Universality of scaling and multiscaling in turbulent symmetric binary fluids

Abstract

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.

Hydrodynamic descriptions for surface roughness in fracture front propagation

“…We consider several hydrodynamic models related to hydrodynamic turbulence. We show that in different limits the model equations formally resemble a range of well-known stochastically driven dynamical equations describing a moving Kardar-Parisi-Zhang surface (KPZ) [9] see also [10] with quenched disorder, passive scalar turbulence [11], magnetohydrodynamic (MHD) turbulence [12] and binary fluid turbulence [13]. We interpret the phenomenological similarities between a fracture surface and hydrodynamic surface in terms of these formal mathematical resemblances between the respective dynamical equations.…”

“…with ∇.v = 0 since we consider an incompressible fluid; and Ampère's law for a conducting fluid becomes ∂b ∂t It is well known that both binary fluid and MHD turbulence display turbulence-like behaviour for sufficiently strong external forces. In fact all the relevant dynamical variables v, b and c display multiscaling [13,27]. With that analogy in mind, it may be concluded that both u and u ⊥ should display turbulence-like behaviour.…”

Two-dimensional Turbulence in Symmetric Binary-Fluid Mixtures: Coarsening Arrest by the Inverse Cascade

“…Some groups have also studied the statistical properties of turbulent, symmetric, binary-fluid mixtures above the consolute point, where the two fluids mix even in the absence of turbulence 40 49 50 . In these studies, there is, of course, neither coarsening nor coarsening arrest.…”

Multiscaling in superfluid turbulence: A shell-model study

“…Ever since their introduction in the early work of Obukhov [27], Desnyansky and Novikov [28], and Gledzer, and Ohkitani and Yamada [29,30] (henceforth GOY), shell models have played valuable roles in elucidating the multiscaling properties of structure functions of fluid turbulence [1,[31][32][33][34][35][36][37][38]. Over the years, such shell models have been used to study magnetohydrodynamic (MHD) turbulence [39][40][41][42][43][44], Hall-MHD turbulence [45][46][47][48], fluid turbulence with polymer additives [49], fluid turbulence in two dimensions [50], fluid turbulence in dimensions in between two and three [51], turbulence in binary-fluid mixtures [52] and in rotating systems [53], and, as we have mentioned above, turbulence in superfluids [24][25][26]. Shell models have also been used to initiate studies of the dynamic multiscaling of time-dependent structure functions [54][55][56].…”