Computation of decaying turbulence in an adaptive wavelet basis

Physica D: Nonlinear Phenomena

Volumn 134, Issue 3, 1999, Pages 337-361

  Fröhlich, Jochen ^a,b   Schneider, Kai ^b  

^a ZUSE INSTITUTE BERLIN   (Germany)

^b UNIVERSITY OF KARLSRUHE   (Germany)

Author keywords

Adaptive discretization; Computational methods in fluid dynamics; Homogeneous turbulence; Wavelets

Indexed keywords

EID: 0008518826     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-2789(99)00139-6     Document Type: Article

References (49)

1. A. Babiano, C. Basdevant, B. Legras, R. Sadourny, Vorticity and passive-scalar dynamics in two-dimensional turbulence, J. Fluid Mech. 183 (1987) 379-397.
2. C. Basdevant, B. Legras, R. Sadourny, M. Beland, A study of barotropic model flows: intermittency waves and predictability, J. Atmos. Sci. 38 (1981) 2305-2326.
3. G.K. Batchelor, Computation of the energy spectrum in homogeneous two-dimensional turbulence, Phys. Fluid Suppl. II 12 (1969) 233-239.
4. R. Benzi, G. Paladin, S. Patarnello, P. Santangelo, A. Vulpiani, Intermittency and coherent structures in two-dimensional turbulence, J. Phys. A 19 (1986) 3771-3784.
5. R. Benzi, S. Patarnello, P. Santangelo, Self-similarity of coherent structures in two-dimensional decaying turbulence, J. Phys. A: Math. Gen 21 (1988) 1221-1237.
6. G. Berkooz, J. Elezgaray, P. Holmes, Coherent structures in random media and wavelets, Physica D 61 (1992) 47-58.
7. M. Cannone, Ondelettes, Paraproduits et Navier-Stokes. Diderot, 1995.
8. Ph. Charton, V. Perrier, A Pseudo-wavelet scheme for the two-dimensional Navier-Stokes equations, Matematica Aplicada e Computacional 15 (1996) 139-160.
9. I. Daubechies, Ten Lectures on Wavelets, SIAM (1992).
10. R.A. DeVore, B. Jawerth, V. Popov, Compression of Wavelet Decomposition, Am. J. Math. 114 (1992) 737-785.
11. M. Do-Khac, C. Basdevant, V. Perrier, K. Dang-Tran, Wavelet analysis of 2D turbulent fields, Physica D 76 (1994) 252-277.
12. D.L. Donoho, I. Johnstone, G. Kerkyacharian, D. Picard, Wavelet shrinkage: Asymptopia? (with discussion), J. Royal Stat. Soc. Ser. B 57 (1995) 301-369.
13. F.W. Elliott, A.J. Majda, A new algorithm with plane waves and wavelets for random velocity fields with many spatial scales, J. Comput. Phys. 117 (1995) 146-162.
14. M. Farge, Wavelet transforms and their applications to turbulence, Ann. Rev. Fluid Mech. 24 (1992) 395-457.
15. M. Farge, E. Goirand, Y. Meyer, F. Pascal, M.V. Wickerhauser, Improved predictability of two-dimensional turbulent flows using wavelet packet compression, Fluid Dyn. Res. 10 (1992) 229-250.
16. M. Farge, Y. Guezennec, C.M. Ho, C. Meneveau, Continuous wavelet analysis of coherent structures, in: Proceedings of the 1990 Summer Program, NASA-Ames and Stanford University, Center for Turbulence Research, 1990, pp. 331-348.
17. M. Farge, N. Kevlahan, V. Perrier, K. Schneider, Turbulence analysis, modelling and computing using wavelets, in J.C. van den Berg (Ed.), Wavelets and Physics, Cambridge University Press, Cambridge, 1999, pp. 117-200.
18. M. Farge, G. Rabreau, Transforméeen ondelettes pour détecter et analyser les structures cohérentes dans les écoulements turbulents bidimensionels, C.R. Acad. Sci. Paris II 307 (1988) 1479-1486.
19. M. Farge, K. Schneider, N. Kevlahan, Coherent structure eduction in wavelet-forced two-dimensional turbulent flows, in E. Krause, K. Gersten (Eds.), IUTAM Symposium on Dynamics of Slender Vortices, Kluwer Academic Publishers, Dordrecht, 1988, pp. 65-83.
20. P. Frick V. Zimin, Hierarchical Models of Turbulence, in: M. Farge, J. Hunt, J. Vassilicos (Eds.), Wavelets, Fractals, and Fourier Transforms, Clarendon Press, Oxford, 1993, pp. 265-283.
21. U. Frisch, Turbulence. The Legacy of A.N. Kolmogorov, Cambridge University Press, Cambridge, 1995.
22. J. Fröhlich, K. Schneider, An adaptive wavelet Galerkin algorithm for one- and two-dimensional flame computations, Eur. J. Mech. B/Fluids 13 (1994) 439-471.
23. J. Fröhlich, K. Schneider, A fast algorithm for lacunary wavelet bases related to the solution of PDEs, C.R. Math. Rep. Acad. Sci. Canada 16 (1995) 83-86.
24. J. Fröhlich, K. Schneider, Numerical simulation of turbulent flows in an adaptive wavelet basis, Appl. Comp. Harm. Anal. 3 (1996) 393-397.
25. J. Fröhlich, K. Schneider, An adaptive wavelet-vaguelette algorithm for the solution of PDEs, J. Comp. Phys. 130 (1997) 174-190.
26. G. Furioli, P. Lemarié-Rieusset, E. Terrano, Sur l'unicité des solutions 'mild' des équations de Navier-Stokes, C.R. Acad. Sci. Paris Série 1235 (1997) 1253-1256.
27. N. Kevlahan, M. Farge, Vorticity filaments in two-dimensional turbulence: Creation, stability and effect, J. Fluid Mech. 346 (1997) 49-76.
28. F. Koster, M. Griebel, N.K.-G. Kevlahan, M. Farge, K. Schneider, Towards an adaptive wavelet based 3D Navier-Stokes solver, in: E.H. Hirschel (Ed.), Notes on Numerical Fluid Mechanics, 1998, pp. 339-364.
29. R.H. Kraichnan, Inertial ranges in two-dimensional turbulence, Phys. Fluids 10 (1967) 1417-1423.
30. M. Lesieur, Turbulence in Fluids, Kluwer Academic Publishers, Dordrecht, 1997.
31. J. Liandrat, F. Moret-Bailly, The wavelet transform. Some applications to fluid dynamics and turbulence, Eur. J. Mech. B/Fluids 9 (1990) 1-19.
32. J. Liandrat, Ph. Tchamitchian, Resolution of the ID regularized Burgers equation using a spatial wavelet approximation algorithm and numerical results, Tech. Rep. ICASE (1990).
33. J.L. Lumley, The structure of inhomogeneous flows, in: A.M. Yaglom, V.I. Tatarski (Eds.), Atmospheric Turbulence and Radio Wave Propagation, Nauka, Moscow, 1967.
34. W.H. Matthaeus, W.T. Stribling, D. Martinez, S. Oughton, D. Montgomery, Decaying, two-dimensional, Navier-Stokes turbulence at very long times, Physica D 51 (1991) 531-538.
35. W.H. Matthaeus, W.T. Stribling, D. Martinez, S. Oughton, D. Montgomery, Selective decaying and coherent vortices in two-dimensional incompressible turbulence, Phys. Rev. Lett. 66 (1991) 2731-2734.
36. C. Meneveau, Analysis of turbulence in the orthonormal wavelet representation, J. Fluid Mech. 232 (1991) 469-520.
37. Y. Meyer, Ondelettes et Opérateurs I/II. Hermann, 1990.
38. S.A. Orszag, Numerical Methods for the Simulation of Turbulence, Phys. Fluids Suppl. II 12 (1969) 250-257.
39. S.A. Orszag, Numerical simulation of incompressible flows within simple boundaries I. Galerkin (spectral) representations, Stud. Appl. Math. 50 (1971) 293.
40. V. Perrier, C. Basdevant, La décomposition en ondelettes périodiques, un outil pour l'analyse de champs inhomogènes, Théorie et algorithmes, Rech. Aérosp. 3 (1989) 53-67.
41. P. Santangelo, R. Benzi, B. Legras, The generation of vortices in high resolution, two-dimensional decaying turbulence and the influence of initial conditions on the breaking of self-similarity, Phys. Fluids 1 (1989) 1027-1034.
42. K. Schneider, M. Farge, Wavelet forcing for numerical simulation of two-dimensional turbulence, C.R. Acad. Sci. Paris Série II 325 (1997) 263-270.
43. K. Schneider, M. Farge, Wavelet approach for modelling and computation of turbulence, in: Lecture Series 1998-05 Advances in Turbulence Modelling, von Karman Institute for Fluid Dynamics, Bruxelles, 1998.
44. H. Tennekes, J.L. Lumley, A First Course in Turbulence, MIT Press, Cambridge, 1972.
45. J.M. Vanel, R. Peyret, P. Bontoux, A pseudo-spectral solution of vorticity-stream function equations using the influence matrix technique, in: Morton and Baines (Eds.), Numerical Methods for Fluid Dynamics, pp. 477-488, 1986.
46. J.C. Mc Williams, The emergence of isolated coherent vortices in turbulent flows, J. Fluid Mech. 146 (1984) 21-43.
47. J.C. Mc Williams, A demonstration of the suppression of turbulent cascades by coherent vortices in two-dimensional turbulence, Phys. Fluids A 2 (1990) 522-547.
48. J.C. Mc Williams, The vortices of two-dimensional turbulence, J. Fluid Mech. 219 (1990) 361-385.
49. V. Zimin, Hierarchical Model of Turbulence, Izvestija Atm. Ocean. Phys. (USA, translated from Russian) 17 (1981) 941-949.