On the development and verification of a 2-D coupled wave-current model on unstructured meshes

Abstract In this paper, the numerical framework for a freely available fully coupled wave-current model, which solves the Shallow Water and the Wave Action Equation (WAE) on unstructured meshes in geographical space and some first applications are presented. It consists of the hydrodynamic model SHYFEM (Shallow Water Hydrodynamic Finite Elements Model), and the 3rd generation spectral wave model WWM (Wind Wave Model). The application of numerical schemes on unstructured meshes renders the coupled model more efficient in resolving the model domain, the bathymetry and the involved gradient fields of currents, water levels and wave action. The source codes of the models have been coupled using FIFO (First In First Out pipes) data files. This technique makes an effective model coupling possible without cumbersome merging of both codes. Furthermore, it gives both source codes a universal interface for coupling with other flow or wave models. The coupled model was applied to simulate extreme events occurring in the Gulf of Mexico and the Adriatic Sea. In particular the wind and wave-induced storm surge generated by Hurricane Ivan was investigated and the results have been compared to the tidal gauge at Dauphin Island with reasonable results. For the case of the Adriatic Sea, the model, validated for the year 2004, has been applied to simulate waves and water levels induced by the century storm in November 1966 that lead to catastrophic and widespread damages in the regions of the Venice Lagoon. The obtained results have been compared to in situ measurements with respect to the wave heights and water level elevations revealing good accuracy of the model in reproduction of the investigated events. Especially, the Hurricane Ivan simulations showed the importance of inclusion of the wave–current interactions for the hindcast of the water levels during the storm surge. In a comparison to water level measurements at Dauphin Island, inclusion of the wave induced water level setup reduced the root mean square error from 0.13 to 0.11 m and increased the correlation coefficient from 0.75 to 0.79. For the case of the Venice Lagoon, the comparison with the measurements showed that the model without wave–current interactions led to a good hindcast of water levels for the location Punta Salute, which is located in the inner part of the Lagoon. Nevertheless, the comparison of subsequent simulations with and without the influence of the waves clearly showed a simulated effect of intense wave setup-up in the coastal area in front of the lagoon, which is plausible given the intensity of flooding that occurred there.

[1]  V. Selmin,et al.  Finite element methods for nonlinear advection , 1985 .

[2]  A. Cucco,et al.  Development and validation of a finite element morphological model for shallow water basins , 2008 .

[3]  Y. Eldeberky,et al.  Nonlinear transformation of wave spectra in the nearshore , 1996 .

[4]  A. Cucco,et al.  Modeling the Venice Lagoon residence time , 2006 .

[5]  R. Buizza,et al.  The 1966 ''century'' flood in Italy: A meteorological and hydrological revisitation , 2006 .

[6]  Tai-Wen Hsu,et al.  Verification of a 3rd Generation FEM Spectral Wave Model for Shallow and Deep Water Applications , 2006 .

[7]  Bertrand Chapron,et al.  Coupled sea surface-atmosphere model: 2. Spectrum of short wind waves , 1999 .

[8]  N. Hashimoto,et al.  Extension and Modification of Discrete Interaction Approximation (DIA) for Computing Nonlinear Energy Transfer of Gravity Wave Spectra , 2001 .

[9]  Luigi Cavaleri,et al.  In Search of the Correct Wind and Wave Fields in a Minor Basin , 1997 .

[10]  K. Hasselmann,et al.  On the Existence of a Fully Developed Wind-Sea Spectrum , 1984 .

[11]  Philip L. Roe,et al.  Compact high‐resolution algorithms for time‐dependent advection on unstructured grids , 2000 .

[12]  Herman Deconinck,et al.  A Conservative Formulation of the Multidimensional Upwind Residual Distribution Schemes for General Nonlinear Conservation Laws , 2002 .

[13]  T. Barnett,et al.  Measurements of wind-wave growth and swell decay during the Joint North Sea Wave Project (JONSWAP) , 1973 .

[14]  Peter A. E. M. Janssen,et al.  The dynamical coupling of a wave model and a storm surge model through the atmospheric boundary layer , 1993 .

[15]  M. Banner,et al.  Impact of a Saturation-Dependent Dissipation Source Function on Operational Hindcasts of Wind-Waves in the Australian Region , 2002 .

[16]  Gerbrand J. Komen,et al.  On the Balance Between Growth and Dissipation in an Extreme Depth-Limited Wind-Sea in the Southern North Sea , 1983 .

[17]  S. Patankar.  Numerical Heat Transfer and Fluid Flow , 2018, Lecture Notes in Mechanical Engineering.

[18]  Tai-Wen Hsu,et al.  Hindcasting nearshore wind waves using a FEM code for SWAN , 2005 .

[19]  K. Hasselmann.  On the non-linear energy transfer in a gravity-wave spectrum Part 1. General theory , 1962, Journal of Fluid Mechanics.

[20]  R. Matarrese,et al.  Application of a finite element model to the taranto sea , 2004 .

[21]  G. Umgiesser,et al.  Hydrodynamic modeling of a coastal lagoon: The Cabras lagoon in Sardinia, Italy , 2005 .

[22]  Herman Deconinck,et al.  Residual distribution for general time-dependent conservation laws , 2005 .

[23]  B. P. Leonard,et al.  The ULTIMATE conservative difference scheme applied to unsteady one-dimensional advection , 1991 .

[24]  H. Tolman.  On the selection of propagation schemes for a spectral wind-wave model , 1995 .

[25]  Fabrice Ardhuin,et al.  Explicit wave-averaged primitive equations using a generalized Lagrangian mean , 2008 .

[26]  J. Donea.  A Taylor–Galerkin method for convective transport problems , 1983 .

[27]  G. Whitham,et al.  Linear and Nonlinear Waves , 1976 .

[28]  U. Zanke,et al.  Verification and improvement of a spectral finite element wave model , 2005 .

[29]  M. Longuet-Higgins,et al.  Radiation stresses in water waves; a physical discussion, with applications , 1964 .

[30]  S. Hasselmann,et al.  Computations and Parameterizations of the Nonlinear Energy Transfer in a Gravity-Wave Spectrum. Part I: A New Method for Efficient Computations of the Exact Nonlinear Transfer Integral , 1985 .

[31]  Gerbrant Ph. van Vledder,et al.  The WRT method for the computation of non-linear four-wave interactions in discrete spectral wave models , 2006 .

[32]  Fabrice Ardhuin,et al.  Swell and Slanting-Fetch Effects on Wind Wave Growth , 2007 .

[33]  J. A. Battjes,et al.  ENERGY LOSS AND SET-UP DUE TO BREAKING OF RANDOM WAVES , 1978 .

[34]  Vipin Kumar,et al.  A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs , 1998, SIAM J. Sci. Comput..

[35]  Jerome A. Smith.  Wave–Current Interactions in Finite Depth , 2006 .

[36]  Luigi Cavaleri,et al.  The oceanographic tower Acqua Alta — activity and prediction of sea states at Venice , 2000 .

[37]  V. Kudryavtsev,et al.  Coupled sea surface-atmosphere model: 1. Wind over waves coupling , 1999 .

[38]  G. Umgiesser,et al.  Modelling the Venice Lagoon , 1997 .

[39]  Billy L. Edge,et al.  Ocean Wave Measurement and Analysis , 1994 .

[40]  Rémi Abgrall,et al.  Construction of second order accurate monotone and stable residual distribution schemes for unsteady flow problems , 2003 .

[41]  Georg Umgiesser,et al.  A finite element model for the Venice Lagoon. Development, set up, calibration and validation , 2004 .

[42]  B. Chapron,et al.  SPECTRAL WAVE DISSIPATION BASED ON OBSERVATIONS: A GLOBAL VALIDATION , 2008 .

[43]  I. Young,et al.  Implementation of new experimental input/dissipation terms for modelling spectral evolution of wind waves , 2007 .

[44]  N. N. Yanenko,et al.  The Method of Fractional Steps , 1971 .