Numerical solutions of the isotropic 3-wave kinetic equation

Physica D: Nonlinear Phenomena

Volumn 238, Issue 23-24, 2009, Pages 2282-2297

  Connaughton, Colm ^a  

^a UNIVERSITY OF WARWICK   (United Kingdom)

Author keywords

Aggregation fragmentation processes; Kinetic equations; Wave turbulence

Indexed keywords

INTEGRAL EQUATIONS; KINETIC THEORY; KINETICS; NUMERICAL METHODS; TURBULENCE;

AGGREGATION-FRAGMENTATION PROCESS; ANALYTICAL CALCULATION; BOTTLENECK EFFECTS; FRAGMENTATION MECHANISM; INTERACTION COEFFICIENT; KINETIC EQUATIONS; NUMERICAL SOLUTION; WAVE TURBULENCE;

KINETIC ENERGY;

EID: 70350564367     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2009.09.012     Document Type: Article

References (44)

1. Zakharov V., Lvov V., and Falkovich G. Kolmogorov Spectra of Turbulence (1992), Springer-Verlag, Berlin
2. Newell A., Nazarenko S., and Biven L. Wave turbulence and intermittency. Physica D 152-153 (2001) 520-550
3. Leyvraz F. Scaling theory and exactly solved models in the kinetics of irreversible aggregation. Phys. Rep. 383 2 (2003) 95-212
4. Connaughton C., Rajesh R., and Zaboronski O. Stationary Kolmogorov solutions of the Smoluchowski aggregation equation with a source term. Phys. Rev. E 69 (2004) 061114. arXiv:cond-mat/0310063
5. Connaughton C., Rajesh R., and Zaboronski O. In: Sattler K. (Ed). Kinetics of Cluster-Cluster Aggregation. Handbook of Nanophysics (2009), Taylor and Francis 1-40
6. Redner S. In: Herrmann H.J., and Roux S. (Eds). Statistical Models for the Fracture of Disordered Media (1990), Plenum
7. Krapivsky P.L., and Ben-Naim E. Shattering transitions in collision-induced fragmentation. Phys. Rev. E 68 2 (2003) 021102
8. Siebesma A.P., Tremblay R.R., Erzan A., and Pietronero L. Multifractal cascades with interactions. Physica A 156 2 (1989) 613-627
9. Ben-Naim E., and Krapivsky P.L. Phase transition with nonthermodynamic states in reversible polymerization. Phys. Rev. E 77 6 (2008) 061132
10. Ernst M. Kinetics of clustering in irreversible aggregation. In: Pietronero L., and Tosatti E. (Eds). Fractals in Physics (1986), North Holland, Amsterdam 289
11. Ernst M.H., and van Dongen P.G.J. Scaling solutions of smoluchowski's coagulation equation. J. Stat. Phys. 1 2 (1988) 295-329
12. Connaughton C., Rajesh R., and Zaboronski O. Breakdown of Kolmogorov scaling in models of cluster aggregation. Phys. Rev. Lett. 94 (2005) 194503. arXiv:cond-mat/0410114
13. Connaughton C., Rajesh R., and Zaboronski O. Cluster-cluster aggregation as an analogue of a turbulent cascade: Kolmogorov phenomenology, scaling laws and the breakdown of self-similarity. Physica D 222 (2006) 97-115. arXiv:cond-mat/0510389
14. Hendriks E., Ernst M., and Ziff R. Coagulation equations with gelation. J. Stat. Phys. 31 (1983) 519-563
15. Hayakawa H. Irreversible kinetic coagulations in the presence of a source. J. Phys. A 20 (1987) L801-L805
16. Kontorovich V. Zakharov's transformation in the problem of galaxy mass distribution function. Physica D 152-153 (2001) 676-681
17. Biven L., Nazarenko S., and Newell A.C. Breakdown of wave turbulence and the onset of intermittency. Phys. Lett. A 280 (2001) 28-32
18. Falkovich G., and Shafarenko A. Non-stationary wave turbulence. J. Nonlinear Sci. 1 (1991) 452-480
19. Kitaigorodskii S.A. On the theory of the equilibrium range in the spectrum of wind-generated gravity waves. J. Phys. Oceanogr. 13 (1983) 816-827
20. C. Connaughton, New directions in wave turbulence, Ph.D. Thesis, University of Warwick, July 2002
21. Newell A.C., and Zakharov V.E. The role of the generalized Phillips' spectrum in wave turbulence. Phys. Lett. A 372 (2008) 4230-4233
22. Newell A.C., and Zakharov V.E. Rough sea foam. Phys. Rev. Lett. 69 (1992) 1149-1151
23. Connaughton C., Newell A., and Nazarenko S. Dimensional analysis and wave turbulence. Physica D 184 1-4 (2003) 86-97
24. Lee M. On the validity of the coagulation equation and the nature of runaway growth. Icarus 143 (2000) 74-86
25. Lee M. A survey of numerical solutions to the coagulation equation. J. Phys. A 34 (2001) 10219-10241
26. Hasselmann S., Hasselmann K., Allender J.H., and Barnett T.P. Computations and parameterizations of the nonlinear energy transfer in a gravity-wave specturm. Part II: Parameterizations of the nonlinear energy transfer for application in wave models. J. Phys. Oceanogr. 15 (1985) 1378-1392
27. Zakharov V.E., and Pushkarev A.N. Diffusion model of interacting gravity waves on the surface of deep fluid. Nonlinear Process. Geophys. 6 (1999) 1-10
28. Polnikov V.G., and Farina L. On the problem of optimal approximation of the four-wave kinetic integral. Nonlinear Process. Geophys. 9 (2002) 497-512
29. Press W.H., Teukolsky S.A., Vetterling W.T., and Flannery B.P. Numerical Recipes in C. 2nd ed. The Art of Scientific Computing (1992), Cambridge University Press, New York, NY, USA
30. Galassi M., Davies J., Theiler J., Gough B., Jungman G., Alken P., Booth M., and Rossi F. GNU Scientific Library Reference Manual. 3rd ed. (2009), Network Theory Ltd.
31. Rosenbrock H.H. An automatic method for finding the greatest or least value of a function. Comput. J. 3 3 (1960) 175-184 10.1093/comjnl/3.3.175
32. Bec J., and Khanin K. Burgers turbulence. Phys. Rep. 447 1-2 (2007) 1-66. arXiv:0704.1611
33. Eyink G.L. Dissipative anomalies in singular euler flows. Euler Equations: 250 Years On - Proceedings of an International Conference. Physica D 237 14-17 (2008) 1956-1968
34. Dobler W., Haugen N.E.L., Yousef T.A., and Brandenburg A. Bottleneck effect in three-dimensional turbulence simulations. Phys. Rev. E 68 2 (2003) 026304
35. Falkovich G. Bottleneck phenomenon in developed turbulence. Phys. Fluids 6 (1994) 1411-1414
36. Falkovich G., and Ryzhenkova I.V. Influence of dissipation on Kolmogorov spectra of wave turbulence. Sov. Phys. JETP 71 (1990) 1085
37. Dyachenko S., Newell A., Pushkarev A., and Zakharov V. Optical turbulence: Weak turbulence, condensates and collapsing filaments in the nonlinear Schrodinger equation. Physica D 57 (1992) 96-160
38. Connaughton C., and Nazarenko S. Warm cascades and anomalous scaling in a diffusion model of turbulence. Phys. Rev. Lett. 92 4 (2004) 044501
39. Cichowlas C., Bonati P., Debbasch F., and Brachet M. Effective dissipation and turbulence in spectrally truncated euler flows. Phys. Rev. Lett. 95 (2005) 264502
40. Frisch U., Kurien S., Pandit R., Pauls W., Ray S.S., Wirth A., and Zhu J.-Z. Hyperviscosity, galerkin truncation, and bottlenecks in turbulence. Phys. Rev. Lett. 101 14 (2008) 144501
41. Bos W.J.T., and Bertoglio J.-P. Dynamics of spectrally truncated inviscid turbulence. Phys. Fluids 18 7 (2006) 071701
42. Krstulovic G., Mininni P.D., Brachet M.E., and Pouquet A. Cascades, thermalization and eddy viscosity in helical Galerkin truncated Euler flows. Phys. Rev. E 79 5 (2009) Article number: 056304
43. Galtier S., Nazarenko S., Newell A., and Pouquet A. A weak turbulence theory for incompressible mhd. J. Plasma Phys. 63 (2000) 447-488
44. Connaughton C., Newell A., and Pomeau Y. Non-stationary spectra of local wave turbulence. Physica D 184 1-4 (2003) 64-85