Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture. (English) Zbl 1456.76060
Summary: We elucidate the universal properties of the nonequilibrium steady states (NESSs) in a driven symmetric binary fluid mixture, an example of active advection, in its miscible phase. We use the symmetries of the equations of motion to establish the appropriate form of the structure functions which characterize the statistical properties of the NESS of a driven symmetric binary fluid mixture. We elucidate the universal properties described by the scaling exponents and the amplitude ratios. Our results suggest that these exponents and amplitude ratios vary continuously with the degree of cross-correlations between the velocity and the gradient of the concentration fields. Furthermore, we demonstrate, in agreement with earlier work, that the conventional structure functions as used in passive scalar turbulence studies exhibit only simple scaling in the problem of a symmetric binary fluid mixture even in the weak concentration limit. We also discuss possible experimental verifications of our results.
MSC:
| 76F30 | Renormalization and other field-theoretical methods for turbulence |
Keywords:
correlation functions (theory); critical exponents and amplitudes (theory); renormalization group; driven diffusive systems (theory)References:
| [1] | Fisher M E 1983 Critical Phenomena(Lect. Notes Phys.) (Berlin: Springer) |
| [2] | Hohenberg P C et al 1977 Rev. Mod. Phys.49 435 · doi:10.1103/RevModPhys.49.435 |
| [3] | Swinney H L et al 1973 Phys. Rev. A 8 2586 · doi:10.1103/PhysRevA.8.2586 |
| [4] | Frisch U 1995 Turbulence: The Legacy of A.N. Kolmogorov (Cambridge: Cambridge University Press) · Zbl 0832.76001 · doi:10.1017/CBO9781139170666 |
| [5] | Dhar S K et al 1997 Pramana J. Phys.48 325 · doi:10.1007/BF02845638 |
| [6] | Celani A et al 2002 Phys. Rev. Lett.89 234502 · doi:10.1103/PhysRevLett.89.234502 |
| [7] | Ruiz R and Nelson D R 1981 Phys. Rev. A 23 3224 · doi:10.1103/PhysRevA.23.3224 |
| [8] | Nandy M K et al 1998 J. Phys. A: Math. Gen.31 2621 |
| [9] | See, e.g., Antonov N V 2000 Physica D 144 370 · Zbl 0986.76026 · doi:10.1016/S0167-2789(00)00089-0 |
| [10] | For some details, see Basu A unpublished |
| [11] | Chertkov M et al 1995 Phys. Rev. E 52 4924 · doi:10.1103/PhysRevE.52.4924 |
| [12] | Chertkov M et al 1996 Phys. Rev. Lett.76 2706 · doi:10.1103/PhysRevLett.76.2706 |
| [13] | Gawedzki K and Kupiainen A 1995 Phys. Rev. Lett.75 3834 · doi:10.1103/PhysRevLett.75.3834 |
| [14] | Bernard D et al 1996 Phys. Rev. E 54 2564 · doi:10.1103/PhysRevE.54.2564 |
| [15] | Adzhemyan L Ts et al 1998 Phys. Rev. E 58 1823 · doi:10.1103/PhysRevE.58.1823 |
| [16] | Basu A 2004 Europhys. Lett.65 505 · doi:10.1209/epl/i2003-10110-7 |
| [17] | Kolmogorov A N 1941 C. R. Acad. Sci. USSR30 301 · JFM 67.0850.06 |
| [18] | Adzhemyan L Ts et al 1999 The Field Theoretic Renormalization Group in Fully Developed Turbulence (London: Gordon and Breach) · Zbl 0956.76002 |
| [19] | Zinn-Justin J 1989 Quantum Field Theory and Critical Phenomena (Oxford: Clarendon) |
| [20] | Poorte R E G and Biesheuvel A 2002 J. Fluid Mech.461 127 · Zbl 0994.76504 · doi:10.1017/S0022112002008273 |
| [21] | Gylfason A and Warhaft Z 2004 Phys. Fluids16 4012 and references therein · Zbl 1187.76198 · doi:10.1063/1.1790472 |
| [22] | See, e.g., Goldberg W I and Huang J S 1975 Fluctuations, Instabilities and Phase Transitions ed T Riste (New York: Plenum) |
| [23] | Sain A et al 1998 Phys. Rev. Lett.81 4377 · doi:10.1103/PhysRevLett.81.4377 |
| [24] | Drossel B et al 2003 Preprint cond-mat/0307579 |
| [25] | Basu A and Frey E 2004 Phys. Rev. E 69 015101(R) · doi:10.1103/PhysRevE.69.015101 |
| [26] | Doering C R and Gibbon J D 1995 Applied Analysis of the Navier-Stokes Equation (Cambridge: Cambridge University Press) · Zbl 0838.76016 · doi:10.1017/CBO9780511608803 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
