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Joerg Schumacher

Publications and source records attributed to Joerg Schumacher.

At least 37 records · Page 2Linked to original sources
arXiv2010

Buoyancy statistics in moist turbulent Rayleigh-Benard convection

We study shallow moist Rayleigh-Benard convection in the Boussinesq approximation in three-dimensional direct numerical simulations. The thermodynamics of phase changes is approximated by a piecewise linear equation of state close to the phase boundary. The impact of phase changes on the turbulent fluctuations and the transfer of buoyancy through the layer is discussed as a function of the Rayleigh number and the ability to form liquid water. The enhanced buoyancy flux due to phase changes is compared with dry convection reference cases and related to the cloud cover in the convection layer. This study indicates that the moist Rayleigh-Benard problem offers a practical framework for the development and evaluation of parametrizations for atmospheric convection.

physics.flu-dyn↗
arXiv2010

Lagrangian tracer dynamics in a closed cylindrical turbulent convection cell

Turbulent Rayleigh-Benard convection in a closed cylindrical cell is studied in the Lagrangian frame of reference with the help of three-dimensional direct numerical simulations. The aspect ratio of the cell Gamma is varied between 1 and 12, and the Rayleigh number Ra between 10^7 and 10^9. The Prandtl number Pr is fixed at 0.7. It is found that both the pair dispersion of the Lagrangian tracer particles and the statistics of the acceleration components measured along the particle trajectories depend on the aspect ratio for a fixed Rayleigh number for the parameter range covered in our studies. This suggests that large-scale circulations present in the convection cell affect the Lagrangian dynamics. Our findings are in qualitative agreement with existing Lagrangian laboratory experiments on turbulent convection.

physics.flu-dyn↗
arXiv2010

Aspect ratio dependence of heat transfer and large-scale flow in turbulent convection

The heat transport and corresponding changes in the large-scale circulation (LSC) in turbulent Rayleigh-Bénard convection are studied by means of three-dimensional direct numerical simulations as a function of the aspect ratio $Γ$ of a closed cylindrical cell and the Rayleigh number $Ra$. For small and moderate aspect ratios, the global heat transfer law $Nu=A\times Ra^β$ shows a power law dependence of both fit coefficients $A$ and $β$ on the aspect ratio. A minimum Nusselt number coincides with the point where the LSC undergoes a transition from a single-roll to a double-roll pattern. With increasing aspect ratio, we detect complex multi-roll LSC configurations. The aspect ratio dependence of the turbulent heat transfer for small and moderate $Γ$ is in line with a varying amount of energy contained in the LSC, as quantified by the Proper Orthogonal Decomposition analysis. For $Γ\gtrsim 8$ the heat transfer becomes independent of the aspect ratio.

physics.flu-dyn↗
arXiv2009

Extreme vorticity growth in Navier-Stokes turbulence

According to statistical turbulence theory, the ensemble averaged squared vorticity rho_E is expected to grow not faster than drho_E/dt ~ rho_E^{3/2}. Solving a variational problem for maximal bulk enstrophy (E) growth, velocity fields were found for which the growth rate is as large as dE/dt ~ E^3. Using numerical simulations with well resolved small scales and a quasi-Lagrangian advection to track fluid subvolumes with rapidly growing vorticity, we study spatially resolved statistics of vorticity growth. We find that the volume ensemble averaged growth bound is satisfied locally to a remarkable degree of accuracy. Elements with dE/dt ~ E^3 can also be identified, but their growth tends to be replaced by the ensemble-averaged law when the intensities become too large.

physics.flu-dyn↗
arXiv2009

Statistics of velocity gradients in wall-bounded shear flow turbulence

The statistical properties of velocity gradients in a wall-bounded turbulent channel flow are discussed on the basis of three-dimensional direct numerical simulations. Our analysis is concentrated on the trend of the statistical properties of the local enstrophy ${\bm ω}^2({\bm x},t)$ and the energy dissipation rate $ε({\bm x},t)$ with increasing distance from the wall. We detect a sensitive dependence of the largest amplitudes of both fields (which correspond with the tail of the distribution) on the spectral resolution. The probability density functions of each single field as well as their joint distribution vary significantly with increasing distance from the wall. The largest fluctuations of the velocity gradients are found in the logarithmic layer. This is in agreement with recent experiments which observe a bursting of hairpin vortex packets into the logarithmic region.

physics.flu-dyn↗
arXiv2009

Measurement of local dissipation scales in turbulent pipe flow

Local dissipation scales are a manifestation of the intermittent small-scale nature of turbulence. We report the first experimental evaluation of the distribution of local dissipation scales in turbulent pipe flows for a range of Reynolds numbers, 2.4x10^4<=Re_D<=7.0x10^4. Our measurements at the nearly isotropic pipe centerline and within the anisotropic logarithmic layer show excellent agreement with distributions that were previously calculated from numerical simulations of homogeneous isotropic box turbulence and with those predicted by theory. The reported results suggest a universality of the smallest-scale fluctuations around the classical Kolmogorov dissipation length.

physics.flu-dyn↗
arXiv2009

Lagrangian studies in convective turbulence

We present high-resolution direct numerical simulations of turbulent three-dimensional Rayleigh-Benard convection with a focus on the Lagrangian properties of the flow. The volume is a Cartesian slab with an aspect ratio of four bounded by free-slip planes at the top and bottom and with periodic side walls. The turbulence is inhomogeneous with respect to the vertical direction. This manifests in different lateral and vertical two-particle dispersion and in a dependence of the dispersion on the initial tracer position for short and intermediate times. Similar to homogeneous isotropic turbulence, the dispersion properties depend in addition on the initial pair separation and yield a short-range Richardson-like scaling regime of two-particle dispersion for initial separations close to the Kolmogorov dissipation length. The Richardson constant is about half the value of homogeneous isotropic turbulence. The multiparticle statistics is very close to the homogeneous isotropic case. Clusters of four Lagrangian tracers show a clear trend to form flat, almost coplanar objects in the long-time limit and deviate from the Gaussian prediction. Significant efforts have been taken to resolve the statistics of the acceleration components up to order four correctly. We find that the vertical acceleration is less intermittent than the lateral one. The joint statistics of the vertical acceleration with the local convective and conductive heat flux suggests that rising and falling thermal plumes are not associated with the largest acceleration magnitudes. It turns out also that the Nusselt number which is calculated in the Lagrangian frame converges slowly in time to the standard Eulerian one.

physics.flu-dyn↗
arXiv2009

Lagrangian views on turbulent mixing of passive scalars

The Lagrangian view of passive scalar turbulence has recently produced interesting results and interpretations. Innovations in theory, experiments, simulations and data analysis of Lagrangian turbulence are reviewed here in brief. Part of the review is closely related to the so-called Kraichnan model for the advection of the passive scalar in synthetic turbulence. Possible implications for a better understanding of the passive scalar mixing in Navier-Stokes turbulence are also discussed.

physics.flu-dyn↗
arXiv2009

Energy dissipation rates in low-$\Re_m$ MHD turbulence with mean shear: Results for channel flow with spanwise field

We examine the changes in kinetic energy dissipation of a turbulent channel flow caused by a spanwise magnetic field. The numerical study is based on our simulation data from [Krasnov, Zikanov, Schumacher, Boeck, Phys. Fluids 20, 095105 (2008)] obtained by direct and large eddy simulations. We find that the Joule dissipation can exceed the viscous dissipation in the weakly dissipative bulk region, but remains comparatively small in the turbulence-generating near-wall region.

physics.flu-dyn↗
arXiv2008

Multiscale modelling strategy using the lattice Boltzmann method for polymer dynamics in a turbulent flow

Polymer dynamics in a turbulent flow is a problem spanning several orders of magnitude of length and time scales. A microscopic simulation covering all those scales from the polymer segment to the inertial scale of turbulence seems impossible within the foreseeable future. We propose a multiscale simulation strategy to enhance the spatio-temporal resolution of local Lagrangian turbulent flow by matching two different simulation techniques, i. e. direct numerical simulation for the flow as a whole, and the lattice Boltzmann method coupled to polymer dynamics at the Kolmogorov dissipation scale. Local turbulent flows sampled by Lagrangian tracer particles in the direct numerical simulation are reproduced in the lattice Boltzmann model with a finer resolution, by supplying the latter with both the correct initial condition as well as the correct time-dependent boundary condition, sampled from the former. When combined with a Molecular Dynamics simulation of a polymer chain in the lattice Boltzmann model, it provides a strategy to simulate the \emph{passive} dynamics of a polymer chain in a turbulent flow covering all those scales. While this approach allows for a fairly realistic model of the macromolecule, the back-coupling to the flow on the large scales is missing.

cond-mat.stat-mech↗
arXiv2008

MHD turbulence in a channel with spanwise magnetic field

The effect of a uniform spanwise magnetic field on a turbulent channel flow is investigated for the case of low magnetic Reynolds number. DNS and LES computations are performed for two values of the hydrodynamic Reynolds number (10^4 and 2\times 10^4) and the Hartmann number varying in a wide range. It is shown that the main effect of the magnetic field is the suppression of turbulent velocity fluctuations and momentum transfer in the wall-normal direction. This leads to drag reduction and transformation of the mean flow profile. The centerline velocity grows, the mean velocity gradients near the wall decrease, and the typical horizontal dimensions of the coherent structures enlarge upon increasing the Hartmann number. Comparison between LES and DNS results shows that the dynamic Smagorinsky model accurately reproduces the flow transformation.

physics.flu-dyn↗
arXiv2008

Lagrangian dispersion and heat transport in convective turbulence

Lagrangian studies of the local temperature mixing and heat transport in turbulent Rayleigh-Benard convection are presented, based on three-dimensional direct numerical simulations. Contrary to vertical pair distances, the temporal growth of lateral pair distances agrees with the Richardson law, but yields a smaller Richardson constant due to correlated pair motion in plumes. Our results thus imply that Richardson dispersion is also found in anisotropic turbulence. We find that extremely large vertical accelerations appear less frequently than lateral ones and are not connected with rising or falling thermal plumes. The height-dependent joint Lagrangian statistics of vertical acceleration and local heat transfer allows us to identify a zone which is dominated by thermal plume mixing.

physics.flu-dyn↗
arXiv2007

Sub-Kolmogorov-Scale Fluctuations in Fluid Turbulence

We relate the intermittent fluctuations of velocity gradients in turbulence to a whole range of local dissipation scales generalizing the picture of a single mean dissipation length. The statistical distribution of these local dissipation scales as a function of Reynolds number is determined in numerical simulations of forced homogeneous isotropic turbulence with a spectral resolution never applied before which exceeds the standard one by at least a factor of eight. The core of the scale distribution agrees well with a theoretical prediction. Increasing Reynolds number causes the generation of ever finer local dissipation scales. This is in line with a less steep decay of the large-wavenumber energy spectra in the dissipation range. The energy spectrum for the highest accessible Taylor microscale Reynolds number R_lambda=107 does not show a bottleneck.

physics.flu-dyn↗
arXiv2007

Asymptotic Exponents from Low-Reynolds-Number Flows

The high-order statistics of fluctuations in velocity gradients in the crossover range from the inertial to the Kolmogorov and sub-Kolmogorov scales are studied by direct numerical simulations (DNS) of homogeneous isotropic turbulence with vastly improved resolution. The derivative moments for orders 0 <= n <= 8 are represented well as powers of the Reynolds number, Re, in the range 380 <= Re <= 5725, where Re is based on the periodic box length L_x. These low-Reynolds-number flows give no hint of scaling in the inertial range even when extended self-similarity is applied. Yet, the DNS scaling exponents of velocity gradients agree well with those deduced, using a recent theory of anomalous scaling, from the scaling exponents of the longitudinal structure functions at infinitely high Reynolds numbers. This suggests that the asymptotic state of turbulence is attained for the velocity gradients at far lower Reynolds numbers than those required for the inertial range to appear. We discuss these findings in the light of multifractal formalism. Our numerical studies also resolve the crossover of the velocity gradient statistics from the Gaussian to non-Gaussian behaviour that occurs as the Reynolds number is increased.

nlin.CD↗
arXiv2007

Two-way coupling of FENE dumbbells with a turbulent shear flow

We present numerical studies for finitely extensible nonlinear elastic (FENE) dumbbells which are dispersed in a turbulent plane shear flow at moderate Reynolds number. The polymer ensemble is described on the mesoscopic level by a set of stochastic ordinary differential equations with Brownian noise. The dynamics of the Newtonian solvent is determined by the Navier-Stokes equations. Momentum transfer of the dumbbells with the solvent is implemented by an additional volume forcing term in the Navier-Stokes equations, such that both components of the resulting viscoelastic fluid are connected by a two-way coupling. The dynamics of the dumbbells is given then by Newton's second law of motion including small inertia effects. We investigate the dynamics of the flow for different degrees of dumbbell elasticity and inertia, as given by Weissenberg and Stokes numbers, respectively. For the parameters accessible in our study, the magnitude of the feedback of the polymers on the macroscopic properties of turbulence remains small as quantified by the global energy budget and the Reynolds stresses. A reduction of the turbulent drag by up to 20% is observed for the larger particle inertia. The angular statistics of the dumbbells shows an increasing alignment with the mean flow direction for both, increasing elasticity and inertia. This goes in line with a growing asymmetry of the probability density function of the transverse derivative of the streamwise turbulent velocity component. We find that dumbbells get stretched referentially in regions where vortex stretching or bi-axial strain dominate the local dynamics and topology of the velocity gradient tensor.

physics.flu-dyn↗
arXiv2006

Geometry of intensive scalar dissipation events in turbulence

Maxima of the scalar dissipation rate in turbulence appear in form of sheets and correspond to the potentially most intensive scalar mixing events. Their cross-section extension determines a locally varying diffusion scale of the mixing process and extends the classical Batchelor picture of one mean diffusion scale. The distribution of the local diffusion scales is analysed for different Reynolds and Schmidt numbers with a fast multiscale technique applied to very high-resolution simulation data. The scales take always values across the whole Batchelor range and beyond. Furthermore, their distribution is traced back to the distribution of the contractive short-time Lyapunov exponent of the flow.

nlin.CD↗
arXiv2006

Links between dissipation, intermittency, and helicity in the GOY model revisited

High-resolution simulations within the GOY shell model are used to study various scaling relations for turbulence. A power-law relation between the second-order intermittency correction and the crossover from the inertial to the dissipation range is confirmed. Evidence is found for the intermediate viscous dissipation range proposed by Frisch and Vergassola. It is emphasized that insufficient dissipation-range resolution systematically drives the energy spectrum towards statistical-mechanical equipartition. In fully resolved simulations the inertial-range scaling exponents depend on both model parameters; in particular, there is no evidence that the conservation of a helicity-like quantity leads to universal exponents.

nlin.CD↗