Polymers in 2D turbulence: suppression of large scale fluctuations

Applications of Water-Soluble Polymers in Turbulent Drag Reduction

Water-soluble polymers with high molecular weights are known to decrease the frictional drag in turbulent flow very effectively at concentrations of tens or hundreds of ppm. This drag reduction efficiency of water-soluble polymers is well known to be closely associated with the flow conditions and rheological, physical, and/or chemical characteristics of the polymers added. Among the many promising polymers introduced in the past several decades, this review focuses on recent progress in the drag reduction capability of various water-soluble macromolecules in turbulent flow including both synthetic and natural polymers such as poly(ethylene oxide), poly(acrylic acid), polyacrylamide, poly(N-vinyl formamide), gums, and DNA. The polymeric species, experimental parameters, and numerical analysis of these water-soluble polymers in turbulent drag reduction are highlighted, along with several existing and potential applications. The proposed drag reduction mechanisms are also discussed based on recent experimental and numerical researches. This article will be helpful to the readers to understand better the complex behaviors of a turbulent flow with various water-soluble polymeric additives regarding experimental conditions, drag reduction mechanisms, and related applications.

Collective Motion of Microorganisms in a Viscoelastic Fluid

We study the collective motion of a suspension of rodlike microswimmers in a two-dimensional film of viscoelastic fluids. We find that the fluid elasticity has a small effect on a suspension of pullers, while it significantly affects the pushers. The attraction and orientational ordering of the pushers are enhanced in viscoelastic fluids. The induced polymer stresses break down the large-scale flow structures and suppress velocity fluctuations. In addition, the energy spectra and induced mixing in the suspension of pushers are greatly modified by fluid elasticity.

Gravity-driven soap film dynamics in subcritical regimes

We undertake the analysis of soap-film dynamics with the classical approach of asymptotic expansions. We focus our analysis in vertical soap film tunnels operating in subcritical regimes with elastic Mach numbers M(e)=O((10(-1))). Considering the associated set of nondimensional numbers that characterize this flow, we show that the flow behaves as a two-dimensional (2D) divergence free flow with variable mass density. When the soap film dynamics agrees with that of a 2D and almost constant mass density flow, the regions where the second invariant of the velocity gradient is non-null correspond to regions where the rate of change of film thickness is non-negligible.

Inhibition of wave-driven two-dimensional turbulence by viscoelastic films of proteins

To model waves, surface flows, and particle dispersion at the air-water interface one needs to know the essential mechanisms affecting the fluid motion at the surface. We show that a thin film (less than 10-nm thick) of adsorbed protein dramatically affects two-dimensional turbulence generated by Faraday waves at the fluid surface. Extremely low concentrations (≈1 ppm) of soluble proteins form a strong viscoelastic layer which suppresses turbulent diffusion at the surface, changes wave patterns, and shows strong resilience to the wave-induced droplet generation. Surface shear properties of the film play a key role in this phenomenon by inhibiting the creation of vorticity at the surface. The addition of surfactants, on the other hand, destroys the nanolayer and restores the fluid mobility.

Two-dimensional homogeneous isotropic fluid turbulence with polymer additives

We carry out an extensive and high-resolution direct numerical simulation of homogeneous, isotropic turbulence in two-dimensional fluid films with air-drag-induced friction and with polymer additives. Our study reveals that the polymers (a) reduce the total fluid energy, enstrophy, and palinstrophy; (b) modify the fluid energy spectrum in both inverse- and forward-cascade régimes; (c) reduce small-scale intermittency; (d) suppress regions of high vorticity and strain rate; and (e) stretch in strain-dominated regions. We compare our results with earlier experimental studies and propose new experiments.

Polymer effects on small- and large-scale two-dimensional turbulence

We investigate the effect of dilute polymers on driven two-dimensional turbulence in a soap film. Transitions from strong to weak turbulence are identified by independently varying the polymer concentration phi and the energy injection rate epsilon(inj) . Studies of velocity structures in small scales reveal that strong saddles are suppressed, whereas weak ones become more populated. Interestingly, this redistribution of saddle points in turbulent flows strongly correlates with the quenching of velocity fluctuations on large scales, suggesting that this hydrodynamic structure may play a role in transferring energy from scale to scale.

Experiments and direct numerical simulations of two-dimensional turbulence

Experiments and direct numerical simulations reveal the coexistence of two cascades in two-dimensional grid turbulence. Several features of this flow such as the energy density and the scalar spectra are found to be consistent with well known theoretical predictions. The energy transfer function displays the expected up-scale energy transfers. The vorticity correlation function is logarithmic and thus consistent with recently proposed models.

Batchelor scaling in fast-flowing soap films

The dynamics of a passive scalar such as a dye in the far dissipative range of fluid turbulence is a central problem in nonlinear physics. An important prediction for this problem was made by Batchelor over 40 years ago and is known as Batchelor's scaling law. We here present strong evidence in favor of this law for the thickness fluctuations in the flow of a soap film past a flat plate. The results also capture the dissipative range of the scalar which turns out to have universal features. The probability density function of the scalar increments and their structure functions come out in nice agreement with theoretical predictions.

Polymers suppress the inverse transfers of energy and the enstrophy flux fluctuations in two-dimensional turbulence

The addition of minute amounts of a flexible polymer to two-dimensional turbulence produced in fast-flowing soap films affects large scales and small scales differently. For large scales, the inverse transfers of energy are suppressed. For small scales, where mean quantities are barely affected, the enstrophy flux fluctuations are significantly reduced, making the flow less chaotic.

Two-dimensional turbulence of dilute polymer solutions

We investigate theoretically and numerically the effect of polymer additives on two-dimensional turbulence by means of a viscoelastic model. We provide compelling evidence that, at vanishingly small concentrations, such that the polymers are passively transported, the probability distribution of polymer elongation has a power law tail: Its slope is related to the statistics of finite-time Lyapunov exponents of the flow, in quantitative agreement with theoretical predictions. We show that at finite concentrations and sufficiently large elasticity the polymers react on the flow with manifold consequences: Velocity fluctuations are drastically depleted, as observed in soap film experiments; the velocity statistics becomes strongly intermittent; the distribution of finite-time Lyapunov exponents shifts to lower values, signaling the reduction of Lagrangian chaos.