Erratum: Drag reduction by polymer additives in decaying turbulence [Phys. Rev. E72, 017301 (2005)]

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)

Elastic turbulence in a shell model of polymer solution

“…Shell models of polymer solutions have been successfully applied to the study of drag reduction in forced [28,32,33] and decaying [29] turbulence, two-dimensional turbulence with polymer additives [34], and turbulent thermal convection in viscoelastic fluids [35,36]. Here, we study a shell model of polymer solution in the regime of low inertia and high elasticity.…”

“…Despite the fact that they are not derived from the principle hydrodynamic equations in any rigorous way, they have played a fundamental role in the study of fluid turbulence since they are numerically tractable [16][17][18][19]. Shell models have also achieved remarkable success in problems related to passive-scalar turbulence [20][21][22][23], magnetohydrodynamic turbulence [24], rotating turbulence [25], binary fluids [26,27], and fluids with polymer additives [28,29]. Furthermore, the mathematical study of shell models has yielded several rigorous results, whose analogs are still lacking for the three-dimensional Navier-Stokes equations (e.g., Refs.…”

“…-We consider the shell model of polymer solution introduced by Kalelkar et al [29], which is based on a shell model initially proposed for three-dimensional magnetohydrodynamics [37,39] and reduces to the GOY model [40,41] when polymers are absent. The shell model by Kalelkar et al [29] can be regarded as a reduced, low-dimensional version of the FENE model [42]. It describes the temporal evolution of a set of complex scalar variables v n and b n representing the velocity field and the polymer end-toend separation field, respectively.…”

“…(2) in order to improve numerical stability [29,32,33], and the forcing f n drives the system to a non-equilibrium statistically stationary state. In particular we use either a deterministic forcing f n = f 0 (1 + ı)δ n,2 or a white-in-time Gaussian stochastic forcing with amplitude f 0 acting on the n = 2 shell.…”

“…It describes the temporal evolution of a set of complex scalar variables v n and b n representing the velocity field and the polymer end-toend separation field, respectively. The variables v n and b n evolve according to the following equations [29]:…”