Unstructured, anisotropic mesh generation for the Northwestern European continental shelf, the continental slope and the neighbouring ocean

A new mesh refinement strategy for generating high quality unstructured meshes of the Northwestern European continental shelf, the continental slope and the neighbouring ocean is presented. Our objective is to demonstrate the ability of anisotropic unstructured meshes to adequately address the challenge of simulating the hydrodynamics occurring in these three regions within a unique mesh. The refinement criteria blend several hydrodynamic considerations as the tidal wave propagation on the continental shelf and the hydrostatic consistency condition in steep areas. Several meshes illustrate both the validity and the efficiency of the refinement strategy. The selection of the refinement parameters is discussed. Finally, an attempt is made to take into account tidal ellipses, providing another cause for anisotropy in the mesh. (c) 2007 Elsevier Ltd. All rights reserved.

[1]  Roy A. Walters,et al.  Coastal ocean models : two useful finite element methods , 2005 .

[2]  C. Blain,et al.  Barotropic tides in the Bab el Mandab Strait—numerical simulations , 2005 .

[3]  Jonathan Richard Shewchuk,et al.  Triangle: Engineering a 2D Quality Mesh Generator and Delaunay Triangulator , 1996, WACG.

[4]  Dale B. Haidvogel,et al.  Numerical Simulation of Flow around a Tall Isolated Seamount. Part I: Problem Formulation and Model Accuracy , 1993 .

[5]  A. Kasahara Various Vertical Coordinate Systems Used for Numerical Weather Prediction , 1974 .

[6]  Paul G. Falkowski,et al.  The shelf edge exchange processes experiment, SEEP-II: an introduction to hypotheses, results and conclusions , 1994 .

[7]  C.R.E. de Oliveira,et al.  Optimisation based bathymetry approximation through constrained unstructured mesh adaptivity , 2006 .

[8]  A. M. Davies,et al.  Processes influencing suspended sediment movement on the Malin–Hebrides shelf , 2002 .

[9]  J. Walsh,et al.  The 1983-1984 Shelf Edge Exchange Processes (SEEP)--I experiment: hypotheses and highlights , 1988 .

[10]  A generalized vertical coordinate for 3D marine models , 1992 .

[11]  Robert L. Haney,et al.  On the Pressure Gradient Force over Steep Topography in Sigma Coordinate Ocean Models , 1991 .

[12]  J. Beckers,et al.  On the use of the σ-coordinate system in regions of large bathymetric variations , 1992 .

[13]  Roy A. Walters,et al.  Geometrically based, automatic generator for irregular triangular networks , 1993 .

[14]  S. Legg Internal Tides Generated on a Corrugated Continental Slope. Part II: Along-Slope Barotropic Forcing* , 2004 .

[15]  John M. Huthnance,et al.  Circulation, exchange and water masses at the ocean margin: the role of physical processes at the shelf edge , 1995 .

[16]  A. M. Davies,et al.  Modelling processes influencing shelf edge exchange of water and suspended sediment , 2005 .

[17]  K. Lamb Numerical experiments of internal wave generation by strong tidal flow across a finite amplitude bank edge , 1994 .

[18]  A. M. Davies,et al.  On the interaction between internal tides and wind-induced near-inertial currents at the shelf edge , 2003 .

[19]  K. Lamb Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography , 2004 .

[20]  Eric Deleersnijder,et al.  Special Issue: The second international workshop on unstructured mesh numerical modelling of coastal, shelf and ocean flows Delft, The Netherlands, September 23-September 25, 2003 , 2005 .

[21]  Fedor Mesinger,et al.  On the convergence and error problems of the calculation of the pressure gradient force in sigma coordinate models , 1982 .

[22]  Joe F. Thompson,et al.  Numerical grid generation , 1985 .

[23]  Joannes J. Westerink,et al.  Two-dimensional, unstructured mesh generation for tidal models , 2001 .

[24]  Eric Deleersnijder,et al.  Delaunay mesh generation for an unstructured-grid ocean general circulation model , 2000 .

[25]  A. M. Davies,et al.  A three‐dimensional model of internal tides on the Malin‐Hebrides shelf and shelf edge , 1998 .

[26]  Alejandro J. Souza,et al.  Flow structure and seasonalityin the Hebridean slope current , 2001 .

[27]  Eric Deleersnijder,et al.  The Second International Workshop on Unstructured Mesh Numerical Modelling in Coastal, Shelf and Ocean Flows , 2005 .

[28]  A. M. Davies,et al.  Sensitivity of Tidal Bed Stress Distributions, Near-Bed Currents, Overtides, and Tidal Residuals to Frictional Effects in the Eastern Irish Sea , 1996 .

[29]  Joe F. Thompson,et al.  Numerical grid generation: Foundations and applications , 1985 .

[30]  Eric Deleersnijder,et al.  An efficient Eulerian finite element method for the shallow water equations , 2005 .

[31]  P. Leitão,et al.  A model for ocean circulation on the Iberian coast , 2002 .

[32]  D. F. Watson Computing the n-Dimensional Delaunay Tesselation with Application to Voronoi Polytopes , 1981, Comput. J..

[33]  W. Frey Selective refinement: A new strategy for automatic node placement in graded triangular meshes , 1987 .

[34]  A. M. Davies,et al.  Formulation of a three-dimensional shelf edge model and its application to internal tide generation , 1998 .

[35]  A. M. Davies,et al.  The Influence of Wind Effects upon Internal Tides in Shelf Edge Regions , 1997 .

[36]  Alistair Adcroft,et al.  On methods for solving the oceanic equations of motion in generalized vertical coordinates , 2006 .

[37]  C.R.E. de Oliveira,et al.  Three-dimensional unstructured mesh ocean modelling , 2005 .

[38]  J. Holt,et al.  Error quantification of a high-resolution coupled hydrodynamic-ecosystem coastal-ocean model: Part 1 model overview and assessment of the hydrodynamics , 2005 .

[39]  Dag L. Aksnes,et al.  Modelling the primary production in the North Sea using a coupled three-dimensional physical-chemical-biological ocean model , 1995 .

[40]  R. F. Henry,et al.  A tidal model for eastern Juan de Fuca Strait and the southern Strait of Georgia , 1995 .

[41]  John J. Walsh,et al.  Importance of continental margins in the marine biogeochemical cycling of carbon and nitrogen , 1991, Nature.

[42]  F. Chen,et al.  A two-dimensional slice model of the shelf edge region off the west coast of Scotland: model response to realistic seasonal forcing and the role of the M2 tide , 1999 .

[43]  P. George,et al.  Mesh Generation: Application to Finite Elements , 2007 .

[44]  Adrian Bowyer,et al.  Computing Dirichlet Tessellations , 1981, Comput. J..

[45]  James C. McWilliams,et al.  A method for computing horizontal pressure‐gradient force in an oceanic model with a nonaligned vertical coordinate , 2003 .

[46]  Richard G. Forbes,et al.  Assessment of the FOAM global data assimilation system for real-time operational ocean forecasting , 2000 .

[47]  Mike Ashworth,et al.  Advective controls on primary production in the stratified western Irish Sea: An eddy-resolving model study , 2004 .

[48]  Alistair Adcroft,et al.  How slippery are piecewise‐constant coastlines in numerical ocean models? , 1998 .

[49]  Eric Deleersnijder,et al.  High-resolution, unstructured meshes for hydrodynamic models of the Great Barrier Reef, Australia , 2006 .

[50]  Keston W. Smith,et al.  Seasonal mean circulation on the Irish shelf—a model-generated climatology , 2004 .

[51]  P. Tett,et al.  Carbon and nitrogen fluxes across the Hebridean shelf break, estimated by a 2D coupled physical-microbiological model. , 2003, The Science of the total environment.

[52]  A. M. Davies,et al.  Comparison of finite difference and element models of internal tides on the Malin–Hebrides shelf , 2005 .