Spectra of turbulence in dilute polymer solutions

We investigate turbulence in dilute polymer solutions when polymers are strongly stretched by the flow. We establish power-law spectrum of velocity, which is not associated with a flux of a conserved quantity, in two cases. The first case is the elastic waves range of high Reynolds number turbulence of polymer solutions above the coil-stretch transition. The second case is the elastic turbulence, where chaotic flow is excited due to elastic instabilities at small Reynolds numbers.Comment: 14 pages, RevTe

The Influence of Ambiguity and Noise on the Measurement of Turbulent Spectra by Doppler Scattering

A fundamental uncertainty in velocity measurement by Doppler scattering is caused by the finite residence time of the scattering particles in the observation volume; the arrival of scattering particles at arbitrary times gives rise to fluctuations in phase (and hence frequency) of the observed Doppler frequency. An estimate is obtained for the spectrum of these frequency fluctuations (called ambiguity noise). The frequency at which the spectral levels of a turbulent signal and the ambiguity noise are equal, provides a limit to the temporal resolution of an instantaneous velocity measurement; this limit is obtained, and shown to be quite restrictive. The influence of electronic noise is also analyzed and found to be negligible. An experimental installation is described in which instantaneous fluctuating turbulent velocities may be measured by Doppler scattering using coherent radiation from a laser. Measurements are presented of the spectra of ambiguity noise end electronic noise. The agreement with theory is excellent

Second-order closures for compressible turbulence

This viewgraph presentation discusses project description, turbulence models, and computational engine and results for second-order closures for compressible turbulence

Toward a structural understanding of turbulent drag reduction: nonlinear coherent states in viscoelastic shear flows

Nontrivial steady flows have recently been found that capture the main structures of the turbulent buffer layer. We study the effects of polymer addition on these "exact coherent states" (ECS) in plane Couette flow. Despite the simplicity of the ECS flows, these effects closely mirror those observed experimentally: Structures shift to larger length scales, wall-normal fluctuations are suppressed while streamwise ones are enhanced, and drag is reduced. The mechanism underlying these effects is elucidated. These results suggest that the ECS are closely related to buffer layer turbulence.Comment: 5 pages, 3 figures, published version, Phys. Rev. Lett. 89, 208301 (2002

Small scale statistics of viscoelastic turbulence

The small scale statistics of homogeneous isotropic turbulence of dilute polymer solutions is investigated by means of direct numerical simulations of a simplified viscoelastic fluid model. It is found that polymers only partially suppress the turbulent cascade below the Lumley scale, leaving a remnant energy flux even for large elasticity. As a consequence, fluid acceleration in viscoelastic flows is reduced with respect to Newtonian turbulence, whereas its rescaled probability density is left unchanged. At large scales the velocity field is found to be unaffected by the presence of polymers.Comment: 7 pages, 4 figure

Dynamics of threads and polymers in turbulence: power-law distributions and synchronization

We study the behavior of threads and polymers in a turbulent flow. These objects have finite spatial extension, so the flow along them differs slightly. The corresponding drag forces produce a finite average stretching and the thread is stretched most of the time. Nevertheless, the probability of shrinking fluctuations is significant and is known to decay only as a power-law. We show that the exponent of the power law is a universal number independent of the statistics of the flow. For polymers the coil-stretch transition exists: the flow must have a sufficiently large Lyapunov exponent to overcome the elastic resistance and stretch the polymer from the coiled state it takes otherwise. The probability of shrinking from the stretched state above the transition again obeys a power law but with a non-universal exponent. We show that well above the transition the exponent becomes universal and derive the corresponding expression. Furthermore, we demonstrate synchronization: the end-to-end distances of threads or polymers above the transition are synchronized by the flow and become identical. Thus, the transition from Newtonian to non-Newtonian behavior in dilute polymer solutions can be seen as an ordering transition.Comment: 13 pages, version accepted to Journal of Statistical Mechanic

Linear Stochastic Models of Nonlinear Dynamical Systems

We investigate in this work the validity of linear stochastic models for nonlinear dynamical systems. We exploit as our basic tool a previously proposed Rayleigh-Ritz approximation for the effective action of nonlinear dynamical systems started from random initial conditions. The present paper discusses only the case where the PDF-Ansatz employed in the variational calculation is ``Markovian'', i.e. is determined completely by the present values of the moment-averages. In this case we show that the Rayleigh-Ritz effective action of the complete set of moment-functions that are employed in the closure has a quadratic part which is always formally an Onsager-Machlup action. Thus, subject to satisfaction of the requisite realizability conditions on the noise covariance, a linear Langevin model will exist which reproduces exactly the joint 2-time correlations of the moment-functions. We compare our method with the closely related formalism of principal oscillation patterns (POP), which, in the approach of C. Penland, is a method to derive such a linear Langevin model empirically from time-series data for the moment-functions. The predictive capability of the POP analysis, compared with the Rayleigh-Ritz result, is limited to the regime of small fluctuations around the most probable future pattern. Finally, we shall discuss a thermodynamics of statistical moments which should hold for all dynamical systems with stable invariant probability measures and which follows within the Rayleigh-Ritz formalism.Comment: 36 pages, 5 figures, seceq.sty for sequential numbering of equations by sectio

The Polymer Stress Tensor in Turbulent Shear Flows

The interaction of polymers with turbulent shear flows is examined. We focus on the structure of the elastic stress tensor, which is proportional to the polymer conformation tensor. We examine this object in turbulent flows of increasing complexity. First is isotropic turbulence, then anisotropic (but homogenous) shear turbulence and finally wall bounded turbulence. The main result of this paper is that for all these flows the polymer stress tensor attains a universal structure in the limit of large Deborah number \De\gg 1. We present analytic results for the suppression of the coil-stretch transition at large Deborah numbers. Above the transition the turbulent velocity fluctuations are strongly correlated with the polymer's elongation: there appear high-quality "hydro-elastic" waves in which turbulent kinetic energy turns into polymer potential energy and vice versa. These waves determine the trace of the elastic stress tensor but practically do not modify its universal structure. We demonstrate that the influence of the polymers on the balance of energy and momentum can be accurately described by an effective polymer viscosity that is proportional to to the cross-stream component of the elastic stress tensor. This component is smaller than the stream-wise component by a factor proportional to \De ^2 . Finally we tie our results to wall bounded turbulence and clarify some puzzling facts observed in the problem of drag reduction by polymers.Comment: 11 p., 1 Fig., included, Phys. Rev. E., submitte

Experimental evolution reveals that sperm competition intensity selects for longer, more costly sperm

It is the differences between sperm and eggs that fundamentally underpin the differences between the sexes within reproduction. For males, it is theorized that widespread sperm competition leads to selection for investment in sperm numbers, achieved by minimizing sperm size within limited resources for spermatogenesis in the testis. Here, we empirically examine how sperm competition shapes sperm size, after more than 77 generations of experimental selection of replicate lines under either high or low sperm competition intensities in the promiscuous flour beetle Tribolium castaneum. After this experimental evolution, populations had diverged significantly in their sperm competitiveness, with sperm in ejaculates from males evolving under high sperm competition intensities gaining 20% greater paternity than sperm in ejaculates from males that had evolved under low sperm competition intensity. Males did not change their relative investment into sperm production following this experimental evolution, showing no difference in testis sizes between high and low intensity regimes. However, the more competitive males from high sperm competition intensity regimes had evolved significantly longer sperm and, across six independently selected lines, there was a significant association between the degree of divergence in sperm length and average sperm competitiveness. To determine whether such sperm elongation is costly, we used dietary restriction experiments, and revealed that protein-restricted males produced significantly shorter sperm. Our findings therefore demonstrate that sperm competition intensity can exert positive directional selection on sperm size, despite this being a costly reproductive trait