Small scale of subgrid scales in the Large Eddy Simulation of compressible turbulent flows

It is proposed a methodology for the automatic selective insertion-elimination of subgrid scale stresses in the numerical simulation of transitional laminar-turbulent flows in both compressible and incompressible regimes. By means of a functional of the filtered vorticity field, it is possible to approximatively locate the flow regions that are rich in small scale motions. In these regions, it can be opportune to filter the equations of motion to carry out a Large Eddy Simulation, that is, a simulation where the larger scales only are resolved, but the small scale dynamics is considered and represented through proper terms in the equations. In case of compressible regimes, a functional of the pressure local variation and divergence can be associated to the functional previously mentioned in order to determine the eventual presence of shocks. In such a way, it is possible to locate the regions where, to capture the shock, it is necessary to insert an explicit numerical dissipation and suppress the subgrid mode

Cross and magnetic helicity in the outer heliosphere from Voyager 2 observations

Plasma velocity and magnetic field measurements from the Voyager 2 mission are used to study solar wind turbulence in the slow solar wind at two different heliocentric distances, 5 and 29 astronomical units, sufficiently far apart to provide information on the radial evolution of this turbulence. The magnetic helicity and the cross-helicity, which express the correlation between the plasma velocity and the magnetic field, are used to characterize the turbulence. Wave number spectra are computed by means of the Taylor hypothesis applied to time resolved single point Voyager 2 measurements. The overall picture we get is complex and difficult to interpret. A substantial decrease of the cross-helicity at smaller scales (over 1-3 hours of observation) with increasing heliocentric distance is observed. At 5 AU the only peak in the probability density of the normalized residual energy is negative, near -0.5. At 29 AU the probability density becomes doubly peaked, with a negative peak at -0.5 and a smaller peak at a positive values of about 0.7. A decrease of the cross-helicity for increasing heliocentric distance is observed, together with a reduction of the unbalance toward the magnetic energy of the energy of the fluctuations. For the smaller scales, we found that at 29 AU the normalized polarization is small and positive on average (about 0.1), it is instead zero at 5 AU. For the larger scales, the polarization is low and positive at 5 AU (average around 0.1) while it is negative (around - 0.15) at 29 AU.Comment: 14 pages 5 figures. Accepted for publication on European Journal of Mechanics B/Fluids (5/8/2015

Accurate direct numerical simulation of two-way coupled particle-laden flows through the nonuniform fast Fourier transform

The ability of the non-uniform Fast Fourier Transform (NUFFT) to predict the particle feedback on the flow in particle-laden flows in the two-way coupling regime is examined. In this regime, the particle back-reaction on the fluid phase can substantially modify the flow statistics across all the scales, when particle loading is significant. While many works in the literature focus on the direct B-spline interpolation, which is now a well-established method for the one-way coupling, only a few methods are available for the computation of particle back-reaction, which are often lower order and reduce the overall accuracy of the simulation. In our implementation, particle momentum and temperature back-reactions on the fluid flow are computed by means of the forward NUFFT with B-spline basis, while the B-spline interpolation is performed as a backward NUFFT. An application of the NUFFT to the simulation of a statistically steady and isotropic turbulent flow, laden with inertial particles is presented. The effect of particle feedback on velocity and temperature structure functions and on particle clustering is discussed as a function of the Stokes number, together with the spectral characterization of the particle phase

Turbulence in the solar wind: spectra from Voyager 2 data at 5 AU

Fluctuations in the flow velocity and magnetic fields are ubiquitous in the Solar System. These fluctuations are turbulent, in the sense that they are disordered and span a broad range of scales in both space and time. The study of solar wind turbulence is motivated by a number of factors all keys to the understanding of the Solar Wind origin and thermodynamics. The solar wind spectral properties are far from uniformity and evolve with the increasing distance from the sun. Most of the available spectra of solar wind turbulence were computed at 1 astronomical unit, while accurate spectra on wide frequency ranges at larger distances are still few. In this paper we consider solar wind spectra derived from the data recorded by the Voyager 2 mission during 1979 at about 5 AU from the sun. Voyager 2 data are an incomplete time series with a voids/signal ratio that typically increases as the spacecraft moves away from the sun (45% missing data in 1979), making the analysis challenging. In order to estimate the uncertainty of the spectral slopes, different methods are tested on synthetic turbulence signals with the same gap distribution as V2 data. Spectra of all variables show a power law scaling with exponents between -2.1 and -1.1, depending on frequency subranges. Probability density functions (PDFs) and correlations indicate that the flow has a significant intermittency.Comment: 14 pages, 7 figures. Discussion improved since the previous versio

Direct numerical simulation of a warm cloud top model interface: Impact of the transient mixing on different droplet population

Turbulent mixing through atmospheric cloud and clear air interface plays an important role in the life of a cloud. Entrainment and detrainment of clear air and cloudy volume result in mixing across the interface, which broadens the cloud droplet spectrum. In this study, we simulate the transient evolution of a turbulent cloud top interface with three initial mono-disperse cloud droplet population, using a pseudo-spectral Direct Numerical Simulation (DNS) along with Lagrangian droplet equations, including collision and coalescence. Transient evolution of in-cloud turbulent kinetic energy (TKE), density of water vapour and temperature is carried out as an initial value problem exhibiting transient decay. Mixing in between the clear air and cloudy volume produced turbulent fluctuations in the density of water vapour and temperature, resulting in supersaturation fluctuations. Small scale turbulence, local supersaturation conditions and gravitational forces have different weights on the droplet population depending on their sizes. Larger droplet populations, with initial 25 and 18 μm radii, show significant growth by droplet-droplet collision and a higher rate of gravitational sedimentation. However, the smaller droplets, with an initial 6 μm radius, did not show any collision but a large size distribution broadening due to differential condensation/evaporation induced by the mixing, without being influenced by gravity significantly

Small scale of subgrid scales in the Large Eddy Simulation of compressible turbulent flows

It is proposed a methodology for the automatic selective insertion-elimination of subgrid scale stresses in the numerical simulation of transitional laminar-turbulent flows in both compressible and incompressible regimes. By means of a functional of the filtered vorticity field, it is possible to approximatively locate the flow regions that are rich in small scale motions. In these regions, it can be opportune to filter the equations of motion to carry out a Large Eddy Simulation, that is, a simulation where the larger scales only are resolved, but the small scale dynamics is considered and represented through proper terms in the equations. In case of compressible regimes, a functional of the pressure local variation and divergence can be associated to the functional previously mentioned in order to determine the eventual presence of shocks. In such a way, it is possible to locate the regions where, to capture the shock, it is necessary to insert an explicit numerical dissipation and suppress the subgrid model

Self-similarity of the turbulent mixing with a constant in time macroscale gradient

In the absence of kinetic energy production, we consider that the influence of the initial conditions is characterized by the presence of an energy gradient or by the concurrency of an energy and a macroscale gradient on turbulent transport. Here, we present a similarity analysis that interprets two new results on the subject recently obtained by means of numerical experiments on shearless mixing (Tordella & Iovieno, 2005). In short, the two results are: i -- The absence of the macroscale gradient is not a sufficient condition for the setting of the asymptotic Gaussian state hypothesized by Veeravalli and Warhaft (1989), where, regardless of the existence of velocity variance distributions, turbulent transport is mainly diffusive and the intermittency is nearly zero up to moments of order four. In fact, it was observed that the intermittency increases with the energy gradient, with a scaling exponent of about 0.29; ii -- If the macroscale gradient is present, referring to the situation where the macroscale gradient is zero but the energy gradient is not, the intermittency is higher if the energy and scale gradients are concordant and is lower if they are opposite. The similarity analysis, which is in fair agreement with the previous experiments, is based on the use of the kinetic energy equation, which contains information concerning the third order moments of the velocity fluctuations. The analysis is based on two simplifying hypotheses: first, that the decays of the turbulences being mixed are almost nearly equal (as suggested by the experiments), second, that the pressure-velocity correlation is almost proportional to the convective transport associated to the fluctuations (Yoshizawa, 2002)