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Antibubbles, which consist of a shell of a low-density fluid inside a high-density fluid, have several promising applications. We show, via extensive direct numerical simulations (DNSs), in both two and three dimensions (2D and 3D), that the spatiotemporal evolution of antibubbles can be described naturally by the coupled Cahn-Hilliard-Navier-Stokes (CHNS) equations for a binary fluid. Our DNSs capture elegantly the gravity-induced thinning and breakup of an antibubble via the time evolution of the Cahn-Hilliard scalar order parameter field $\phi$, which varies continuously across interfaces, so we do not have to enforce complicated boundary conditions at the moving antibubble interfaces. To ensure that our results are robust, we supplement our CHNS simulations with sharp-interface Volume-of-Fluid (VoF) DNSs. We track the thickness of the antibubble and calculate the dependence of the lifetime of an antibubble on several parameters; we show that our DNS results agree with various experimental results; in particular, the velocity with which the arms of the antibubble retract after breakup scales as $\sigma^{1/2}$, where $\sigma$ is the surface tension., Comment: Ancillary folder contains movies and supplementary material -->

We present a study of a two-point spectral turbulence model (Local Wave-Number model or LWN model) for the Rayleigh-Taylor (RT) instability. The model outcomes are compared with statistical quantities extracted from three-dimensional simulation of the RT problem. These simulations are initialized with high wavenumber perturbations at the interface of a heavy fluid placed on top of a light fluid so that the density gradient is in the direction opposite to acceleration due to gravity. We consider flows of low to medium density contrast and compare the LWN model against simulation data using the mix-width evolution as the primary metric. The original model specified physically reasonable but largely \emph{ad hoc} terms to account for the inhomogeneous mechanisms involved in growing the mixing layer. We systematically assess the role of each of the terms in the LWN model equations by comparison with simulation. Two of these, the kinematic source term, introduced to maintain a finite covariance between density and specific volume, and a spectral distortion term, introduced as spectral modifications of the density-specific-volume covariance, both result in severely over-predicting the mix layer growth. A simplified model eliminating those two terms is shown to improve the capture of both mix-width evolution as well as the turbulent mass flux velocity profiles across the mix layer at different times. However, this simplification reveals that fidelity to other metrics such as the density-specific-volume covariance, and the turbulent kinetic energy are somewhat compromised. The implications of this outcome are discussed with respect to the physics of the RT problem, and we provide this study as a guide for the practical use of such a model.

A string of tracers, interacting elastically, in a turbulent flow is shown to have a dramatically different behaviour when compared to the non-interacting case. In particular, such an elastic chain shows strong preferential sampling of the turbulent flow unlike the usual tracer limit: an elastic chain is trapped in the vortical regions and not the straining ones. The degree of preferential sampling and its dependence on the elasticity of the chain is quantified via the Okubo-Weiss parameter. The effect of modifying the deformability of the chain, via the number of links that form it, is also examined., Comment: 6 pages, 4 figures

We present a study of buoyancy-driven variable-density homogeneous turbulence, using a two-point spectral closure model. We compute the time-evolution of the spectral distribution in wavenumber $k$ of the correlation of density and specific-volume $b(k)$, the mass flux $\bm{a}(k)$, and the turbulent kinetic energy $E(k)$, using a set of coupled equations. Under the modeling assumptions, each dynamical variable has two coefficients governing spectral transfer among modes. In addition, the mass flux $\bm{a}(k)$ has two coefficients governing the drag between the two fluids. Using a prescribed initial condition for $b(k)$ and starting from a quiescent flow, we first evaluate the relative importance of the different coefficients used to model this system, and their impact on the statistical quantities. We next assess the accuracy of the model, relative to Direct Numerical simulation of the complete hydrodynamical equations, using $b$, ${\bm a}$ and $E$ as metrics. We show that the model is able to capture the spectral distribution and global means of all three statistical quantities at both low and high Atwood number for a set of optimized coefficients. The optimization procedure also permits us to discern a minimal set of four coefficients which are sufficient to yield reasonable results while pointing to the mechanisms that dominate the mixing process in this problem., Comment: 15 pages, 11 figures

In quantum systems, signatures of multifractality are rare. They have been found only in the multiscaling of eigenfunctions at critical points. Here we demonstrate multifractality in the magnetic-field-induced universal conductance fluctuations of the conductance in a quantum condensed-matter system, namely, high-mobility single-layer graphene field-effect transistors. This multifractality decreases as the temperature increases or as doping moves the system away from the Dirac point. Our measurements and analysis present evidence for an incipient Anderson-localization near the Dirac point as the most plausible cause for this multifractality. Our experiments suggest that multifractality in the scaling behaviour of local eigenfunctions are reflected in macroscopic transport coefficients. We conjecture that an incipient Anderson-localization transition may be the origin of this multifractality. It is possible that multifractality is ubiquitous in transport properties of low-dimensional systems. Indeed, our work suggests that we should look for multifractality in transport in other low-dimensional quantum condensed-matter systems.

The Beale-Kato-Majda theorem contains a single criterion that controls the behaviour of solutions of the $3D$ incompressible Euler equations. Versions of this theorem are discussed in terms of the regularity issues surrounding the $3D$ incompressible Euler and Navier-Stokes equations together with a phase-field model for the statistical mechanics of binary mixtures called the $3D$ Cahn-Hilliard-Navier-Stokes (CHNS) equations. A theorem of BKM-type is established for the CHNS equations for the full parameter range. Moreover, for this latter set, it is shown that there exists a Reynolds number and a bound on the energy-dissipation rate that, remarkably, reproduces the $Re^{3/4}$ upper bound on the inverse Kolmogorov length normally associated with the Navier-Stokes equations alone. An alternative length-scale is introduced and discussed, together with a set of pseudo-spectral computations on a $128^{3}$ grid., Comment: 3 figures and 3 tables

We consider the 3D Cahn-Hilliard equations coupled to, and driven by, the forced, incompressible 3D Navier-Stokes equations. The combination, known as the Cahn-Hilliard-Navier-Stokes (CHNS) equations, is used in statistical mechanics to model the motion of a binary fluid. The potential development of singularities (blow-up) in the contours of the order parameter $\phi$ is an open problem. To address this we have proved a theorem that closely mimics the Beale-Kato-Majda theorem for the $3D$ incompressible Euler equations [Beale et al. Commun. Math. Phys., Commun. Math. Phys., ${\rm 94}$, $ 61-66 ({\rm 1984})$]. By taking an $L^{\infty}$ norm of the energy of the full binary system, designated as $E_{\infty}$, we have shown that $\int_{0}^{t}E_{\infty}(\tau)\,d\tau$ governs the regularity of solutions of the full 3D system. Our direct numerical simulations (DNSs), of the 3D CHNS equations, for (a) a gravity-driven Rayleigh Taylor instability and (b) a constant-energy-injection forcing, with $128^3$ to $512^3$ collocation points and over the duration of our DNSs, confirm that $E_{\infty}$ remains bounded as far as our computations allow., Comment: 11 pages, 3 figures

We present an extensive direct numerical simulation of statistically steady, homogeneous, isotropic turbulence in two-dimensional, binary-fluid mixtures with air-drag-induced friction by using the Cahn-Hilliard-Navier-Stokes equations. We choose parameters, e.g., the surface tension, such that we have a droplet of the minority phase moving inside a turbulent background of the majority phase. We characterize the deformation of the droplet and show that it displays multifractal dynamics. The probability distribution functions of the components of the acceleration of the center of mass of the droplet exhibit wide, non-Gaussian tails. Our study reveals that the droplet enhances the energy spectrum $E(k)$ when the wavenumber $k$ is large; this enhancement leads to dissipation reduction., Comment: 11 pages, 5 figures

We study two-dimensional (2D) binary-fluid turbulence by carrying out an extensive direct numerical simulation (DNS) of the forced, statistically steady turbulence in the coupled Cahn-Hilliard and Navier-Stokes equations. In the absence of any coupling, we choose parameters that lead (a) to spinodal decomposition and domain growth, which is characterized by the spatiotemporal evolution of the Cahn-Hilliard order parameter $\phi$, and (b) the formation of an inverse-energy-cascade regime in the energy spectrum $E(k)$, in which energy cascades towards wave numbers $k$ that are smaller than the energy-injection scale $k_{inj}$ in the turbulent fluid. We show that the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale $L_c$, which we evaluate from $S(k)$, the spectrum of the fluctuations of $\phi$. We demonstrate that (a) $L_c \sim L_H$, the Hinze scale that follows from balancing inertial and interfacial-tension forces, and (b) $L_c$ is independent, within error bars, of the diffusivity $D$. We elucidate how this coupling modifies $E(k)$ by blocking the inverse energy cascade at a wavenumber $k_c$, which we show is $\simeq 2\pi/L_c$. We compare our work with earlier studies of this problem.