Renormalization-group analysis for the infrared properties of a randomly stirred binary fluid

Nandy, Malay K.; Bhattacharjee, Jayanta K.

doi:10.1088/0305-4470/31/11/012

Cited by 13 publications

(20 citation statements)

References 26 publications

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“…Furthermore, for calculational convenience (see below), we write ∇ψ Such a parametrization of ∇ψ yields the Eqs. of motion [6,7,8]…”

Section: Pacs Numbersmentioning

confidence: 99%

“…[6], that they exhibit only simple scaling.a. Equations of motion, their symmetries and structure functions:-It is well-known [6,7,8] that in the dynamics of a symmetric binary fluid mixture the velocity fields u couple with the concentration gradient ∇ψ and not with ψ itself. Thus it is useful to write the coupled evolution equations in terms of u and ∇ψ.…”

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confidence: 99%

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Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

Basu¹

2005

J. Stat. Mech.

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We elucidate the universal properties of the nonequilibrium steady states (NESS) 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 characterise 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 crosscorrelations between the velocity and the gradient of the concentration fields. Furthermore, we demonstrate, in agreement with Celani et al, [Phys. Rev. Lett., 89, 234502 (2002)], that the conventional structure functions as used in passive scalar turbulence studies exhibit only simple scaling in the problem of symmetric binary fluid mixture even in the weak concentration limit. We also discuss possible experimental verifications of our results. PACS numbers:Critical dynamics of equilibrium systems show universal scaling properties for thermodynamic functions and correlation functions characterised by universal scaling exponents that depend on the spatial dimension d and the symmetry of the order parameter (e.g., Ising, XY etc.) and conservation laws [1, 2], but not on the parameters that specify the details of the Hamiltonian. A different situation arises in driven, dissipative, nonequilibrium systems with nonequilibrium statistical steady states (NESS). In this letter we demonstrate that in the NESS of externally driven turbulent homogeneous and isotropic symmetric binary fluid mixtures (50-50 concentration of the two components) universal properties are characterised by certain structure functions, determined by the symmetries of the equations of motion, and which are different from those used in pasive scalar turbulence studies. We find that the universal properties vary continuously with the degree of crosscorrelations between the velocity and the gradient of the concentration fields, a situation which has no analogue in equilibrium.The turbulent hydrodynamics of an incompressible symmetric binary fluid is described by the coupled evolution of the velocity field u(x, t) and the concentration field gradient ∇ψ(x, t) with ψ(x, t) = [ρ A (x, t) − ρ B (x, t)]/ρ 0 where ρ 0 is the mean density, and ρ A and ρ B are the densities of the two components. In a symmetric binary fluid ψ(x, t) = 0. Experiments performed on such systems have been typically concerned with the measurements of effective transport coefficients [3]. In a symmetric binary mixture, ψ is not simply advected passively by the u-field, but is active, i.e., concentration gradient ∇ψ reacts back on u to produce flows. In ordinary fluid turbulence the NESS is characterised by the multiscaling exponents of the structure functions of the velocity fields (see below) [4,5]. Compared to the studies of ordinary fluid turbulence the study of turbulent binary mixtures is in it...

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“…Furthermore, for calculational convenience (see below), we write ∇ψ Such a parametrization of ∇ψ yields the Eqs. of motion [6,7,8]…”

Section: Pacs Numbersmentioning

confidence: 99%

mentioning

confidence: 99%

Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

Basu¹

2005

J. Stat. Mech.

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“…It also would be interesting to study the feedback of the KPZ scalar field on the dynamics of the advecting velocity ("active scalar"). The RG study of this problem for the linear advection-diffusion equation shows that the active term in the NS equation appears IR irrelevant for the turbulent case [56] and for the case thermal equilibrium [57]. One can hope that inclusion of the KPZ nonlinearity will produce a fully nontrivial scaling behaviour where the velocity dynamics is affected by the scalar field.…”

Section: Discussionmentioning

confidence: 99%

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation

Antonov,

Gulitskiy,

Kakin

et al. 2020

Preprint

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The Kardar-Parisi-Zhang model of non-equilibrium critical behaviour (kinetic surface roughening) with turbulent motion of the environment taken into account is studied by the field theoretic renormalization group approach. The turbulent motion is described by the stochastic Navier-Stokes equation with the random stirring force whose correlation function includes two terms that allow one to account both for a turbulent fluid and for a fluid in thermal equilibrium. The renormalization group analysis performed in the leading order of perturbation theory (one-loop approximation) reveals six possible types of scaling behaviour (universality classes). The most interesting values of the spatial dimension d = 2 and 3 correspond to the universality class of a pure turbulent advection where the nonlinearity of the Kardar-Parisi-Zhang model is irrelevant.

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“…The functions f and f ψ are forcing terms which drive the system to a statistically steady state. Galilean invariance of the system enforces λ 1 = λ 3 = 1 [14,16]. Further, λ 2 may be set to unity by appropriately choosing the unit of ψ (equivalently, by exploiting the rescaling invariance of ψ) [14].…”

Section: Model Equationsmentioning

confidence: 99%

“…where k is a wavenumber, t time, i, j Cartesian components in d-dimensions, A f and A ψ are a constant amplitude and P ij (k) = δ ij − k i k j /k 2 is the transverse projector which enforces the incompressibility condition [14]. One-loop renormalisation group studies [14,16] of this model yield K41 energy spectra for u and b fields:…”

Section: Structure Functions and Multiscalingmentioning

confidence: 99%

Universality of scaling and multiscaling in turbulent symmetric binary fluids

Ray

Basu

2011

Phys. Rev. E

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We elucidate the universal scaling and multiscaling properties of the nonequilibrium steady states (NESS) in a driven symmetric binary fluid (SBF) mixture in its homogeneous miscible phase in three dimensions (3d). We show, for the first time, via Direct Numerical Simulations (DNS) that structure functions of the velocity and the concentration gradient exhibit multiscaling in 3d and extended selfsimilarity (ESS). We also find that, in contrast to the well-known passive scalar turbulence problem, structure functions of the concentration show simple scaling. We propose a new shell model for SBF turbulence which preserve all the invariances in the ideal limit of the SBF equations and which reduces to a well-known shell model for fluid turbulence in the zero concentration field limit. We show that the shell model has the same scaling properties as the 3d SBF equations. Our combined results from our DNS of the SBF equations and shell-model studies consistently bring out the multiscaling of the velocity and concentration gradient fields and simple scaling of the concentration field.

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Renormalization-group analysis for the infrared properties of a randomly stirred binary fluid

Cited by 13 publications

References 26 publications

Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

Symmetries and novel universal properties of turbulent hydrodynamics in a symmetric binary fluid mixture

Effects of turbulent environment on the surface roughening: The Kardar-Parisi-Zhang model coupled to the stochastic Navier-Stokes equation

Universality of scaling and multiscaling in turbulent symmetric binary fluids

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