s Stéphan Grilli Research Projects



Nonlinear wave shoaling breaking and runup on slopes/beaches



Mt. Fuji off Kanagawa by Katsushika Hokusai (1760-1849) (Thanks to CACR !)                          Three-dimensional wave computation by Grilli et al. (2000)



Background :

With the increasingly clear risk of global warming, possibly due to greenhouse effects, and resulting sea level rise due to icecap melting, coastal protection is becoming a problem of major concern in many countries having large regions with low level coastal areas. In the US, the result of a one-meter sea level rise scenario, as some forecasting studies predict by the year 2,050, would be disastrous, not only in terms of lost land area but the increased frequency of severely damaging storms for various existing coastal developments (e.g., harbors, industries, real estate, recreational beaches...).

As a result of these concerns, over the past decade, a renewal of activity has been stimulated in the coastal research community for developing more accurate predictions of environmental forcing from waves and currents and more reliable, and thus more economical, design methods under extreme wave loading, for both artificially renourished beaches and structures used for coastal protection. These are the main focuses of  coastal engineering.

Wave propagation studies start with predictions of wave characteristics in deep water, based on available or predicted wind data (hindcasting/forecasting). Deep water waves are then propagated over shallow water topography up to the shore where shoaling and breaking occur. In natural (or renourished) beaches, the momentum flux released by breaking waves creates set-up and surf-zone currents (longshore and cross-shore). These currents are the main forcing for littoral sediment transport and, ultimately, the cause of beach erosion and shoreline recession observed in many coastal environments (e.g. Rhode Island). On protected shorelines, waves (broken or unbroken) impinge on coastal structures (e.g., groins, jetties, seawalls, breakwaters,...) and induce hydrodynamic pressures and forces under which both the structure and its foundation must be stable.

Coastal structures are usually made of a combination of emerged and submerged rubble mound berms and, in some cases, of a capping vertical or slightly sloping seawall. Under extreme storm waves and simultaneous increase in Mean Water Level (MWL) due to storm surge (possibly worsened by sea level rise), capping seawalls can be subjected to direct impact loads from breaking waves. Hence, new design procedures must be developed to better estimate both the local (structural) and global stability against overturning of seawalls under extreme wave impact. Since beaches and most coastal structures are made of porous material, wave-induced flow and pore pressure transmission through porous media, are also topics of importance in coastal engineering research.

In all of the above problems, characteristics of breaking waves are the prime factors for predicting the magnitude of both littoral currents and impact forces on structures and/or flow through structures. Wave transformations up to breaking and littoral current generation are thus the objects of intense research in the coastal engineering/science academic and industrial community, as well as in federal agencies with branches dealing with nearshore problems (NRL, ONR, NSF, ARO,...). In addition, for the latter agencies affiliated with DOD, the gathering of data and information useful for littoral warfare is of great concern, due to its increasing importance to the defense community. A detailed knowledge, i.e. prediction, of characteristics of nearshore waves and currents and of their relationship with bottom topography (and vice versa), indeed, is required for the success of military operations in coastal regions, particularly in foreign lands for which little or no data is available.

Finally, coastal engineering must also deal with projects involving water quality and environmental problems. Waves, currents, and sediment transport effects on sewage outfalls, de-salination plant intakes, or oil containment equipment, for instance, are but a few of the problems where the fate of either solid or fluid contaminants must be predicted under specified or forecast environmental conditions.



Project summary :

Since 1980, I have worked on developing and improving various numerical models of wave propagation in coastal areas. These models were tested and validated versus analytical and experimental results, and then used as tools to gain insight into coastal processes. The present project deals with the development of a numerical model for fully nonlinear water waves and wave-structure interaction. I started developing this model while working at the University of Delaware and continued upgrading it since joining URI. This model is considered as one of the most versatile models of its kind and has been/is used (or re-developed) at a few other Universities, both in the US and abroad (e.g., Caltech (Passadena), U. of Southern California (Los Angeles), U. of Cantabria (Santander, Spain), and U. of Toulon (France)). In its most recent applications, the model is being used as a tool (``numerical wave tank''), in combination with laboratory experiments, for investigating many different problems of interest to ocean engineering.

In 1991, I received funding from NSF and, in 1992 and 1993, from URI Seagrant for upgrading, further developing, and documenting this model. In 1994 and 1996, I received funding from NRL (ONR) to use this model as a tool to study nearshore wave propagation. Intensive computations of wave shoaling over slopes were conducted, to analyze shoaling properties of nonlinear waves over various specified nearshore bottom topographies. This has required developing and testing a new absorbing beach for the model.

The latest developments in this project deal with the so-called depth-inversion problem in shallow water. In this problem, one attempts to predict the shape of the ocean bottom based on observed properties of waves on the free surface (e.g., obtained through remote sensing). Most state-of-the-art methods are still based on using linear wave theory to predict wave properties. This, however, may be inaccurate in shallow water, due to strong wave nonlinearity. Using nonlinear properties of shoaling waves calculated in a fully nonlinear wave model, I developed two new depth-inversion algorithms and tested them on various mildly sloping bottoms. Preliminary results indicate a 3-10 factor improvement in accuracy, as compared to results obtained using linear wave theory.

At all stages of model developments, laboratory experiments were used for calibrating and verifying numerical results. These were generally obtained in collaboration with other institutions (e.g., U. of Delaware, and U. of Cantabria (Santander, Spain)).



Funding history :

  1. 1991-92 : Grant No. BCS-9111827 (PI with N. Kobayashi, $36,851) of the "National Science Foundation" (NSF) Engineering/Earthquake, Hazards and Mitigation Program, to support the : Documentation and Maintenance of a Numerical Software for Calculating Nonlinear Wave Runup.
  2. 1992-93 : Grant No. NA89AA/D/SG/082 (PI, $44,330) of the University of Rhode Island Sea Grant College Program, to support the study of : Breaking Waves on Beaches.
  3. 1994-95 : Grant No. N-00014-94-I-C607 (PI, $31,064) of the DOD U.S. Naval Research Laboratory (Stennis Space Center), Remote Sensing Division, to support the : Mapping of Nearshore Ocean Bottom Topography Through the Solution of Inverse Wave Propagation Problems.
  4. 1996-97 : Grant No. N-00014-96-C012 (PI, $49,987) of the DOD U.S. Naval Research Laboratory (Stennis Space Center), Remote Sensing Division : Determination of Nearshore Bottom Topography Through the Solution of Inverse Wave Propagation Problems.
  5. 1999-2000: Grant from Vibtech Inc. (PI, $15,000) to the Ocean Engineering Instrument System Laboratory, to support the : Building of an adjustable beach for wave tank tests of a causeway-FastShip system deployed in the surfzone.
  6. 1999-2001 : Grant No. N-00014-99-10439 (PI, $102,278) of the DOD Office of Naval Research (ONR) Ocean Science Division, to support the : Development and validation of depth-inversion algorithms for barred-beaches based on nonlinear properties of shoaling waves.
  7. 2001 : Gift-grant from U.S. Wave Energy Inc. (PI, $5,000) to the Ocean Engineering Coastal Engineering Laboratory, to support : Research in the area of Ocean Wave Energy uitlization.
  8. 2001 : Gift-grant from from Vibtech Inc. (PI, $3,000) to the Ocean Engineering Coastal Engineering Laboratory, to support : Wave tank tests of a causeway-FastShip system deployed in the surfzone.
  9. 2001-2003 : Grant No. N-00014-01-10349 (Co-PI, $249,985; URI subcontract for $50,000) of the DOD Office of Naval Research (ONR) Ocean Science Division, to support the : Studies of Mine Burial in Coastal Environment.
  10. 2003-2004 : Grant from Ocean Dynamics Inc. (PI, $172,506), to support : Hydrodynamic Modeling and Laboratory Experiments for the Harley SES FastShip.
  11. Grant (Co-PI, 2003-2004, $49,954) from RI Renewable Energy Office : Proposed Energetech wave power plant site off Pt Judith Harbor of Refuge.
  12. 2003-2004 : Grant of the DOD Office of Naval Research (ONR) Ocean Science Division (R. Street, PI, $175,581; URI subcontract for $37,668), to support : Large Eddy Simulation of Sediment Transport in the Presence of Surface Gravity Waves, Currents and Complex Bedforms.
  13. 2004-2005 : Grant No. N000140510068 of the DOD Office of Naval Research (ONR) Coastal Geosciences Division (code 321CG; S. Grilli, PI, $65,439), to support : Wave Induced Mine Burial and Sediment Transport in Coastal Environment. Wave modeling studies.
  14. 2004-2006 Grant (PI,$34,500) from the University of Rhode Island Partnership for Ocean Instrumentation (POI), to support : Development of an Inverted Echo Sounder for Surface and Internal Wave Measurements in Ocean and Coastal Observatories.
  15. 2005-2007 : Grant No. N000140510068 ( ) of the DOD Office of Naval Research (ONR) Coastal Geosciences Division (code 321CG; S. Grilli PI, $146,377), to support : Wave Induced Mine Burial and Sediment Transport in Coastal Environment : Wave and sediment transport modeling studies.


Recent key personnel at URI or in collaboration :

  1. S.T. Grilli : Ph.D, Distinguished Professor in OE, Principal investigator.
  2. R. Subramanya : MS in OE, research associate 1992-94
  3. J. Horrillo : MS in OE, graduate research assistant 1994-1997
  4. P. Guyenne : Ph.D student  1999-2002
  5. S. Guignard : Post-doctoral associate 2000-2001
  6. C. Brandini : Ph.D student  1998-2000
  7. F. Enet : Ph.D student  2001-
  8. C. Fochesato : Ph.D student  2001-2004
  9. R. Gilbert : M.S. student  2003-2005
  10. J. Harris : Ph.D student  2003-
  11. M. Shultz : M.S. student  2004-2005
  12. H.G. Sung : Post-doctoral associate  2004-2005


Collaborations :

  1. I.A. Svendsen : Ph.D, Professor, Center for Applied Coastal Research, University of Delaware (1987-1998)
  2. J. Skourup : Ph.D (1989), at the University of Delaware (1987-89)
  3. M.A. Losada : Ph.D, Professor, University of Cantabria, Santander (Spain) (1988-1995)
  4. A. Otta : Ph.D (1992), at the University of Delaware (1989-92)
  5. J.T. Kirby : Ph.D, Professor, Center for Applied Coastal Research, University of Delaware (1993-)
  6. Ph. Fraunie : Ph.D, Professor, V. Rey : Ph.D, Assistant Professor, and S. Guignard, Ph.D (2001), University of Toulon-Var, Institute for Sciences and Technology (La Garde, France) (1998-)
  7. F. Dias : Ph.D, Professor, and P. Guyenne, Ph.D (2000), Ecole Normal Superieure (Cachan, Paris, France) (1998-)
  8. R.L. Street : Ph.D, Professor, and E.A. Zedler, Ph. D., Stanford University (2003-)


Publications :

  1. Grilli, S.T., Skourup, J. and Svendsen, I.A. 1988 The Modeling of Highly Nonlinear Waves : A Step Toward the Numerical Wave Tank. In Proc. 10th Intl. Conf. on Boundary Elements (BEM10, Southampton, England, September 88) (ed. C.A. Brebbia) Vol. 1, pp. 549-564. Computational Mechanics Publication. Springer-Verlag, Berlin.(invited paper)
  2. Skourup, J., Grilli, S.T. and Svendsen, I.A. 1988 Modeling of Steep and Breaking Waves by the Boundary Element Method. Inst. Hydrodyn. and Hydraulic Engng., Technical University of Denmark, Progress Report No. 68, 59-71.
  3. Grilli, S.T., Skourup, J. and Svendsen, I.A. 1989 An Efficient Boundary Element Method for Nonlinear Water Waves. Engineering Analysis with Boundary Elements, 6 (2), 97-107.
  4. Grilli, S.T. and Svendsen, I.A. 1989 Runup and Reflection of a Solitary Wave on Steep Slopes in a Numerical Wave Tank. In Proc. 4th Intl. Workshop on Water Waves and Floating Bodies (Oystese, Norway, May 89) (ed. J. Grue), pp. 77-82. Department of Mathematics, University of Oslo, Oslo.(invited paper)
  5. Grilli, S.T. and Svendsen, I.A. 1990 Corner Problems and Global Accuracy in the Boundary Element Solution of Nonlinear Wave Flows. Engineering   [pdf] (828K)Analysis with Boundary Elements, 7 (4), 178-195.
  6. Grilli, S.T. and Svendsen, I.A. 1990 The Propagation and Runup of Solitary Waves on Steep Slopes. Center for Applied Coastal Research, University of Delaware, Research Report No. 91-4.
  7. Svendsen, I.A. and Grilli, S.T. 1990 Nonlinear Waves on Steep Slopes. Journal of Coastal Research, ``Special Issue on Rational Design of Mound Structures'' SI 7, 185-202.
  8. Grilli, S.T. (guest ed.) 1990 Special Issue on Highly Nonlinear Waves. Engineering Analysis with Boundary Elements 7 (4).
  9. Grilli, S.T. and Svendsen, I.A. 1990 Computation of Nonlinear Wave Kinematics during Propagation and Runup on a Slope. Chapter in Water Wave Kinematics (ed. A. Torum and O.T. Gudmestad), NATO ASI Series E: Applied Sciences Vol. 178, 387-412. Klüwer Academic Publishers.
  10. Grilli, S.T., Svendsen, I.A. and Otta, A.K. 1990 Corner Effects Using BEM for Nonlinear Waves. In Computational Engineering with Boundary Elements (Proc. 5th Intl. Conf. on Boundary Element Technology, BETECH90, University of Delaware, USA, July 90)
  11. Grilli, S.T. 1991 Modeling of Nonlinear Long Wave Transformation in Coastal Areas. In Proc. 2nd Intl. Conf. on Computer Methods and Water Resources, (Rabat, Morocco, October 91) (ed. D. Ouazar, D. Ben Sari and C.A. Brebbia) Vol. 2, pp. 329-342. Computational Mechanics Publications, Springer-Verlag, Berlin.(invited keynote address)
  12. Grilli, S.T. 1992 BEM Modelling of Wave Shoaling and Breaking. International Association for Boundary Element Methods Newsletter, 6, 4-5.
  13. Otta, A.K., Svendsen, I.A. and Grilli, S.T. 1992 Unsteady Free Surface Waves in a Region of Arbitrary Shape. Center for Applied Coastal Research, University of Delaware, Research Report No. 92-10, 153 pps.
  14. Grilli, S.T., Losada, M.A., Martin, F. and Svendsen, I.A. 1992 Nonlinear Shoaling and Impact of Waves on Coastal Structures. In Proc. 9th Engineering Mechanics Conf. (College Station, Texas, May 92) (eds. L.D. Lutes and J.M. Niedzwecki), pp. 79-82. ASCE edition.(invited paper)
  15. Grilli, S.T. and Subramanya, R. 1993 Nonlinear Wave Modeling in very Shallow Water. In Proc. 15th Intl. Conf. on Boundary Elements in Engineering (BEM15, Worcester, MA, August 1993) (ed. J. Rencis and C.A. Brebbia), Fluid Flow and Computational Aspects, pp. 194-206. Computational Mechanics Publications, Elsevier Applied Science. (invited paper)
  16. Grilli, S.T. 1993 Modeling of Nonlinear Wave Motion in Shallow Water. Chapter 3 in Computational Methods for Free and Moving Boundary Problems in Heat and Fluid Flow (eds. L.C. Wrobel and C.A. Brebbia), pps. 37-65, Computational Mechanics Publication, Elsevier Applied Sciences, London, UK.
  17. Grilli, S.T. and Subramanya, R. 1993 A Computer Program for Transient Wave Runup. Center for Applied Coastal Research, University of Delaware, Research Report No. 93-02, 131 pps.
  18. Otta, A.K., Svendsen, I.A. and Grilli, S.T. 1993 The Breaking and Runup of Solitary Waves on Beaches. In Proc. 23rd Intl. Conf. on Coastal Engineering (ICCE23, Venice, Italy, October 92) Vol. 2, pps. 1461-1474. ASCE edition.
  19. Grilli, S.T., Losada, M.A. and Martin, F. 1994. Characteristics of Solitary Wave Breaking Induced by Breakwaters. Journal of Waterway Port Coastal and Ocean Engineering 120(1), 74-92. [abstract]
  20. Grilli, S.T. and Subramanya, R. 1994 Quasi-singular Integrations in the Modelling of Nonlinear Water Waves. Engineering Analysis with Boundary Elements, 13 (2), 181-191.
  21. Subramanya, R. and Grilli, S.T. 1994 Domain Regridding in the Computation of Nonlinear Waves. In Proc. 2nd Intl. Workshop on Bound. Elements in Fluid Mech. (Southampton, UK, July 1994) (eds. H. Power, C.A. Brebbia and D.B. Ingham), pps. 139-150. Computational Mechanics Publications, Elsevier Applied Science. (invited paper).
  22. Grilli, S.T., Subramanya, R., Kirby, J.T. and Wei, J. 1994 Comparison of Modified Boussinesq and Fully Nonlinear Potential Models for Shoaling Solitary Waves. In Proc. Intl. Symposium on Waves - Physical and Num. Modelling (Vancouver BC, Canada, Aug. 1994) (eds. M. Isaacson & M. Quick), Vol. 1, pps. 524-533, IAHR.
  23. Subramanya, R. and Grilli, S.T. 1994 Kinematics and Properties of Fully Nonlinear Waves Shoaling and Breaking over a Gentle Slope. In Proc. Intl. Symposium on Waves - Physical and Num. Modelling (Vancouver BC, Canada, Aug. 1994) (eds. M. Isaacson and M. Quick), Vol. 2, pps. 1106-1115, IAHR.
  24. Grilli, S., Subramanya, R., Svendsen, I.A. and Veeramony, J. 1994 Shoaling of Solitary Waves on Plane Beaches. Journal of Waterway Port Coastal and Ocean Engineering, 120 (6), 609-628. [abstract]
  25. Grilli, S.T. and R. Subramanya 1995 Recent Advances in the BEM Modelling of Nonlinear Water Waves. Chapter 4 in Boundary Element Applications in Fluid Mechanics (ed. H. Power), pps. 91-122. Advances in Fluid Mechanics Series. Computational Mechanics Publication, Southampton, UK. [abstract]
  26. Wei, J., Kirby, J.T, Grilli, S.T. and Subramanya, R. 1995 A Fully Nonlinear Boussinesq Model for Surface Waves. Part1. Highly Nonlinear Unsteady Waves. Journal of Fluid Mechanics, 294, 71-92.   [abstract]
  27. Grilli, S.T. and Horrillo J. 1995 Numerical Modeling of Wave Breaking on Beaches and over Coastal Structures. In Proc. 2nd. Intl. Conf. on Computer Modeling of Seas and Coastal Regions (COASTAL95 Cancun, Mexico, September 1995)(eds. C.A. Brebbia, L. Traversoni and L.C. Wrobel), pps. 151-158. Computational Mechanics Publications, Boston. (invited paper).
  28. Grilli, S.T., Subramanya, R., and Horrillo, J. 1995 A BEM model for fully nonlinear waves shoaling and breaking over a slope. Presented at the IABEM95 Intl. Symposium (Mauna Lani, Hawaii, August 1995)
  29. Grilli, S.T. and Subramanya, R. 1996 Numerical Modeling of Wave Breaking Induced by Fixed or Moving Boundaries. Computational Mechanics, 17 (6), 374-391.  [abstract]   [pdf]  (2,300K)
  30. Grilli, S.T., Svendsen, I.A. and Subramanya, R. 1997 Breaking Criterion and Characteristics for Solitary Waves on Slopes. Journal of Waterway Port Coastal and Ocean Engineering 123 (3), 102-112   [abstract]   [pdf file]  (375K)
  31. Grilli, S.T. and Horrillo, J. 1997 Exact periodic wave generation and absorption for nonlinear wave computations. Journal of Engineering Mechanics, 123 (10), 1060-1069.   [abstract]   [pdf] (4,000K)
  32. Grilli, S.T. and Horrillo J. 1997 Fully Nonlinear Properties of Periodic Waves Shoaling over Slopes. In Proc. 25th Intl. Conf. on Coastal Engineering (ICCE25, Orlando, USA, September 96), Vol  1, 717-730. ASCE Edition. [abstract]   [pdf] (792K)
  33. Grilli, S.T. 1997 Fully Nonlinear Potential Flow Models used for Long Wave Runup Prediction. Chapter in Long-Wave Runup Models (eds. H. Yeh, P. Liu, and C. Synolakis), pps. 116-180. World Scientific Publishing, Singapore.  [abstract]   [pdf]   (3,800K)
  34. Grilli, S.T. and Horrillo J. 1997 Fully Nonlinear Properties of Shoaling Periodic Waves Calculated in a Numerical Wave Tank. In Proc. 12th Intl. Workshop on Water Waves and Floating Bodies (Carry-Le-Rouet, France, March 97), 4 pps.
  35. Grilli, S.T. 1997 Free Surface Nonlinear Flows. Section in 1998 Mc Graw Hill Yearbook of Sciences and Technology (a yearly supplement to the Encyclopedia of Sciences and Technology). Mc Graw Hill, pp. 134-136.
  36. Grilli, S.T. 1998 The depth inversion problem in shallow water. In Proc. 3rd Intl. Intl. Sympos. on Ocean Wave Measurement and Analysis (WAVES97, Virginia Beach, VA, USA, November 1997) (eds. B. Edge, &J.M. Hemsley), 701-715, ASCE Publication. [abstract]   [compressed postcript] (155K)
  37. Grilli, S.T. and Horrillo, J. 1998 Computation of periodic wave shoaling over barred-beaches in a fully nonlinear numerical wave tank. In Proc. ISOPE98 (ISOPE98, Montreal, Canada, May 1998)(eds. Chung, J.S., Olagnon, M., Kim, C.H., Koterayama, W.), Vol. III, pps. 294-300. Intl. Society of Offshore and Polar Engng., Golden Colorado.   [compressed postcript]  (247K).
  38. Grilli, S.T. 1998  Depth Inversion in Shallow Water Based on Nonlinear Properties of Shoaling Periodic Waves. Coastal Engineering, 35(3), 185-209 [pdf]  (604K).
  39. Grilli, S.T., Svendsen, I.A. and Subramanya, R. 1998 Closure of : Breaking Criterion and Characteristics for Solitary Waves on Slopes. Journal of Waterway Port Coastal and Ocean Engineering, 124 (6), 333-335.
  40. Grilli, S.T. and Skourup, J. 1998 Depth inversion for nonlinear waves shoaling over a barred-beach. In Proc. 26th Intl. Conf. on Coastal Engineering (ICCE26, Copenhagen, Denmark, June 1998), 603-616   [pdf]  (216K).
  41. Guignard, S., Grilli, S.T., Marcer, R. and Rey, V. Computation of shoaling and breaking waves in nearshore areas by the coupling of BEM and VOF methods. In Proc. 9th Offshore and Polar Engng. Conf. (ISOPE99, Brest, France, May 1999), Vol. III, 304-309   [pdf]  (3,300K).
  42. Grilli, S.T. and Horrillo, J. 1999 Shoaling of periodic waves over barred-beaches in a fully nonlinear numerical wave tank. Intl. Journal of Offshore and Polar Engineering, 9(4), 257-263    [pdf]  (1,000K).
  43. Grilli, S.T., Guyenne, P. and F., Dias. 2000 Numerical computation of 3D overturning waves. Abstract in Proc. 15th Workshop on Water Waves and Floating Bodies(Dan Caesarea, Israel, February 2000), 4pps [pdf file]  (140K).
  44. Grilli, S.T., Guyenne, P. and Dias, F. 2000 Modeling of overturning waves over arbitrary bottom in a 3D numerical wave tank. In In Proc. 10th Offshore and Polar Engng. Conf. (ISOPE00, Seattle, USA, May 2000), Vol. III, 221-228   [compressed postcript]  (104K).
  45. Brandini, C. and S.T., Grilli. 2000 Sul Focusing delle Onde di Gravita in un Dominio Tridimensionale. In Proc. XXVII Convegno di Idraulica e Costruzioni Idrauliche (IDRA2000, Genova, Italy, September 2000), 8 pps.
  46. Brandini, C. and S.T., Grilli. 2001 Evolution of three-dimensional unsteady wave modulations. Proc. ROGUE WAVES 2000 Workshop (Brest, France, November 2000), 275-282.    [compressed pdf]  (2,110K).
  47. Grilli, S.T., Guyenne, P. and F., Dias. Numerical modeling of fully nonlinear 3D overturning waves over arbitrary bottom. Abstract accepted for 27th Intl. Conf. on Coastal Engineering (ICCE27, Sidney, Australia, July 2000)  
  48. Brandini, C. and S.T. Grilli. Sul Focusing delle Onde di Gravita in un Dominio Tridimensionale. To appear in Proc. XXVII Convegno di Idraulica e Costruzioni Idrauliche (IDRA2000, Genova, Italy, September 2000), 8pps.  
  49. Grilli, S.T., Guyenne, P. and Dias, F. 2001 A fully nonlinear model for three-dimensional overturning waves over arbitrary bottom. International Journal for Numerical Methods in Fluids, 35(7), 829-867.   [pdf file]  (604K).
  50. Brandini, C. and S.T., Grilli 2001 Modeling of freak wave generation in a 3D-NWT. In Proc. 11th Offshore and Polar Engng. Conf. (ISOPE01, Stavanger, Norway, June 2001), Vol III, 124-131 [pdf file]  (2,450K).
  51. Guignard, S. and S.T., Grilli. 2001 Modeling of shoaling and breaking waves in a 2D-NWT by using a spilling breaker model. Proc. 11th Offshore and Polar Engng. Conf. (ISOPE01, Stavanger, Norway, June 2001), Vol III, 116-123. [pdf file]  (484K).
  52. Guignard, S. and S.T., Grilli 2002 Implementation and validation of a breaker model in a fully nonlinear wave propagation model. In Proc. 4th Intl. Symp. on Ocean Wave Measurement and Analysis (WAVES 2001, San Francisco, USA, Sept. 2001) 1,012-1,021, ASCE Publication    [pdf file]  (360K).
  53. Guyenne, P., Grilli, S.T. and Dias, F. 2002 Three-dimensional numerical model for fully nonlinear waves over arbitrary bottom. In Proc. 4th Intl. Symp. on Ocean Wave Measurement and Analysis (WAVES 2001, San Francisco, USA, Sept. 2001) 1,072-1,081, ASCE Publication    [pdf file]  (344K).
  54. Brandini, C. and Grilli, S.T. 2002 Three-dimensional wave focusing in fully nonlinear wave models. In Proc. 4th Intl. Symp. on Ocean Wave Measurement and Analysis (WAVES 2001, San Francisco, USA, Sept. 2001) 1,102-1,111, ASCE Publication    [pdf file]  (2,700K).
  55. Biausser, B., Grilli, S.T., Marcer, R. and Fraunie, P., 2003 Numerical Analysis of the Internal Kinematics and Dynamics of 3D Breaking Waves on Slopes. In Proc. 18th Workshop on Water Waves and Floating Bodies (Nantes, France, Avril 2003), 6 pps. [pdf file]  (192K).
  56. Biausser, B., Grilli, S.T. and Fraunie, P., 2003 Numerical Simulations of Three-dimensional Wave Breaking by Coupling of a VOF Method and A Boundary Element Method. In Proc. 13th Offshore and Polar Engng. Conf. (ISOPE03, Honolulu, USA, May 2003), 333-339. [pdf file]  (1,100K)
  57. Biausser, B., Grilli, S.T. and Fraunie, P., 2003 Numerical Analysis of the Internal Kinematics and Dynamics of Three-Dimensional Breaking Waves on Slopes. In Proc. 13th Offshore and Polar Engng. Conf. (ISOPE03, Honolulu, USA, May 2003), 340-346. [pdf file]  (2,500K)
  58. Guyenne, P. and Grilli, S.T., 2003 Computations of 3D Overturning Waves in Shallow Water. In Proc. 13th Offshore and Polar Engng. Conf. (ISOPE03, Honolulu, USA, May 2003), 347-352. [pdf file]  (552K)
  59. Lachaume, C., Biausser, B., Grilli, S.T., Fraunie, P. and Guignard, S. 2003 Modeling of breaking and post-breaking waves on slopes by coupling of BEM and VOF methods. In Proc. 13th Offshore and Polar Engng. Conf. (ISOPE03, Honolulu, USA, May 2003), 353-359. [pdf file]  (900K)
  60. Fochesato, C., Dias, F., and Grilli, S.T., 2003. Numerical Model Using the Fast Multipole Algorithm for Nonlinear Three-dimensional Free Surface Waves over Arbitrary Bottom. In Proc. 13th Offshore and Polar Engng. Conf. (ISOPE03, Honolulu, USA, May 2003).
  61. Grilli, S.T., Voropayev, S., Testik, F.Y. and Fernando, H.J.S., 2003. Numerical Modeling and Experiments of Wave Shoaling over Buried Cylinders in Sandy Bottom. In Proc. 13th Offshore and Polar Engng. Conf. (ISOPE03, Honolulu, USA, May 2003), 405-412. [pdf file]  (448K)
  62. Fochesato C., Dias F. and Grilli S.T. 2003. Modèle Numérique Tridimensionnel pour les Ondes de Surface sur un Fond Quelconque. In Proc. 9th Journées de l'Hydrodynamique, (Nantes, France) pp. 355-367.
  63. Grilli, S.T., Gilbert, R., Lubin, P., Vincent, S., Legendre, D., Duvam, M., Kimmoun, O., Branger, H., Devrard, D., Fraunie, P., Abadie, S. 2004 Numerical modeling and experiments for solitary wave shoaling and breaking over a sloping beach. In Proc. 14th Offshore and Polar Engng. Conf. (ISOPE04, Toulon, France, May 2004), 306-312. [pdf file]  (472K).
  64. Biausser B., S.T. Grilli, Fraunie P. and Marcer, R. 2004. Numerical analysis of the internal kinematics and dynamics of three-dimensional breaking waves on slopes. Intl. J. Offshore and Polar Engng., 14(4), 247-256.   [pdf file]  (5,000K).
  65. Fochesato, C., Grilli, S.T. and Guyenne P. 2005. Note on non-orthogonality of local curvilinear co-ordinates in a three-dimensional boundary element method. Intl. J. Numer. Meth. In Fluids , 48 , 305-324    [pdf file]  (316K).
  66. Sung H.G. and Grilli S.T., 2005. A Note on Accuracy and Convergence of a Third-order Boundary Element Method for Three Dimensional Nonlinear Free Surface Flows. J. Ships and Ocean Engineering, 40, 31-41. [pdf file]  (772K).
  67. Helluy Ph., Golay F., Caltagirone J.-P., Lubin P., Vincent S., Drevard D., Marcer R., Seguin N., Grilli S., Lesage A.-C. and Dervieux A. 2005. Numerical simulations of wave breaking. Math. Modeling and Numer. Analys. , 39(3), 591-607. [pdf file]  (372K).
  68. Sung H.G. and Grilli S.T. 2005. Numerical Modeling of Nonlinear Surface Waves caused by Surface Effect Ships. Dynamics and Kinematics. In Proc. 15th Offshore and Polar Engng. Conf. (ISOPE05, Seoul, South Korea, June 2005), 3, 124-131. [pdf file]  (2,000K).
  69. Fochesato C., Dias F. and Grilli S.T. 2005. Wave energy focusing in a three-dimensional numerical wave tank. In Proc. 15th Offshore and Polar Engng. Conf. (ISOPE05, Seoul, South Korea, June 2005), 3, 24-31. [pdf file]  (1,200K).
  70. Gilbert R.W., Zedler E.A., Grilli S.T. and Street R.L., 2005. Modelling of Wave-Driven Sediment Transport in the Shoaling Zone. In Proc. 5th Intl. Symp. on Ocean Wave Measurement and Analysis (WAVES 2005, Madrid, Spain, July 2005), IAHR Publication, paper 121, 10 pps.    [pdf file]  (376K).
  71. Grilli S.T., Fochesato C. and Dias F., 2005. Wave Energy Focusing in a Three-dimensional Numerical Wavetank. In Proc. 5th Intl. on Ocean Wave Measurement and Analysis (WAVES 2005, Madrid, Spain, July 2005), IAHR Publication, paper 197, 10 pps.    [pdf file]  (2,000K).
  72. Devrard D., Marcer R., Grilli S.T., Fraunie P. and Rey V., 2005. Experimental Validation of a Coupled BEM-Navier-Stokes Model for Solitary Wave Shoaliing and Breaking. In Proc. 5th Intl. on Ocean Wave Measurement and Analysis (WAVES 2005, Madrid, Spain, July 2005), IAHR Publication, paper 166, 10 pps.    [pdf file]  (300K).
  73. Fochesato C., Dias F. and Grilli S.T. 2005. Wave Energy Focusing in a Three-dimensional Numerical Wavetank. In Proc. Rogue Waves 2004 Conf. (Brest, France, June 2004). [pdf file]  (1,100K).
  74. Guyenne, P. and Grilli, S.T. 2006. Numerical study of three-dimensional overturning waves in shallow water. J. Fluid Mechanics 547, 361-388.    [pdf file]  (1,600K).
  75. Sung H.G. and Grilli S.T. 2006. Combined Eulerian-Lagrangian or Pseudo-Lagrangian Descriptions of Waves Caused by an Advancing Free Surface Disturbance. In Proc. 16th Offshore and Polar Engng. Conf. (ISOPE06, San Francisco, California, June 2006), 3, 487-494. [pdf file]  (1.4M).
  76. Corte, C. and Grilli S.T. 2006. Numerical Modeling of Extreme Wave Slamming on Cylindrical Offshore Support Structures. In Proc. 16th Offshore and Polar Engng. Conf. (ISOPE06, San Francisco, California, June 2006), 3, 394-401. [pdf file]  (428K).
  77. Fochesato Ch. and Grilli, S.T. and Dias F. 2007. Numerical modeling of extreme rogue waves generated by directional energy focusing. Wave Motion , doi:10.1016/j.wavemoti.2007.01.03 , 44, 395-416. [pdf file]  (1.4M).
  78. Gilbert R.W., Zedler E.A., Grilli S.T., and Street R.L. 2007. Progress on Nonlinear-Wave-Forced Sediment Transport Simulation. IEEE J. of Oceanic Engng., 32(1), 236-248, doi:10.1109/JOE.2007.890979.   [pdf file]  (748K).
  79. Grilli, A., R., Merrill, J., Grilli, S.T., Spaulding, M.L., and Cheung, J.T. 2007. Experimental and numerical study of spar buoy-magnet/spring oscillators used as wave energy absorbers. Proc. 17th Offshore and Polar Engng. Conf. (ISOPE07, Lisbon, Portugal, July 2007), 489-496. [pdf file]  (1.4M).
  80. Harris, J.C., and Grilli S.T. 2007. Computation of the wavemaking resistance of a Harley surface effect ship. Proc. 17th Offshore and Polar Engng. Conf. (ISOPE07, Lisbon, Portugal, July 2007), 3732-3739. [pdf file]  (1.0M).
  81. Harris, J., and Grilli, S.T., 2007. Validating a perturbation approach to the large eddy simulation of wave induced sediment transport, EOS Trans. AGU, 88(52), Fall Meet. Suppl., Abstract H51I-0885.
  82. Pomeau, Y., M. Le Berre, P. Guyenne and S.T. Grilli 2008. Wave breaking and generic singularities of nonlinear hyperbolic equations. Nonlinearity, 21, T61-T79, doi: 10.1088/0951-7715/21/5/T01. [pdf]  (364K).
  83. Pomeau Y., Le Bars M., Le Gal P., Jamin T., Le Berre M., Guyenne Ph., Grilli S.T. and Audoly B. 2008. Sur le déferlement des vagues (Comptes-rendus de la 11¸me Rencontre du Non-linˇaire, Paris, 2008), p. 155. In Publications Non-linéaires (pnl@lps.u-psud.fr). [pdf]  (460K).
  84. Sung H.G. and Grilli, S.T. 2008. BEM Computations of 3D Fully Nonlinear Free Surface Flows Caused by Advancing Surface Disturbances. Intl. J. Offshore and Polar Engng. (accepted). [pdf]  (1,200K).
  85. Grilli , S.T., Dias, F., Guyenne, P., Fochesato, C. and F. Enet 2008. Progress In Fully Nonlinear Potential Flow Modeling Of 3D Extreme Ocean Waves. Chapter in Advances in Numerical Simulation of Nonlinear Water Waves (Series in Advances in Coastal and Ocean Engineering). World Scientific Publishing Co.Pte.Ltd., 55 pps. (accepted). [pdf]  (8.6Mb).
  86. Grilli, S.T., Voropayev, S., Testik, F.Y. and Fernando, H.J.S., Numerical modeling and experiments of periodic waves shoaling over semi-buried cylinders in sandy bottom. Journal of Waterway Port Coastal and Ocean Engineering (in revision).    [pdf file]  (540K).


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