Numerical simulations of internal solitary waves interacting with uniform slopes using an adaptive model

Ocean Modelling

Volumn 30, Issue 1, 2009, Pages 16-28

  Rickard, Graham ^a   O'Callaghan, Joanne ^a   Popinet, Stéphane ^a  

^a NATIONAL INSTITUTE OF WATER AND ATMOSPHERIC RESEARCH   (New Zealand)

Author keywords

Internal wave breaking; Modelling

Indexed keywords

ADAPTIVE MODELS; ADAPTIVITY; BOUSSINESQ; CPU MEMORY; DYNAMICAL CORE; FINITE VOLUME; FLUID CODES; INTERNAL SOLITARY WAVES; INTERNAL WAVE BREAKING; LABORATORY EXPERIMENTS; MODEL CONVERGENCE; MODEL RESOLUTION; MODELLING; NON-LINEAR; NUMERICAL SIMULATION; SEMI-STRUCTURED; SLOPE ANGLES; TIME SAVINGS; TWO-DIMENSION; WAVEBREAKING;

ENERGY TRANSFER; OCEANOGRAPHY; WAVES;

SIMULATORS;

FINITE VOLUME METHOD; INTERNAL WAVE; NUMERICAL MODEL; SOLITARY WAVE; WAVE BREAKING; WAVE RUNUP;

GERRIS;

EID: 67650609831     PISSN: 14635003     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ocemod.2009.05.008     Document Type: Article

References (30)

1. Almgren A.S., Bell J.B., and Crutchfield W.Y. Approximate projection methods: part I. Inviscid analysis. SIAM J. Sci. Comput. 22 (2000) 1139-1159
2. Behrens J. Adaptive atmospheric modeling: scientific computing at its best. Comput. Sci. Eng. 7 (2005) 76-83
3. Bell J.B., Colella P., and Glaz H.M. A second-order projection method for the incompressible Navier-Stokes equations. J. Comput. Phys. 85 (1989) 257-283
4. Berntsen, J., 2000. USERS GUIDE for a modesplit σ-coordinate numerical ocean model. Technical Report 135, Department of Applied Mathematics, University of Bergen, Johs. Bruns gt. 12, N-5008, Bergen, Norway, 48pp.
5. Berntsen J., Xing J., and Alendal G. Assessment of non-hydrostatic ocean models using laboratory scale problems. Cont. Shelf Res. 26 (2006) 1433-1447
6. Blayo E., and Debreu L. Adaptive mesh refinement for finite difference ocean models: first experiments. J. Phys. Oceanogr. 29 (1999) 1239-1250
7. Bogucki D., and Garrett C. A simple model for the shear-induced decay of an internal solitary wave. J. Phys. Oceanogr. 23 (1993) 1767-1776
8. Bourgault D., and Kelley D.E. Wave-induced boundary mixing in a partially mixed estuary. J. Mar. Res. 61 (2003) 553-576
9. Bourgault D., and Kelley D.E. A laterally averaged nonhydrostatic ocean model. J. Atmos. Ocean. Technol. 21 (2004) 1910-1924
10. Bourgault D., Blokhina M.D., Mirshak R., and Kelley D.E. Evolution of a shoaling internal solitary wavetrain. Geophys. Res. Lett. 34 (2007) L03601 10.1029/2006GL028462
11. Bourgault D., and Kelley D.E. On the reflectance of uniform slopes for normally incident interfacial solitary waves. J. Phys. Oceanogr. 37 (2007) 1156-1162
12. Burchard H., and Beckers J.-M. Non-uniform adaptive vertical grids in one-dimensional numerical ocean models. Ocean Modell. 6 (2004) 51-81
13. Chorin A. Numerical solution of the Navier-Stokes equations. Math. Comput. 22 104 (1968) 745-762
14. Hanert E., Deleersnijder E., and Legat V. An adaptive finite element water column model using the Mellor Yamada level 2.5 turbulence closure scheme. Ocean Modell. 12 (2006) 205-223
15. Härtel C., Meiburg E., and Necker F. Analysis and direct numerical simulation of the flow at a gravity-current head. Part 1. Flow topology and front speed for slip and no-slip boundaries. J. Fluid Mech. 418 (2000) 189-212
16. Helfrich K.R. Internal solitary wave breaking and run-up on a uniform slope. J. Fluid Mech. 243 (1992) 133-154
17. Helfrich K.R., and Melville W.K. Long nonlinear internal waves. Annu. Rev. Fluid Mech. 38 (2006) 395-425
18. Iribarren C.R., and Nogales C. Protection des ports. Section II, Comm. 4 (1949), XVIIth Int. Nav. Congress, Lisbon
19. Marshall J., Adcroft A., Hill C., Perelman L., and Heisey C. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res. 102 C3 (1997) 5753-5766
20. Matsumura Y., and Hasumi H. A non-hydrostatic ocean model with a scalable multigrid Poisson solver. Ocean Modell. 24 (2008) 15-28
21. Michallet H., and Ivey G.N. Experiments on mixing due to internal solitary waves breaking on uniform slopes. J. Geophys. Res. 104 C6 (1999) 13467-13477
22. Pain C.C., Piggott M.D., Goddard A.J.H., Fang F., Gorman G.J., Marshall D.P., Eaton M.D., Power P.W., and de Oliveira C.R.E. Three-dimensional unstructured mesh ocean modelling. Ocean Modell. 10 (2005) 5-33
23. Piggott M.D., Gorman G.J., Pain C.C., Allison P.A., Candy A.S., Martin B.T., and Wells M.R. A new computational framework for multi-scale ocean modelling based on adapting unstructured meshes. Int. J. Numer. Meth. Fluids 56 (2008) 1003-1015
24. Popinet S. A tree-based adaptive solver for the incompressible Euler equations in complex geometries. J. Comput. Phys. 190 2 (2003) 572-600
25. Popinet, S., 2006. The Gerris Flow Solver, available from: http://gfs.sourceforge.net.
26. Popinet S., and Rickard G.J. A tree-based solver for adaptive ocean modelling. Ocean Modell. 16 (2007) 224-249
27. Segur H., and Hammack J.L. Soliton models of long internal waves. J. Fluid Mech. 118 (1982) 285-304
28. Simpson A.E. Effects of the lower boundary on the head of a gravity current. J. Fluid Mech. 53 (1972) 759-768
29. Simpson A.E. Gravity Current (1997), Cambridge University Press
30. Venayagamoorthy S.K., and Fringer O.B. On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech. 577 (2007) 137-159