Influence of polymer additives on turbulent energy cascading in forced homogeneous isotropic turbulence studied by direct numerical simulations

Direct numerical simulations(DNS) were performed for the forced homogeneous isotropic turbulence(FHIT) with/without polymer additives in order to elaborate the characteristics of the turbulent energy cascading influenced by drag-reducing effects.The finite elastic non-linear extensibility-Peterlin model(FENE-P) was used as the conformation tensor equation for the viscoelastic polymer solution.Detailed analyses of DNS data were carried out in this paper for the turbulence scaling law and the topological dynamics of FHIT as well as the important turbulent parameters,including turbulent kinetic energy spectra,enstrophy and strain,velocity structure function,small-scale intermittency,etc.A natural and straightforward definition for the drag reduction rate was also proposed for the drag-reducing FHIT based on the decrease degree of the turbulent kinetic energy.It was found that the turbulent energy cascading in the FHIT was greatly modified by the drag-reducing polymer additives.The enstrophy and the strain fields in the FHIT of the polymer solution were remarkably weakened as compared with their Newtonian counterparts.The small-scale vortices and the small-scale intermittency were all inhibited by the viscoelastic effects in the FHIT of the polymer solution.However,the scaling law in a fashion of extended self-similarity for the FHIT of the polymer solution,within the presently simulated range of Weissenberg numbers,had no distinct differences compared with that of the Newtonian fluid case.     

Simultaneous numerical simulation of direct and inverse cascades in wave turbulence

The results of the direct numerical simulation of isotropic turbulence of surface gravity waves in the framework of Hamiltonian equations are presented. For the first time, the simultaneous formation of both direct and inverse cascades has been observed in the framework of the primordial dynamical equations. At the same time, a strong long wave background has been developed. It has been shown that the Kolmogorov spectra obtained are very sensitive to the presence of this condensate. Such a situation has to be typical for experimental wave tanks, flumes, and small lakes.     

Resolution effects and scaling in numerical simulations of passive scalar mixing in turbulence

The effects of finite grid resolution on the statistics of small scales in direct numerical simulations of turbulent mixing of passive scalars are addressed in this paper. Simulations at up to 2048³ grid points with grid spacing Δx varied from about 2 to 1/2 Batchelor scales (η_B) show that most conclusions on Schmidt number (Sc) dependence from prior work at less stringent resolution remain qualitatively correct, although simulations at resolution Δx≈η_B are preferred and will give adequate results for many important quantities including the scalar dissipation intermittency exponent and structure functions at moderately high orders. For Sc≥1, since η_B=ηSc^−1/2 (where η is the Kolmogorov scale), the requirement Δx≈η_B is more stringent than the corresponding criterion Δx≈η for the velocity field, which is thus well resolved in simulations aimed at high Schmidt number mixing. A simple argument is given to help interpret the effects of Schmidt and Reynolds numbers on trends towards local isotropy and saturation of intermittency at high Schmidt number. The present results also provide evidence for a trend to isotropy at high Reynolds number with fixed Sc=1.0. This is a new observation apparently not detected in less well resolved simulations in the past, and will require further investigation in the future.     

Parallelization in time of numerical simulations of fully-developed plasma turbulence using the parareal algorithm

It is shown that numerical simulations of fully-developed plasma turbulence can be successfully parallelized in time using the parareal algorithm. The result is far from trivial, and even unexpected, since the exponential divergence of Lagrangian trajectories as well as the extreme sensitivity to initial conditions characteristic of turbulence set these type of simulations apart from the much simpler systems to which the parareal algorithm has been applied to this day. It is also shown that the parallel gain obtainable with this method is very promising (close to an order of magnitude for the cases and implementations described), even when it scales with the number of processors quite differently to what is typical for spatial parallelization.     

Assessment of high-resolution methods for numerical simulations of compressible turbulence with shock waves

Flows in which shock waves and turbulence are present and interact dynamically occur in a wide range of applications, including inertial confinement fusion, supernovae explosion, and scramjet propulsion. Accurate simulations of such problems are challenging because of the contradictory requirements of numerical methods used to simulate turbulence, which must minimize any numerical dissipation that would otherwise overwhelm the small scales, and shock-capturing schemes, which introduce numerical dissipation to stabilize the solution. The objective of the present work is to evaluate the performance of several numerical methods capable of simultaneously handling turbulence and shock waves. A comprehensive range of high-resolution methods (WENO, hybrid WENO/central difference, artificial diffusivity, adaptive characteristic-based filter, and shock fitting) and suite of test cases (Taylor–Green vortex, Shu–Osher problem, shock-vorticity/entropy wave interaction, Noh problem, compressible isotropic turbulence) relevant to problems with shocks and turbulence are considered. The results indicate that the WENO methods provide sharp shock profiles, but overwhelm the physical dissipation. The hybrid method is minimally dissipative and leads to sharp shocks and well-resolved broadband turbulence, but relies on an appropriate shock sensor. Artificial diffusivity methods in which the artificial bulk viscosity is based on the magnitude of the strain-rate tensor resolve vortical structures well but damp dilatational modes in compressible turbulence; dilatation-based artificial bulk viscosity methods significantly improve this behavior. For well-defined shocks, the shock fitting approach yields good results.     

Vortex rings moving into turbulence

We report on an experimental study of turbulent vortex rings injected with velocity U _v0 into a grid-generated turbulent flow (with RMS streamwise velocity u _*) and followed relative to the mean flow. The initial Reynolds number of the vortices varies from 4500 to 11,500. The turbulence was characterised by an intensity I_t =u _*/U _v0, which varied over the range 0<I_t <0.03. A mathematical model based on a stochastic model of the vortex core is developed to explain and interpret the results. The vortex radius grows diffusively in time with the rate of increase of the square of the vortex radius increasing linearly with I_t . As the vortices grow, they slow down sufficiently rapidly in a manner that they penetrate a finite distance into the turbulence. The vortex velocity, averaged over many experiments, showed an initial t ^?1 decay, consistent with Maxworthy’s experiments. The analysis and experiments show that such vortices ultimately only move a finite distance from their point of generation and this distance varies inversely with I_t .     

Mode locking in quantum optics

Mode locking phenomena in acoustics and in laser physics are discussed and are shown to share a feature of the forced oscillator: Oscillation takes place at the forcing frequency (or frequencies). The phenomena differ from simple forced oscillations in that they involve sustained oscillators (e.g., clocks, lasers) whose sustaining sources compete against the forcing signals in the choice of oscillation frequency. The locking phenomena are compared to second-order phase transitions in ferromagnetism and superconductivity where corresponding competition occurs between disordering thermal fluctuations and ordering correlations which reduce system energy.     

A review of direct numerical simulations of astrophysical detonations and their implications

Multi-dimensional direct numerical simulations (DNS) of astrophysical detonations in degenerate matter have revealed that the nuclear burning is typically characterized by cellular structure caused by transverse instabilities in the detonation front. Type Ia supernova modelers often use onedimensional DNS of detonations as inputs or constraints for their whole star simulations.While these one-dimensional studies are useful tools, the true nature of the detonation is multi-dimensional. The multi-dimensional structure of the burning influences the speed, stability, and the composition of the detonation and its burning products, and therefore, could have an impact on the spectra of Type Ia supernovae. Considerable effort has been expended modeling Type Ia supernovae at densities above 1×10⁷ g·cm^-3 where the complexities of turbulent burning dominate the flame propagation. However, most full star models turn the nuclear burning schemes off when the density falls below 1×10⁷ g·cm^-3 and distributed burning begins. The deflagration to detonation transition (DDT) is believed to occur at just these densities and consequently they are the densities important for studying the properties of the subsequent detonation. This work will review the status of DNS studies of detonations and their possible implications for Type Ia supernova models. It will cover the development of Detonation theory from the first simple Chapman–Jouguet (CJ) detonation models to the current models based on the time-dependent, compressible, reactive flow Euler equations of fluid dynamics.     

Vortex clusters in quantum dots

We study electronic structures of two-dimensional quantum dots in strong magnetic fields using mean-field density-functional theory and exact diagonalization. Our numerically accurate mean-field solutions show a reconstruction of the uniform-density electron droplet when the magnetic field flux quanta enter one by one the dot in stronger fields. These quanta correspond to repelling vortices forming polygonal clusters inside the dot. We find similar structures in the exact treatment of the problem by constructing a conditional operator for the analysis. We discuss important differences and limitations of the methods used.     

Study of the sound-vortex interaction: direct numerical simulations and experimental results

We present a study of sound propagation through a single vortex by direct numerical simulations (DNS) compared to experimental measurements. We analyse the amplitude and the phase shift of the sound wave when it interacts with the vortical flow and we display the focusing effects produced by the vortex. We show that the turbulent fluctuations have a little effect on the sound phase shift whereas they induce a strong defocusing effect on the sound amplitude. Received 9 October 2002 / Received in final form 20 January 2003 Published online 1st April 2003 RID="a" ID="a"e-mail: rberthet@lps.ens.fr RID="b" ID="b"UMR CNRS 8550     

Assessment of counterflow to measure laminar burning velocities using direct numerical simulations

The laminar burning velocity is a fundamental property that is extensively used in the study and modelling of premixed combustion processes. A counterflow flame configuration is commonly used to measure this quantity for different combustion systems. In this procedure, the burning velocities are typically measured at various low stretch conditions and the unstretched burning velocity is extrapolated from these measurements. This extrapolation is done assuming a theoretically one-dimensional system along the centre-line. We analyse the validity of this assumption by performing DNS studies with finite rate chemistry of the experimental counterflow configuration. The extrapolation process using one-dimensional computations is performed on the DNS data and the extrapolated value is compared to the computed laminar burning velocity for the chemical mechanism used. We show that the assumption works well if the nozzle exit velocity has a nearly top-hat profile. For non-uniform velocity profiles, it is shown that the temperature curvature at the centre-line becomes important. This effect cannot be captured by the one-dimensional formulation. Thus, experimental studies measuring laminar burning velocity need to ensure that the nozzle velocity profile is very close to uniform. The extrapolation to zero stretch using 1D counterflow simulations can be performed in different ways. Based on the results obtained in this paper, a simple and accurate extrapolation method is proposed.     

Thermodynamic potential in local turbulence simulations

For the reduced local equations customary in, e.g., the computation of turbulence in tokamaks the energy is still a conserved quantity. However, kinetic and magnetic energy do not appear in the reduced energy functional and thus are not constrained by it, since they are ordered small compared to the fluctuations of internal energy in the reduction process. Constraints on velocity and field fluctuations can be derived using instead the generalized grand canonical potential, which is conserved in reversible processes. This is exemplified for the Boltzmann, gyrokinetic, and fluid equations.     

Vortex burst as a source of turbulence

An important issue in turbulence theory is to understand what kinds of elementary flow structures are responsible for the part of the turbulent energy spectrum described by Kolmogorov's celebrated k(-5/3) law. A model for such structure has been proposed by Lundgren [Phys. Fluids 25, 2193-2203 (1982)]] in the form of a vortex with spiral structure subjected to an axially straining field. We report experimental results of a vortex burst in a laminar-flow environment showing that this structure is responsible for a k(-5/3) part in the energy spectrum. If there are many experimental evidences of the existence of vortices with spiral structures in turbulent flows, it is the first time that such an elementary structure is experimentally shown to be responsible for the turbulent energy cascade.     

Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence

The effects of different filtering strategies on the statistical properties of the resolved-to-subfilter scale (SFS) energy transfer are analysed in forced homogeneous and isotropic turbulence. We carry out a-priori analyses of the statistical characteristics of SFS energy transfer by filtering data obtained from direct numerical simulations with up to 2048³ grid points as a function of the filter cutoff scale. In order to quantify the dependence of extreme events and anomalous scaling on the filter, we compare a sharp Fourier Galerkin projector, a Gaussian filter and a novel class of Galerkin projectors with non-sharp spectral filter profiles. Of interest is the importance of Galilean invariance and we confirm that local SFS energy transfer displays intermittency scaling in both skewness and flatness as a function of the cutoff scale. Furthermore, we quantify the robustness of scaling as a function of the filtering type.     

Thermal dissipation in quantum turbulence

The microscopic mechanism of thermal dissipation in quantum turbulence is numerically studied by solving the coupled system involving the Gross-Pitaevskii equation and the Bogoliubov-de Gennes equation. At low temperatures, the obtained dissipation does not work at scales greater than the vortex core size. However, as the temperature increases, dissipation works at large scales and it affects the vortex dynamics. We successfully obtain the mutual friction coefficients of the vortex in dilute Bose-Einstein condensates dynamics as functions of temperature.     

Drag reduction by herringbone riblet texture in direct numerical simulations of turbulent channel flow

A bird-feather-inspired herringbone riblet texture was investigated for turbulent drag reduction. The texture consists of blade riblets in a converging/diverging or herringbone pattern with spanwise wavelength Λ_f. The aim is to quantify the drag change for this texture as compared to a smooth wall and to study the underlying mechanisms. To that purpose, direct numerical simulations of turbulent flow in a channel with height L_z were performed. The Fukagata-Iwamoto-Kasagi identity for drag decomposition was extended to textured walls and was used to study the drag change mechanisms. For Λ_f/L_z ? O(10), the herringbone texture behaves similarly to a conventional parallel-riblet texture in yaw: the suppression of turbulent advective transport results in a slight drag reduction of 2%. For Λ_f/L_z ? O(1), the drag increases strongly with a maximum of 73%. This is attributed to enhanced mean and turbulent advection, which results from the strong secondary flow that forms over regions of riblet convergence/divergence. Hence, the employment of convergent/divergent riblets in the texture seems to be detrimental to turbulent drag reduction.