Statistical properties of turbulence: An overview

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 ϕ, 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 kin j in the turbulent fluid. We show that the Cahn-Hilliard-Navier-Stokes coupling leads to an arrest of phase separation at a length scale Lc, which we evaluate from S(k), the spectrum of the fluctuations of ϕ. We demonstrate that (a) Lc ~ LH, the Hinze scale that follows from balancing inertial and interfacial-tension forces, and (b) Lc 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 kc, which we show is ≃2π/Lc. We compare our work with earlier studies of this problem.

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“…We are interested in 2D incompressible fluids, so we use the following stream-function-vorticity formulation363738 for the momentum equation:…”

Section: Resultsmentioning

confidence: 99%

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

Perlekar

Pal

Pandit

2017

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“…In turbulent flows, the non-Newtonian nature of polymer solutions manifests itself through a considerable reduction of the turbulent drag compared to that of the solvent alone [2][3][4][5][6]. What renders this phenomenon even more remarkable is that an appreciable drag reduction can already be observed at very small polymer concentrations (of the order of a few parts per million).…”

Section: Introductionmentioning

confidence: 99%

Impact of the Peterlin approximation on polymer dynamics in turbulent flows

et al. 2015

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We study the impact of the Peterlin approximation on the statistics of the end-to-end separation of polymers in a turbulent flow. The finitely extensible nonlinear elastic (FENE) model and the FENE model with the Peterlin approximation (FENE-P) are numerically integrated along a large number of Lagrangian trajectories resulting from a direct numerical simulation of three-dimensional homogeneous isotropic turbulence. Although the FENE-P model yields results in qualitative agreement with those of the FENE model, quantitative differences emerge. The steady-state probability of large extensions is overestimated by the FENE-P model. The alignment of polymers with the eigenvectors of the rate-of-strain tensor and with the direction of vorticity is weaker when the Peterlin approximation is used. At large Weissenberg numbers, the correlation times of both the extension and of the orientation of polymers are underestimated by the FENE-P model.

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“…For equal-time structure functions, multiscaling means that the scaling exponents are a nonlinear, convex, monotonically increasing function of p and not a linear function as suggested by simple dimensional analysis [6,17]. Given the large range of scales that we can cover in this shell model [18], E b ðkÞ reveals two distinct, power-law ranges.…”

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“…We show that a shell-model version of the 3D Hall-MHD equations [11,12], which is a generalization of MHD shell models [14][15][16], provides a natural theoretical model for investigating such multiscaling behaviors in structure functions. For equal-time structure functions, multiscaling means that the scaling exponents are a nonlinear, convex, monotonically increasing function of p and not a linear function as suggested by simple dimensional analysis [6,17]. Given the large range of scales that we can cover in this shell model [18], E b ðkÞ reveals two distinct, power-law ranges.…”

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confidence: 99%

Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model

et al. 2013

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We show that a shell-model version of the three-dimensional Hall-magnetohydrodynamic (3D Hall-MHD) equations provides a natural theoretical model for investigating the multiscaling behaviors of velocity and magnetic structure functions. We carry out extensive numerical studies of this shell model, obtain the scaling exponents for its structure functions, in both the low-k and high-k power-law ranges of three-dimensional Hall-magnetohydrodynamic, and find that the extended-self-similarity procedure is helpful in extracting the multiscaling nature of structure functions in the high-k regime, which otherwise appears to display simple scaling. Our results shed light on intriguing solar-wind measurements.

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Statistical properties of turbulence: An overview

Cited by 65 publications

References 142 publications

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

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

Impact of the Peterlin approximation on polymer dynamics in turbulent flows

Multiscaling in Hall-Magnetohydrodynamic Turbulence: Insights from a Shell Model

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