Colloquium: Theory of Drag Reduction by Polymers in Wall Bounded Turbulence

The flow of fluids in channels, pipes or ducts, as in any other wall-bounded flow (like water along the hulls of ships or air on airplanes) is hindered by a drag, which increases many-folds when the fluid flow turns from laminar to turbulent. A major technological problem is how to reduce this drag in order to minimize the expense of transporting fluids like oil in pipelines, or to move ships in the ocean. It was discovered in the mid-twentieth century that minute concentrations of polymers can reduce the drag in turbulent flows by up to 80%. While experimental knowledge had accumulated over the years, the fundamental theory of drag reduction by polymers remained elusive for a long time, with arguments raging whether this is a "skin" or a "bulk" effect. In this colloquium review we first summarize the phenomenology of drag reduction by polymers, stressing both its universal and non-universal aspects, and then proceed to review a recent theory that provides a quantitative explanation of all the known phenomenology. We treat both flexible and rod-like polymers, explaining the existence of universal properties like the Maximum Drag Reduction (MDR) asymptote, as well as non-universal cross-over phenomena that depend on the Reynolds number, on the nature of the polymer and on its concentration. Finally we also discuss other agents for drag reduction with a stress on the important example of bubbles.Comment: Invited Colloquium Paper for Reviews of Modern Physics, 24 pages, 18 Figs., submitte

Identification of Kelvin waves: numerical challenges

Kelvin waves are expected to play an essential role in the energy dissipation for quantized vortices. However, the identification of these helical distortions is not straightforward, especially in case of vortex tangle. Here we review several numerical methods that have been used to identify Kelvin waves within the vortex filament model. We test their validity using several examples and estimate whether these methods are accurate enough to verify the correct Kelvin spectrum. We also illustrate how the correlation dimension is related to different Kelvin spectra and remind that the 3D energy spectrum E(k) takes the form 1/k in the high-k region, even in the presence of Kelvin waves.Comment: 6 pages, 5 figures. The final publication is available at http://www.springerlink.co

Observation of an Inverse Energy Cascade in Developed Acoustic Turbulence in Superfluid Helium

We report observation of an inverse energy cascade in second sound acoustic turbulence in He II. Its onset occurs above a critical driving energy and it is accompanied by giant waves that constitute an acoustic analogue of the rogue waves that occasionally appear on the surface of the ocean. The theory of the phenomenon is developed and shown to be in good agreement with the experiments.Comment: 4 pages, 5 figures. The final version just prior to publicatio

Interaction of ballistic quasiparticles and vortex configurations in superfluid He3-B

The vortex line density of turbulent superfluid He3-B at very low temperature is deduced by detecting the shadow of ballistic quasiparticles which are Andreev reflected by quantized vortices. Until now the measured total shadow has been interpreted as the sum of shadows arising from interactions of a single quasiparticle with a single vortex. By integrating numerically the quasi-classical Hamiltonian equations of motion of ballistic quasiparticles in the presence of nontrivial but relatively simple vortex systems (such as vortex-vortex and vortex-antivortex pairs and small clusters of vortices) we show that partial screening can take place, and the total shadow is not necessarily the sum of the shadows. We have also found that it is possible that, upon impinging on complex vortex configurations, quasiparticles experience multiple reflections, which can be classical, Andreev, or both.Comment: To appear in Phys Rev

Dispersion Effects in Nucleon Polarisabilities

We present a formalism to extract the dynamical nucleon polarisabilities defined via a multipole expansion of the structure amplitudes in nucleon Compton scattering. In contradistinction to the static polarisabilities, dynamical polarisabilities gauge the response of the internal degrees of freedom of a composed object to an external, real photon field of arbitrary energy. Being energy dependent, they therefore contain additional information about dispersive effects induced by internal relaxation mechanisms, baryonic resonances and meson production thresholds of the nucleon. We give explicit formulae to extract the dynamical electric and magnetic dipole as well as quadrupole polarisabilities from low energy nucleon Compton scattering up to the one pion production threshold and discuss the connection to the definition of static nucleon polarisabilities. As a concrete example, we examine the results of leading order Heavy Baryon Chiral Perturbation Theory for the four leading spin independent iso-scalar polarisabilities of the nucleon. Finally, we consider the possible r{\^o}le of energy dependent effects in low energy extractions of the iso-scalar dipole polarisabilities from Compton scattering on the deuteron.Comment: 17 pages LaTeX2e with 2 figures, using includegraphicx (5 .eps files). Minor corrections, references updated. Contents identical to version to appear in Phys. Rev. C 65, spelling differen

Stable topological textures in a classical 2D Heisenberg model

We show that stable localized topological soliton textures (skyrmions) with $\pi_2$ topological charge $\nu \geq 1$ exist in a classical 2D Heisenberg model of a ferromagnet with uniaxial anisotropy. For this model the soliton exist only if the number of bound magnons exceeds some threshold value $N_{\rm cr}$ depending on $\nu$ and the effective anisotropy constant $K_{\rm eff}$. We define soliton phase diagram as the dependence of threshold energies and bound magnons number on anisotropy constant. The phase boundary lines are monotonous for both $\nu=1$ and $\nu >2$, while the solitons with $\nu=2$ reveal peculiar nonmonotonous behavior, determining the transition regime from low to high topological charges. In particular, the soliton energy per topological charge (topological energy density) achieves a minimum neither for $\nu=1$ nor high charges, but rather for intermediate values $\nu=2$ or $\nu=3$.Comment: 8 pages, 4 figure

Far-off-resonant wave interaction in one-dimensional photonic crystals with quadratic nonlinearity

We extend a recently developed Hamiltonian formalism for nonlinear wave interaction processes in spatially periodic dielectric structures to the far-off-resonant regime, and investigate numerically the three-wave resonance conditions in a one-dimensional optical medium with $\chi^{(2)}$ nonlinearity. In particular, we demonstrate that the cascading of nonresonant wave interaction processes generates an effective $\chi^{(3)}$ nonlinear response in these systems. We obtain the corresponding coupling coefficients through appropriate normal form transformations that formally lead to the Zakharov equation for spatially periodic optical media.Comment: 14 pages, 4 figure

Generalized dipole polarizabilities and the spatial structure of hadrons

We present a phenomenological discussion of spin-independent, generalized dipole polarizabilities of hadrons entering the virtual Compton scattering process gamma* h -> gamma h. We introduce a new method of obtaining a tensor basis with appropriate Lorentz-invariant amplitudes which are free from kinematical singularities and constraints. We then motivate a gauge-invariant separation into a generalized Born term containing ground-state properties only, and a residual contribution describing the model-dependent internal structure. The generalized dipole polarizabilities are defined in terms of Lorentz-invariant residual amplitudes. Particular emphasis is laid on a physical interpretation of these quantities as characterizing the spatial distributions of the induced electric polarization and magnetization of hadrons. It is argued that three dipole polarizabilities, namely the longitudinal electric alpha_L(q^2), the transverse electric alpha_T(q^2), and the magnetic beta(q^2) ones are required in order to fully reconstruct local polarizations induced by soft external fields in a hadron. One of these polarizabilities, alpha_T(q^2), describes an effect of higher order in the soft final-photon momentum q'. We argue that the associated spatial distributions obtained via the Fourier transforms in the Breit frame are meaningful even for such a light particle as the pion. The spatial distributions are determined at large distances r ~ 1/m_pi for pions, kaons, and octet baryons by use of ChPT.Comment: 41 pages, 5 figures, RevTex fil

Parametric generation of second sound in superfluid helium: linear stability and nonlinear dynamics

We report the experimental studies of a parametric excitation of a second sound (SS) by a first sound (FS) in a superfluid helium in a resonance cavity. The results on several topics in this system are presented: (i) The linear properties of the instability, namely, the threshold, its temperature and geometrical dependencies, and the spectra of SS just above the onset were measured. They were found to be in a good quantitative agreement with the theory. (ii) It was shown that the mechanism of SS amplitude saturation is due to the nonlinear attenuation of SS via three wave interactions between the SS waves. Strong low frequency amplitude fluctuations of SS above the threshold were observed. The spectra of these fluctuations had a universal shape with exponentially decaying tails. Furthermore, the spectral width grew continuously with the FS amplitude. The role of three and four wave interactions are discussed with respect to the nonlinear SS behavior. The first evidence of Gaussian statistics of the wave amplitudes for the parametrically generated wave ensemble was obtained. (iii) The experiments on simultaneous pumping of the FS and independent SS waves revealed new effects. Below the instability threshold, the SS phase conjugation as a result of three-wave interactions between the FS and SS waves was observed. Above the threshold two new effects were found: a giant amplification of the SS wave intensity and strong resonance oscillations of the SS wave amplitude as a function of the FS amplitude. Qualitative explanations of these effects are suggested.Comment: 73 pages, 23 figures. to appear in Phys. Rev. B, July 1 st (2001

Exact Resummations in the Theory of Hydrodynamic Turbulence: II A Ladder to Anomalous Scaling

In paper I of this series on fluid turbulence we showed that exact resummations of the perturbative theory of the structure functions of velocity differences result in a finite (order by order) theory. These findings exclude any known perturbative mechanism for anomalous scaling of the velocity structure functions. In this paper we continue to build the theory of turbulence and commence the analysis of nonperturbative effects that form the analytic basis of anomalous scaling. Starting from the Navier-Stokes equations (at high Reynolds number Re) we discuss the simplest examples of the appearance of anomalous exponents in fluid mechanics. These examples are the nonlinear (four-point) Green's function and related quantities. We show that the renormalized perturbation theory for these functions contains ``ladder`` diagrams with (convergent!) logarithmic terms that sum up to anomalous exponents. Using a new sum rule which is derived here we calculate the leading anomalous exponent and show that it is critical in a sense made precise below. This result opens up the possibility of multiscaling of the structure functions with the outer scale of turbulence as the renormalization length. This possibility will be discussed in detail in the concluding paper III of this series.Comment: PRE in press, 15 pages + 21 figures, REVTeX, The Eps files of figures will be FTPed by request to [email protected]