

Approximation and analysis are used for investigating accurate soliton solutions of the ill-posed Boussinesq (IPB) equation. The investigated model explains shallow-water gravitational waves. It examines one-dimensional nonlinear strings and lattices. IPB explains small-amplitude surface waves on nonlinear strings and lattices. We provide unique analytical solutions to analyze numerical beginning and boundary conditions. A solution’s quality is judged by its divergence from analytical predictions. Physical wave properties are illustrated.

In this paper, at first results of experiments in sheet flow conditions under nonlinear asymmetric irregular oscillations with and without long wave components are presented and a method for estimating the net transport rates is proposed. Then the importance of phase lag between free long waves and irregular short waves as well as the effect of steady currents on the magnitude of transport rate are discussed. Implications of the results are further demonstrated by applying the proposed formulation to calculating the cross-shore distributions of sediment transport rates on a sheet flow dominated beach under incident irregular waves with low frequency components. It is found that long waves can significantly enhance the seaward transport of sediments inside the surf zone during a storm. It is also shown that the presence of a standing long wave system may lead to large spatial gradients in the cross-shore transport rates and eventually, to formation of a multiple longshore bar system.

A hybrid analytical-numerical method for standing waves in water of any depth exactly satisfies the field equation, the bottom boundary condition, the periodic lateral boundary conditions and the mean water level constraint. The wave height and the kinematic and dynamic free surface boundary conditions are imposed numerically, as a problem in nonlinear optimization. The algorithm is confirmed against an existing fifth-order analytical theory. The method extends the available predictive range for standing waves to near-limit waves in deep, transitional, and shallow water. The limitations of the numerical method are clearly identified. The limit wave cannot be predicted but near-limit extreme wave indicators for wave height, wave number, and crest elevation are defined over the complete range of water depths.

The two-dimensional shallow water equations were formulated and numerically solved in an arbitrary curvilinear coordinate system, which offers a relatively high degree of flexibility in representing the natural flow domains with structured meshes. The model employs an efficient TVD-MacCormack scheme, which has second-order accuracy in both time and space. Refinements were made to enhance the model's accuracy and stability in computing the shallow wave dynamics in real-world scenarios, with irregular boundaries and uneven beds. In particular, advanced open boundary conditions have been proposed according to the method of characteristics, and rigorous mass conservation has been enforced during the computation at both the inner-domain and the boundaries. These refinements are necessary when modeling the flood inundation over a large area and the tidal oscillation in a macro-tidal estuary. The effectiveness of the refinements was verified by simulating the forced tidal resonance in an idealized condition and the Malpasset dam-break flood in the Reyran river valley. The application of the refined model in the study of tidal oscillations in the Severn Estuary and Bristol Channel can be found in the companion paper.

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.

Infragravity waves play an important role in port operations and many nearshore processes, and therefore their characterization is of major interest for oceanographers and coastal engineers. The lack of proper measurement networks and historic databases makes the development of hindcasting techniques essential. This work presents a fully developed infragravity wave hindcast methodology through Artificial Neural Networks (ANNs) and its application to a case study. The characteristic wave-heights of the low frequency band and the swell band inside a port basin are computed for a period of eight years on the basis of the long-term offshore wave conditions, a short record of sea-level oscillations and the historic tidal harmonic constituents. Based on the results, we construct and analyze the single and the joint probability density functions of the two characteristic wave-heights studied. In addition, we study the relationships between the infragravity energy inside the port and the offshore wave parameters and explore the extreme events during which the low frequency band energy exceeds the swell energy. The findings highlight the potential of the methodology to characterize the infragravity wave conditions inside a port basin and its suitability to study other coastal problems in which these waves are involved.

Motivated by recent field observations of tsunamis, a new wave maker, namely bottom-tilting wave maker, has been designed and investigated in order to generate very long waves in the laboratory. Theoretical results from the linear wave theory and the numerical modeling based on the weakly nonlinear and weakly dispersive wave theory show good agreement with the measurements. Using both theoretical and experimental results, the relation between the bottom motion and the resulting waves have been investigated. Wave amplitude and period of the generated waves are the subject of the parametric analysis, which verifies that the wave maker is able to generate waves longer than the effective wavelength of the solitary wave with the same wave amplitude.

An experimental study is carried out to investigate the transformation of oscillatory boundary layer from ordinary to depth-limited one by using an oscillating tunnel with triangular roughness pasted on the top and bottom surfaces. The velocity is measured by one-component LDV. It is proved that only longer period of oscillation is not sufficient to induce depth-limited properties. Instead, the ratio of boundary layer thickness to the distance from the bottom to the free surface must be used in order to distinguish a depth-limited oscillatory boundary layer from an ordinary one. The experimental data for mean velocity, phase difference, fluctuating velocity, friction coefficient and boundary layer thickness are presented in order to elaborate the structure of depth-limited oscillatory boundary layers on a rough bottom. On the basis of the present experiments, a modification has been made in an existing criterion to distinguish between ordinary and depth-limited wave boundary layers. A typical field situation is discussed to show the usefulness of the proposed criterion.

It is widely assumed that incident bound long waves are released during short wave breaking, subsequently propagating to the shore as a free wave. Statements asserting this release are either unattributed, or loosely attributed to Longuet-Higgins and Stewart (1962). However, the author is unaware of convincing evidence of such release of bound long waves as a result of short wave breaking, while there appears to be strong evidence to the contrary. The author's interpretation is that Longuet-Higgins and Stewart (1962) suggest that the bound wave will decay in amplitude following short wave breaking. This is in agreement with a number of the author's data sets and some data from other recent data sets, including field observations of strong nearshore dissipation of long waves. A surf beat similarity parameter is also suggested, which distinguishes different regimes of surf beat generation.

Some twenty ultrasonic wave gages were employed to measure the water surface level as well as the bottom sand level near the shoreline in the field. Obtained data during a storm reveals that the long period waves were really dominant in and just outside the swash zone. It is also shown that the long waves provided the swash oscillation in the form of the loop by standing waves. In addition, data recorded for different conditions of beach slopes and incident waves are also presented for comparison with some analysis.