Angela Busse

Universal intermittent properties of particle trajectories in highly turbulent flows

We present a collection of eight data sets from state-of-the-art experiments and numerical simulations on turbulent velocity statistics along particle trajectories obtained in different flows with Reynolds numbers in the range R{lambda}in[120:740]. Lagrangian structure functions from all data sets are found to collapse onto each other on a wide range of time lags, pointing towards the existence of a universal behavior, within present statistical convergence, and calling for a unified theoretical description. Parisi-Frisch multifractal theory, suitably extended to the dissipative scales and to the Lagrangian domain, is found to capture the intermittency of velocity statistics over the whole three decades of temporal scales investigated here.

Influence of an anisotropic slip-length boundary condition on turbulent channel flow

The effects of an anisotropic Navier slip-length boundary condition on turbulent channel flow are investigated parametrically by direct numerical simulations. The slip-length boundary condition is made direction dependent by specifying the value of the slip length independently for the streamwise and spanwise direction. The change in drag is mapped versus a wide range of streamwise and spanwise slip-length combinations at two different friction Reynolds numbers, Reτ0=180 and Reτ0=360. For moderate slip lengths both drag-reducing and drag-increasing slip-length combinations are found. The percentage drag increase saturates at approximately 60% for high spanwise slip. Once a threshold value for the streamwise slip length is exceeded, drag is reduced in all cases irrespective of the value of the spanwise slip length. The Reynolds number appears to have only little influence on the change in drag for the moderate Reynolds numbers studied here. A detailed comparison with the implicit theoretical formula of Fuk...

Lagrangian Statistics of Navier-Stokes- and MHD-Turbulence

We report on a comparison of high-resolution numerical simulations of Lagrangian particles advected by incompressible turbulent hydro- and magneto- hydrodynamic (MHD) flows. Numerical simulations were performed with up to 1024 3 collocation points and 10 million particles in the Navier-Stokes case and 512 3 collocation points and 1 million particles in the MHD case. In the hydrodynamics case our findings compare with recent experiments from Mordant et al. (2004 New J. Phys. 6, 116) and Xu et al. (2006 Phys. Rev. Lett.96, 024503). They differ from the simulations of Biferale et al. (2004 Phys. Rev. Lett. 93, 064502) due to differences of the ranges chosen for evaluating the structure functions. In Navier- Stokes turbulence intermittency is stronger than predicted by the multifractal approach of Biferale et al. (2004 Phys. Rev. Lett. 93, 064502) whereas in MHD tur- bulence the predictions from the multifractal approach are more intermittent than observed in our simulations. In addition, our simulations reveal that Lagrangian Navier-Stokes turbulence is more intermittent than MHD turbulence, whereas the situation is reversed in the Eulerian case. Those findings can not consistently be described by the multifractal modeling. The crucial point is that the geometry of the dissipative structures have different implications for Lagrangian and Eulerian intermittency. Application of the multifractal approach for the modeling of the acceleration probability density functions works well for the Navier-Stokes case but in the MHD case just the tails are well described.

Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence

The nonlinear dynamics of magnetic helicity HM, which is responsible for large-scale magnetic structure formation in electrically conducting turbulent media, is investigated in forced and decaying three-dimensional magnetohydrodynamic turbulence. This is done with the help of high-resolution direct numerical simulations and statistical closure theory. The numerically observed spectral scaling of HM is at variance with earlier work using a statistical closure model [Pouquet et al., J. Fluid Mech. 77, 321 (1976)]. By revisiting this theory, a universal dynamical balance relation is found that includes the effects of kinetic helicity as well as kinetic and magnetic energies on the inverse cascade of HM and explains the above-mentioned discrepancy. Consideration of the result in the context of mean-field dynamo theory suggests a nonlinear modification of the α-dynamo effect, which is important in the context of magnetic-field excitation in turbulent plasmas.

Statistics of passive tracers in three-dimensional magnetohydrodynamic turbulence

Magnetohydrodynamic(MHD)turbulence is studied from the Lagrangian viewpoint by following fluid particle tracers in high resolution direct numerical simulations. Results regarding turbulent diffusion and dispersion as well as Lagrangian structure functions are presented. Whereas turbulent single-particle diffusion exhibits essentially the same behavior in Navier-Stokes and MHDturbulence, two-particle relative dispersion in the MHD case differs significantly from the Navier-Stokes behavior. This observation is linked to the local anisotropy of MHDturbulence which is clearly reflected by quantities measured in a Lagrangian frame of reference. In the MHD case the Lagrangian structure functions display a lower level of intermittency as compared to the Navier-Stokes case contrasting Eulerian results. This is not only true for short time increments [H. Homann, R. Grauer, A. Busse, and W.-C. Muller, J. Plasma Phys.73, 821 (2007)] but also holds for increments up to the order of the integral time scale. The apparent discrepancy can be explained by the difference in the characteristic shapes of fluid particle trajectories in the vicinity of most singular dissipative structures.

Surface correlations of hydrodynamic drag for transitionally rough engineering surfaces

ABSTRACTRough surfaces are usually characterised by a single equivalent sand-grain roughness height scale that typically needs to be determined from laboratory experiments. Recently, this method has been complemented by a direct numerical simulation approach, whereby representative surfaces can be scanned and the roughness effects computed over a range of Reynolds number. This development raises the prospect over the coming years of having enough data for different types of rough surfaces to be able to relate surface characteristics to roughness effects, such as the roughness function that quantifies the downward displacement of the logarithmic law of the wall. In the present contribution, we use simulation data for 17 irregular surfaces at the same friction Reynolds number, for which they are in the transitionally rough regime. All surfaces are scaled to the same physical roughness height. Mean streamwise velocity profiles show a wide range of roughness function values, while the velocity defect profiles...

Fluctuation dynamo amplified by intermittent shear bursts in convectively driven magnetohydrodynamic turbulence

Intermittent large-scale high-shear flows are found to occur frequently and spontaneously in direct numerical simulations of statistically stationary turbulent Boussinesq magnetohydrodynamic (MHD) convection. The energetic steady state of the system is sustained by convective driving of the velocity field and small-scale dynamo action. The intermittent emergence of flow structures with strong velocity and magnetic shearing generates magnetic energy at an elevated rate on time scales that are longer than the characteristic time of the large-scale convective motion. The resilience of magnetic energy amplification suggests that intermittent shear bursts are a significant driver of dynamo action in turbulent magnetoconvection.

Scaling Properties of Convective Turbulence

This report presents the current status of a computational project investigating the statistical properties and physical mechanisms of convective turbulence. Three-dimensional direct numerical simulations (DNS) based on the Boussinesq equations are conducted without introducing any additional physical approximations. The numerical resolution of 20483 collocation points used by the FFT-based pseudospectral scheme renders this project the largest numerical effort in turbulent convection world-wide. In the first stage the simulation code was successfully ported to the ALTIX 4700 supercomputer where several scalability and benchmarking test were performed. Utilizing this analysis the code was optimized, allowing the determination of the optimal numerical setup. The production phase has begun recently leading to first preliminary results.

Lagrangian frequency spectrum as a diagnostic for magnetohydrodynamic turbulence dynamics.

For the phenomenological description of magnetohydrodynamic turbulence competing models exist, e.g., Boldyrev [Phys. Rev. Lett. 96, 115002 (2006)] and Gogoberidze [Phys. Plasmas 14, 022304 (2007)], which predict the same Eulerian inertial-range scaling of the turbulent energy spectrum although they employ fundamentally different basic interaction mechanisms. A relation is found that links the Lagrangian frequency spectrum with the autocorrelation time scale of the turbulent fluctuations τ(ac) and the associated cascade time scale τ(cas). Thus, the Lagrangian energy spectrum can serve to identify weak (τ(ac) ≪ τ(cas)) and strong (τ(ac) ∼ τ(cas)) interaction mechanisms providing insight into the turbulent energy cascade. The new approach is illustrated by results from direct numerical simulations of two- and three-dimensional incompressible MHD turbulence.

Recent developments in the theory of magnetohydrodynamic turbulence

Recent results based on high‐resolution direct numerical simulations of incompressible magnetohydrodynamic (MHD) turbulence are summarized. With regard to the nonlinear dynamics of turbulent energy a yet unexplained scaling behavior is found in systems permeated by a strong mean magnetic field which contradicts the phenomenological Goldreich‐Sridhar picture. For macroscopically isotropic and anisotropic MHD turbulence EDQNM closure analysis leads to a simple relation between the spectra of total (EkK + EkM) and residual (|EkK − EkM|) energy. The relation is based on a clear physical picture and is well confirmed by numerical simulations. In addition, the Lagrangian approach is presented as a straightforward diagnostic for the investigation of turbulent diffusion and pair‐dispersion. Some results from a comparative study of pair‐dispersion in Navier‐Stokes and MHD turbulence are briefly outlined. It is shown that the presence of magnetic fluctuations significantly reduces turbulent dispersion due to the al...