No abstract

We have just become aware of the following typographical errors: 1. The second equation of Eq. (1) should read asThe corresponding definition of T αβ , 10 lines below Eq. (1), should read as2. The second equation of Eq.(2) should read as3. On the second page, the definitions of n,vv , n,bb , n,bv , and n,vb are missing a complex conjugate symbol "*" over the brackets "(...)".The corrections above do not affect the results presented in the paper because our computer program used the correct equations. We thank Sagar Chakraborty for discussions. 039903-1 1539-3755/2011/83(3)/039903 (1)

We derive relations for the decay of the kinetic and magnetic energies and the growth of the Taylor and integral scales in unforced, incompressible, homogeneous and isotropic three-dimensional magnetohydrodynamic (3DMHD) turbulence with power-law initial energy spectra. We also derive bounds for the decay of the cross-and magnetic helicities. We then present results from systematic numerical studies of such decay both within the context of an MHD shell model and direct numerical simulations (DNS) of 3DMHD. We show explicitly that our results about the power-law decay of the energies hold for times t < t * , where t * is the time at which the integral scales become comparable to the system size. For t < t * , our numerical results are consistent with those predicted by the principle of 'permanence of large eddies'.

We present results from a systematic direct-numerical simulation study of pressure fluctuations in an unforced, incompressible, homogeneous, and isotropic three-dimensional turbulent fluid. At cascade completion, isosurfaces of low pressure are found to be organized as slender filaments, whereas the predominant isostructures appear sheetlike. We exhibit several results, including plots of probability distributions of the spatial pressure difference, the pressure-gradient norm, and the eigenvalues of the pressure-Hessian tensor. Plots of the temporal evolution of the mean pressure-gradient norm, and the mean eigenvalues of the pressure-Hessian tensor are also exhibited. We find the statistically preferred orientations between the eigenvectors of the pressure-Hessian tensor, the pressure gradient, the eigenvectors of the strain-rate tensor, the vorticity, and the velocity. Statistical properties of the nonlocal part of the pressure-Hessian tensor are also exhibited. We present numerical tests (in the viscous case) of some conjectures of Ohkitani [Phys. Fluids A 5, 2570 (1993)] and Ohkitani and Kishiba [Phys. Fluids 7, 411 (1995)] concerning the pressure-Hessian and the strain-rate tensors, for the unforced, incompressible, three-dimensional Euler equations.

We present results from a systematic numerical study of decaying turbulence in a dilute polymer solution by using a shell-model version of the FENE-P equations. Our study leads to an appealing definition of drag reduction for the case of decaying turbulence. We exhibit several new results, such as the potential-energy spectrum of the polymer, hitherto unobserved features in the temporal evolution of the kinetic-energy spectrum, and characterize intermittency in such systems. We compare our results with the GOY shell model for fluid turbulence.PACS numbers: 47.27.Gs, 83.60.YzThe phenomenon of drag reduction by polymer additives[1], whereby dilute solutions of linear, flexible, high-molecular-weight polymers exhibit frictional resistance to flow much lower than that of the pure solvent, has almost exclusively been studied within the context of statistically steady turbulent flows since the pioneering work of Toms [2]. By contrast, there is an extreme scarcity of results concerning the effects of polymer additives on decaying turbulence [3]. Experimental studies of decaying, homogeneous turbulence behind a grid indicate, for such dilute polymer solutions, a turbulent energy spectrum similar to that found without polymers [4,5]. However, flow visualization via die-injection tracers[5] and particle image velocimetry [6] show an inhibition of small-scale structures in the presence of polymer additives. To the best of our knowledge decaying turbulence in such polymer solutions has not been studied numerically. We initiate such a study here by using a shell model that is well suited to examining the effects of polymer additives in turbulent flows that are homogeneous and in which bounding walls have no direct role. We obtain several interesting results including a natural definition of the percentage dragreduction DR, which has been lacking for the case of decaying turbulence. We show that the dependence of DR on the polymer concentration c is in qualitative accord with experiments[1] as is the suppression of small-scale structures which we quantify by obtaining the filteredwavenumber-dependence of the flatness of the velocity field. We will use a shell-model version of the FENE-P (Finitely Extensible Nonlinear Elastic -Peterlin) [7,8] model for dilute polymer solutions that has often been used for studying viscoelastic effects since it contains the basic characteristics of molecular stretching, orientation and finite extensibility seen in polymer molecules. A direct numerical simulation of the FENE-P equations is computationally prohibitive. This motivates the use of a shell model that captures the essential features of the FENE-P equations. Recent studies [9] have exploited a formal analogy[10] of the FENE-P equations with those of magnetohydrodynamics (MHD) to construct such a shell model. We investigate decaying turbulence in a dilute polymer solution by developing a similar shell model for the FENE-P equations. The unforced FENE-P equations [7,8] arewhere p is the pressure, ν s the kinematic viscosity of the solven...