Phase-averaged Model Research Articles

Numerical modeling of vegetation-induced dissipation using an extended mild-slope equation

This paper presents an incorporation of vegetation-induced wave dissipation in a planar numerical wave propagation model based on the extended mild-slope equation (EMSE). The implementation was incorporated in a purely mathematical method in the light of current theoretical studies. To examine the performance of the phase-resolving model, a comprehensive comparison with phase-averaged SWAN is made to test and validate the implementation. Moreover, new in-situ measurements in a mangrove forest are presented aiming to test the wave energy damping by vegetation using the observed wave spectra. From our validation results it can be concluded that wave dissipation due to vegetation is equally well reproduced in this model. It is found that the wave parameters (wave height and period) and vegetation parameters (plant width, height and density) are all influencing factors. An interesting finding is that relatively high-frequency waves are more dissipated than low frequency waves, especially for larger wave heights. In this study, we found that diffraction is of great significance in wave propagation over inhomogeneously distributed vegetation. Theoretically, the phase resolving EMSE represents the physical process of diffraction better than the phase-averaged model SWAN.

A 3-D phase-averaged model for shallow-water flow with waves in vegetated water

A 3-D shallow-water flow model has been developed to simulate the flow in coastal vegetated waters with short waves. The model adopts the 3-D phase-averaged shallow-water flow equations with radiation stresses induced by short waves. It solves the governing equations using an implicit finite volume method based on quadtree rectangular mesh in the horizontal plane and stretching mesh in the vertical direction. The flow model is coupled with a spectral wave deformation model called CMS-Wave. The wave model solves the spectral wave-action balance equation and provides wave characteristics to the flow model. The model considers the effects of vegetation on currents and waves by including the drag and inertia forces of vegetation in the momentum equations and the wave energy loss due to vegetation resistance in the wave-action balance equation. The model has been tested using several sets of laboratory experiments, including steady flows in a straight channel with submerged vegetation and in a compound channel with vegetated floodplain and random waves through a vegetated channel and on a vegetated beach slope. The calculated water levels, current velocities, and wave heights are in general good agreement with the measured data.

Modeling Waves in Open Coastal Areas and Harbors with Phase-Resolving and Phase-Averaged Models

Rusu, E. and Guedes Soares, C., 2013. Modeling waves in open coastal areas and harbors with phase-resolving and phase-averaged models. Journal of Coastal Research, 29(6), 1309–1325. Coconut Creek (Florida), ISSN 0749-0208. A wave-prediction system based on spectral models was validated against in situ measurements in the Portuguese continental nearshore and is now operational. As a final extension of this system, the present article describes the implementation and validation of high-resolution wave models. In this connection, the objective of the present work was to evaluate the performance of such models in different coastal environments. The first target was an open coastal area located in the central part of the Portugal continental. An evaluation of the two state-of-the-art phase-resolving wave models, REFDIF1 and FUNWAVE, was carried out, and the results are compared with those from a field experiment.

Coupled wave action and shallow-water modelling for random wave runup on a slope

Wave runup statistics on beaches, dunes and coastal structures are needed for coastal management and engineering designs. Spectral wave energy–action models are widely used to predict wave propagation in deep and shallow water, incorporating the effects of refraction, bed friction, breaking and wave–wave interactions. To calculate nearshore runup or overtopping, wave-by-wave or phase-resolving modelling is necessary as spectral, phase-averaged models only give the spectral evolution and wave-induced setup. Herein, unidirectional wave propagation up a uniform slope predicted by the Simulating WAves Nearshore (SWAN) model is compared with experimental data. The surface elevation time series near the breaking position is then created from the predicted nearshore spectra and input to a non-linear shallow-water equation solver to give statistical runup predictions which are also compared with experimental data. Sensitivity to the offshore position for wave input is investigated. Runup statistics are shown to be reasonably well predicted.

Assessment of TELEMAC system performances, a hydrodynamic case study of Anglet, France

The wave propagation and flow modules of the TELEMAC system have been applied to the Adour River mouth and the adjacent beaches of Anglet (France). The wave propagation has been simulated using the phase-averaged model TOMAWAC. In addition, the phase-resolving REFDIF S model has been also used, as the diffraction of wind waves, which is not taken into account in TOMAWAC, can occur in the vicinity of the River mouth. Next, the hydrodynamics has been simulated using the two-dimensional depth-averaged flow TELEMAC 2D model. The numerical results are compared with field measurements collected in March 2003. Model performance statistics are calculated in order to assess the accuracy of the predictions at six locations. Regarding the computation of the wave propagation, a root mean square error (RMSE) is evaluated for the significant wave height, the mean period and the peak direction of propagation. For the flow computation, a mean absolute error (MAE) is used as it is applicable to vector quantities. A classification is also adopted that categorises the quality of the results. Regarding the significant wave height, the average relative RMSE is of 18.2% for the TOMAWAC computations whereas the error is of 30.8% for the REFDIF S simulations. Concerning the peak wave direction, the RMSE is about 10°. Both models predict the wave direction normal to the shore whereas the experimental parameters are more variable. However, the areas, where energy concentrates, are well reproduced. The classification of errors shows that TELEMAC 2D flow predictions are in a range from excellent to reasonable.

Non-linear propagation of unidirectional wave fields over varying topography

The present study aims at investigating the non-linear triad interaction process affecting shoaling surface gravity wave fields. The triad interaction phenomenon being enhanced towards the shore, the domain of study is extended up to the surf zone. Three 1D non-linear wave models (one phase-resolving and two phase-averaged spectral models) have been implemented and compared to laboratory experiments performed in a wave flume. This set of models includes two existing models and a new one which has been developed in the frame of this work. The models include a breaking dissipation term based on the parametrical model of Battjes and Janssen [Battjes, J.A., Janssen, P.A.E.M., 1978. Energy loss and set-up due to breaking of random waves. Proc. 16th Int. Conf. Coastal Eng. (ASCE), Vol. 1, pp. 569–587.]. The investigations concern the evolution of variance spectra, spectral significant wave height and mean period over a barred bathymetric profile. In addition, the performances of the different models are analysed by computing the spectral source term for triad interactions. We found that all models are able to reproduce the main features of non-linear mechanisms affecting a wave field in the near-shore zone. The phase-resolving model gives the most accurate results for non-breaking situations. It correctly reproduces the non-linear coupling effect in decreasing water depths due to wave–wave interactions, as well as the harmonic release after a bar. However, the model is computationally time-consuming. The CPU time is considerably reduced using phase-averaged models. They give satisfactorily results on harmonic generation. However, they do not reproduce the release of harmonics as water depth increases. In breaking conditions, the variance spectra undergo significant changes under the combined effects of non-linear energy transfers and dissipation. The depth-induced wave breaking model included in the equations provides a good estimate of the energy decay in the surf zone.

Modelling of nonlinear shoaling based on stochastic evolution equations

A one-dimensional stochastic model is derived to simulate the transformation of wave spectra in shallow water including generation of bound sub- and super-harmonics, near-resonant triad wave interaction and wave breaking. Boussinesq type equations with improved linear dispersion characteristics are recast into evolution equations for the complex amplitudes, and serve as the underlying deterministic model. Next, a set of evolution equations for the cumulants is derived. By formally introducing the well-known Gaussian closure hypothesis, nonlinear evolution equations for the power spectrum and bispectrum are derived. A simple description of depth-induced wave breaking is incorporated in the model equations, assuming that the total rate of dissipation may be distributed in proportion to the spectral energy density on each discrete frequency. The proposed phase-averaged model is compared with experimental data in four different cases as well as with the underlying deterministic model. In general, the agreement is found to be acceptable, even far beyond the region where Gaussianity (Gaussian sea state) may be justified.

A study of unsteady wake flows past a two-dimensional square cylinder with and without planar jet injection into the vortex formation region

The present work describes the study of unsteady turbulent wake flows past two-dimensional square cylinders with and without planar jet injection into the vortex formation region. An experimental investigation provided LDV measurements of the mean and turbulent near and middle wake development at Reynolds numbers of 8520 and 14285 and for various jet to approach flow velocity ratios. In the computational work a Large Eddy Simulation employing the Smagorinsky subgrid scale model was initially performed for the higher Reynolds number plane wake configuration. Further, a hybrid phase-averaged Navier-Stokes model was formulated that encompasses aspects from both the LES formalism and the conventional eddy-viscosity procedures. Comparisons of the hybrid model calculations with the LES and measurements demonstrated the ability of the hybrid method to reproduce the range of complex unsteady flow phenomena studied here.

Techniques of Linear Prediction for Systems with Periodic Statistics

Abstract Many parameters that measure climatic variability have nonstationary statistics, that is, they depend strongly on the phase of the annual cycle. In this case normal statistical analysis techniques based on time-invariant models are inappropriate. Generalized methods accounting for seasonal nonstationarity (phase averaged or cyclostationary models) have been developed to treat such data. The methods are applied to the problem of predicting El Nino off South America. It is shown that El Ninos may be predicted up to a year in advance with considerably more confidence and accuracy using phase-averaged models than with time-invariant models. In a second application surface air temperature anomalies are predicted over North America from Pacific Ocean sea surface temperatures. Again, the phase-averaged models consistently outperform models based on standard statistical procedures.