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Clark Di Leoni, P.; Cobelli, P.J.; Mininni, P.D. "Wave turbulence in shallow water models" (2014) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 89(6)
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Abstract:

We study wave turbulence in shallow water flows in numerical simulations using two different approximations: the shallow water model and the Boussinesq model with weak dispersion. The equations for both models were solved using periodic grids with up to 20482 points. In all simulations, the Froude number varies between 0.015 and 0.05, while the Reynolds number and level of dispersion are varied in a broader range to span different regimes. In all cases, most of the energy in the system remains in the waves, even after integrating the system for very long times. For shallow flows, nonlinear waves are nondispersive and the spectrum of potential energy is compatible with ∼k-2 scaling. For deeper (Boussinesq) flows, the nonlinear dispersion relation as directly measured from the wave and frequency spectrum (calculated independently) shows signatures of dispersion, and the spectrum of potential energy is compatible with predictions of weak turbulence theory, ∼k-4/3. In this latter case, the nonlinear dispersion relation differs from the linear one and has two branches, which we explain with a simple qualitative argument. Finally, we study probability density functions of the surface height and find that in all cases the distributions are asymmetric. The probability density function can be approximated by a skewed normal distribution as well as by a Tayfun distribution. © 2014 American Physical Society.

Registro:

Documento: Artículo
Título:Wave turbulence in shallow water models
Autor:Clark Di Leoni, P.; Cobelli, P.J.; Mininni, P.D.
Filiación:Departamento de Física, Facultad de Ciencias Exactas y Naturales, Cuidad Universitaria, Buenos Aires 1428, Argentina
Palabras clave:Coastal engineering; Dispersions; Normal distribution; Potential energy; Probability density function; Reynolds number; Turbulence; Water waves; Boussinesq model; Frequency spectra; Nonlinear dispersion relation; Nonlinear waves; Shallow water flow; Shallow water model; Wave turbulence; Weak turbulence; Dispersion (waves); water; chemical model; chemistry; computer simulation; flow kinetics; hydrodynamics; nonlinear system; procedures; statistical model; water flow; Computer Simulation; Hydrodynamics; Models, Chemical; Models, Statistical; Nonlinear Dynamics; Rheology; Water; Water Movements
Año:2014
Volumen:89
Número:6
DOI: http://dx.doi.org/10.1103/PhysRevE.89.063025
Título revista:Physical Review E - Statistical, Nonlinear, and Soft Matter Physics
Título revista abreviado:Phys. Rev. E Stat. Nonlinear Soft Matter Phys.
ISSN:15393755
CODEN:PLEEE
CAS:water, 7732-18-5; Water
Registro:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_15393755_v89_n6_p_ClarkDiLeoni

Referencias:

  • Iafrati, A., Babanin, A., Onorato, M., (2013) Phys. Rev. Lett., 110, p. 184504. , PRLTAO 0031-9007 10.1103/PhysRevLett.110.184504
  • D'Asaro, E., Lee, C., Rainville, L., Harcourt, R., Thomas, L., (2011) Science, 332, p. 318. , SCIEAS 0036-8075 10.1126/science.1201515
  • Ivey, G.N., Winters, K.B., Koseff, J.R., Density stratification, turbulence, but how much mixing? (2008) Annual Review of Fluid Mechanics, 40, pp. 169-184. , DOI 10.1146/annurev.fluid.39.050905.110314
  • Rose, K.A., Sikes, E.L., Guilderson, T.P., Shane, P., Hill, T.M., Zahn, R., Spero, H.J., (2010) Nature, 466, p. 1093. , (London),. NATUAS 0028-0836 10.1038/nature09288
  • Cavaleri, L., Fox-Kemper, B., Hemer, M., (2012) Bull. Am. Meteorol. Soc., 93, p. 1651. , BAMIAT 0003-0007 10.1175/BAMS-D-11-00170.1
  • Falnes, J., A review of wave-energy extraction (2007) Marine Structures, 20 (4), pp. 185-201. , DOI 10.1016/j.marstruc.2007.09.001, PII S0951833907000482
  • Hasselmann, K., (1962) J. Fluid Mech., 12, p. 481. , JFLSA7 0022-1120 10.1017/S0022112062000373
  • Hasselmann, K., (1963) J. Fluid Mech., 15, p. 385. , JFLSA7 0022-1120 10.1017/S002211206300032X
  • Hasselmann, K., (1963) J. Fluid Mech., 15, p. 273. , JFLSA7 0022-1120 10.1017/S0022112063000239
  • Zakharov, V.E., Lvov, V.S., Falkovic, G., (1992) Kolmogorov Spectra of Turbulence i - Wave Turbulence, , (Springer, Berlin)
  • Newell, A.C., Rumpf, B., (2011) Annu. Rev. Fluid Mech., 43, p. 59. , ARVFA3 0066-4189 10.1146/annurev-fluid-122109-160807
  • Nazarenko, S., (2011) Wave Turbulence, , 1st ed. (Springer, Berlin)
  • During, G., Josserand, C., Rica, S., Weak turbulence for a vibrating plate: Can one hear a kolmogorov spectrum? (2006) Physical Review Letters, 97 (2), p. 025503. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevLett.97.025503&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevLett.97.025503
  • Galtier, S., (2003) Phys. Rev. e, 68, p. 015301. , 1063-651X 10.1103/PhysRevE.68.015301
  • Galtier, S., Nazarenko, S.V., Newell, A.C., Pouquet, A., (2000) J. Plasma Phys., 63, p. 447. , JPLPBZ 0022-3778 10.1017/S0022377899008284
  • Schekochihin, A.A., Nazarenko, S.V., Yousef, T.A., (2012) Phys. Rev. e, 85, p. 036406. , PLEEE8 1539-3755 10.1103/PhysRevE.85.036406
  • Deike, L., Berhanu, M., Falcon, E., (2012) Phys. Rev. e, 85, p. 066311. , PLEEE8 1539-3755 10.1103/PhysRevE.85.066311
  • Falcón, C., Falcon, E., Bortolozzo, U., Fauve, S., (2009) Europhys. Lett., 86, p. 14002. , EULEEJ 0295-5075 10.1209/0295-5075/86/14002
  • Kolmakov, G.V., Levchenko, A.A., Brazhnikov, M.Y., Mezhov-Deglin, L.P., Silchenko, A.N., McClintock, P.V.E., (2004) Phys. Rev. Lett., 93, p. 074501. , PRLTAO 0031-9007 10.1103/PhysRevLett.93.074501
  • Cobelli, P., Przadka, A., Petitjeans, P., Lagubeau, G., Pagneux, V., Maurel, A., (2011) Phys. Rev. Lett., 107, p. 214503. , PRLTAO 0031-9007 10.1103/PhysRevLett.107.214503
  • Mordant, N., (2008) Phys. Rev. Lett., 100, p. 234505. , PRLTAO 0031-9007 10.1103/PhysRevLett.100.234505
  • Boudaoud, A., Cadot, O., Odille, B., Touzé, C., (2008) Phys. Rev. Lett., 100, p. 234504. , PRLTAO 0031-9007 10.1103/PhysRevLett.100.234504
  • Cobelli, P., Petitjeans, P., Maurel, A., Pagneux, V., Mordant, N., (2009) Phys. Rev. Lett., 103, p. 204301. , PRLTAO 0031-9007 10.1103/PhysRevLett.103.204301
  • Leerink, S., Bulanin, V.V., Gurchenko, A.D., Gusakov, E.Z., Heikkinen, J.A., Janhunen, S.J., Lashkul, S.I., Petrov, A.V., (2012) Phys. Rev. Lett., 109, p. 165001. , PRLTAO 0031-9007 10.1103/PhysRevLett.109.165001
  • Mininni, P.D., Pouquet, A., (2007) Phys. Rev. Lett., 99, p. 254502. , PRLTAO 0031-9007 10.1103/PhysRevLett.99.254502
  • Chen, Q., Chen, S., Eyink, G.L., Holm, D.D., Resonant interactions in rotating homogeneous three-dimensional turbulence (2005) Journal of Fluid Mechanics, 542, pp. 139-164. , DOI 10.1017/S0022112005006324, PII S0022112005006324
  • Phillips, O.M., (1958) J. Fluid Mech., 4, p. 426. , JFLSA7 0022-1120 10.1017/S0022112058000550
  • Toba, Y., (1973) Journal of the Oceanographical Society of Japan, 29, p. 209. , NKGKB4 0029-8131 10.1007/BF02108528
  • Donelan, M.A., Hamilton, J., Hui, W.H., (1985) Philos. Trans. R. Soc. London A, 315, p. 509. , PTRMAD 1364-503X 10.1098/rsta.1985.0054
  • Badulin, S.I., Babanin, A.V., Zakharov, V.E., Resio, D., (2007) J. Fluid Mech., 591, p. 339. , JFLSA7 0022-1120 10.1017/S0022112007008282
  • Phillips, O.M., (1985) J. Fluid Mech., 156, p. 505. , JFLSA7 0022-1120 10.1017/S0022112085002221
  • Korotkevich, A.O., (2008) Phys. Rev. Lett., 101, p. 074504. , PRLTAO 0031-9007 10.1103/PhysRevLett.101.074504
  • Zakharov, V., (1999) European Journal of Mechanics, B/Fluids, 18, p. 327. , EJBFEV 0997-7546 10.1016/S0997-7546(99)80031-4
  • Onorato, M., Osborne, A.R., Janssen, P.A.E.M., Resio, D., (2009) J. Fluid Mech., 618, p. 263. , JFLSA7 0022-1120 10.1017/S0022112008004229
  • Smith, J.M.K., Vincent, C.L., (2003) J. Geophys. Res., 108, p. 3366. , JGREA2 0148-0227 10.1029/2003JC001930
  • Kaihatu, J.M., Veeramony, J., Edwards, K.L., Kirby, J.T., Asymptotic behavior of frequency and wave number spectra of nearshore shoaling and breaking waves (2007) Journal of Geophysical Research C: Oceans, 112 (6), pp. C06016. , DOI 10.1029/2006JC003817
  • Falcon, E., Laroche, C., (2011) Europhys. Lett., 95, p. 34003. , EULEEJ 0295-5075 10.1209/0295-5075/95/34003
  • Landau, L.D., Lifshitz, E.M., (2004) Fluid Mechanics, , (Elsevier/Butterworth-Heinemann, Amsterdam)
  • Pedlosky, J., (1987) Geophysical Fluid Dynamics, , 2nd ed. (Springer-Verlag, New York)
  • Whitham, G.B., (1974) Linear and Nonlinear Waves, , (Wiley, New York)
  • Dyachenko, A.I., Korotkevich, A.O., Zakharov, V.E., (2004) Phys. Rev. Lett., 92, p. 134501. , PRLTAO 0031-9007 10.1103/PhysRevLett.92.134501
  • Yokoyama, N., Statistics of gravity waves obtained by direct numerical simulation (2004) Journal of Fluid Mechanics, 501, pp. 169-178. , DOI 10.1017/S0022112003007444
  • Marche, F., Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects (2007) European Journal of Mechanics, B/Fluids, 26 (1), pp. 49-63. , DOI 10.1016/j.euromechflu.2006.04.007, PII S0997754606000719
  • Choi, W., (1995) J. Fluid Mech., 295, p. 381. , JFLSA7 0022-1120 10.1017/S0022112095002011
  • Mininni, P.D., Montgomery, D.C., Pouquet, A.G., A numerical study of the alpha model for two-dimensional magnetohydrodynamic turbulent flows (2005) Physics of Fluids, 17 (3), pp. 0351121-03511217. , DOI 10.1063/1.1863260, 035112
  • Mininni, P.D., Montgomery, D.C., Pouquet, A., Numerical solutions of the three-dimensional magnetohydrodynamic α model (2005) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 71 (4), pp. 046304/1-046304/11. , http://scitation.aip.org/getpdf/servlet/GetPDFServlet?filetype= pdf&id=PLEEE8000071000004046304000001&idtype=cvips, DOI 10.1103/PhysRevE.71.046304, 046304
  • Foias, C., Holm, D.D., Titi, E.S., The Navier-Stokes-alpha model of fluid turbulence (2001) Physica D: Nonlinear Phenomena, 152-153, pp. 505-519. , DOI 10.1016/S0167-2789(01)00191-9, PII S0167278901001919
  • Camassa, R., Holm, D.D., (1993) Phys. Rev. Lett., 71, p. 1661. , PRLTAO 0031-9007 10.1103/PhysRevLett.71.1661
  • Graham, J.P., Holm, D.D., Mininni, P.D., Pouquet, A., Highly turbulent solutions of the Lagrangian-averaged Navier-Stokes α model and their large-eddy-simulation potential (2007) Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 76 (5), p. 056310. , http://oai.aps.org/oai?verb=GetRecord&Identifier=oai:aps.org: PhysRevE.76.056310&metadataPrefix=oai_apsmeta_2, DOI 10.1103/PhysRevE.76.056310
  • L'Vov, V.S., L'Vov, Y., Newell, A.C., Zakharov, V., (1997) Phys. Rev. e, 56, p. 390. , 1063-651X 10.1103/PhysRevE.56.390
  • Gomez, D.O., Mininni, P.D., Dmitruk, P., MHD simulations and astrophysical applications (2005) Advances in Space Research, 35 (5), pp. 899-907. , DOI 10.1016/j.asr.2005.02.099, PII S0273117705004734, Fundamentals of Space Environment Science
  • Gomez, D.O., Mininni, P.D., Dmitruk, P., Parallel simulations in turbulent MHD (2005) Physica Scripta T, T116, pp. 123-127. , DOI 10.1238/Physica.Topical.116a00123, International Workshop on Theoretical Plasma Physics: Modern Plasma Science
  • Mininni, P., Rosenberg, D., Reddy, R., Pouquet, A., (2011) Parallel Computing, 37, p. 316. , PACOEJ 0167-8191 10.1016/j.parco.2011.05.004
  • Canuto, C., Hussaini, M., Quarteroni, A., Zang, T., (1988) Spectral Methods in Fluid Dynamics, , corrected 3rd print ed. (Springer-Verlag, Berlin/New York)
  • Falkovich, G., (1994) Phys. Fluids, 6, p. 1411. , PHFLE6 1070-6631 10.1063/1.868255
  • Krstulovic, G., Brachet, M., (2011) Phys. Rev. Lett., 106, p. 115303. , PRLTAO 0031-9007 10.1103/PhysRevLett.106.115303
  • Miquel, B., Mordant, N., (2011) Phys. Rev. e, 84, p. 066607. , PLEEE8 1539-3755 10.1103/PhysRevE.84.066607
  • Longuet-Higgins, M.S., (1963) J. Fluid Mech., 16, p. 138. , JFLSA7 0022-1120 10.1017/S0022112063000641
  • Herbert, E., Mordant, N., Falcon, E., (2010) Phys. Rev. Lett., 105, p. 144502. , PRLTAO 0031-9007 10.1103/PhysRevLett.105.144502
  • Azzalini, A., (1985) Scandinavian Journal of Statistic, 12, p. 171
  • Tayfun, M.A., (1980) J. Geophys. Res.: Oceans, 85, p. 1548. , JGREA2 0148-0227 10.1029/JC085iC03p01548
  • Choi, Y., Lvov, Y.V., Nazarenko, S., (2004) Phys. Lett. A, 332, p. 230. , PYLAAG 0375-9601 10.1016/j.physleta.2004.09.062
  • Lvov, Y.V., Nazarenko, S., (2004) Phys. Rev. e, 69, p. 066608. , PLEEE8 1539-3755 10.1103/PhysRevE.69.066608
  • Choi, Y., Lvov, Y.V., Nazarenko, S., Joint statistics of amplitudes and phases in wave turbulence (2005) Physica D: Nonlinear Phenomena, 201 (1-2), pp. 121-149. , DOI 10.1016/j.physd.2004.11.016, PII S016727890400466X

Citas:

---------- APA ----------
Clark Di Leoni, P., Cobelli, P.J. & Mininni, P.D. (2014) . Wave turbulence in shallow water models. Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, 89(6).
http://dx.doi.org/10.1103/PhysRevE.89.063025
---------- CHICAGO ----------
Clark Di Leoni, P., Cobelli, P.J., Mininni, P.D. "Wave turbulence in shallow water models" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics 89, no. 6 (2014).
http://dx.doi.org/10.1103/PhysRevE.89.063025
---------- MLA ----------
Clark Di Leoni, P., Cobelli, P.J., Mininni, P.D. "Wave turbulence in shallow water models" . Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, vol. 89, no. 6, 2014.
http://dx.doi.org/10.1103/PhysRevE.89.063025
---------- VANCOUVER ----------
Clark Di Leoni, P., Cobelli, P.J., Mininni, P.D. Wave turbulence in shallow water models. Phys. Rev. E Stat. Nonlinear Soft Matter Phys. 2014;89(6).
http://dx.doi.org/10.1103/PhysRevE.89.063025