arXiv subjects

Bruno Eckhardt

Publications and source records attributed to Bruno Eckhardt.

At least 73 records · Page 4Linked to original sources

arXiv2007

Turbulence transition and the edge of chaos in pipe flow

The linear stability of pipe flow implies that only perturbations of sufficient strength will trigger the transition to turbulence. In order to determine this threshold in perturbation amplitude we study the \emph{edge of chaos} which separates perturbations that decay towards the laminar profile and perturbations that trigger turbulence. Using the lifetime as an indicator and methods developed in (Skufca et al, Phys. Rev. Lett. {\bf 96}, 174101 (2006)) we show that superimposed on an overall $1/\Re$-scaling predicted and studied previously there are small, non-monotonic variations reflecting folds in the edge of chaos. By tracing the motion in the edge we find that it is formed by the stable manifold of a unique flow field that is dominated by a pair of downstream vortices, asymmetrically placed towards the wall. The flow field that generates the edge of chaos shows intrinsic chaotic dynamics.

nlin.CD↗

arXiv2006

Statistical analysis of coherent structures in transitional pipe flow

Numerical and experimental studies of transitional pipe flow have shown the prevalence of coherent flow structures that are dominated by downstream vortices. They attract special attention because they contribute predominantly to the increase of the Reynolds stresses in turbulent flow. In the present study we introduce a convenient detector for these coherent states, calculate the fraction of time the structures appear in the flow, and present a Markov model for the transition between the structures. The fraction of states that show vortical structures exceeds 24% for a Reynolds number of about Re=2200, and it decreases to about 20% for Re=2500. The Markov model for the transition between these states is in good agreement with the observed fraction of states, and in reasonable agreement with the prediction for their persistence. It provides insight into dominant qualitative changes of the flow when increasing the Reynolds number.

physics.flu-dyn↗

arXiv2006

Time resolved quantum dynamics of double ionization in strong laser fields

Quantum calculations of a 1+1-dimensional model for double ionization in strong laser fields are used to trace the time evolution from the ground state through ionization and rescattering to the two electron escape. The subspace of symmetric escape, a prime characteristic of nonsequential double ionization, remains accessible by a judicious choice of 1-d coordinates for the electrons. The time resolved ionization fluxes show the onset of single and double ionization, the sequence of events during the pulse, and the influences of pulse duration, and reveal the relative importance of sequential and non-sequential double ionization, even when ionization takes place during the same field cycle.

physics.atom-ph↗

arXiv2006

Classical threshold behaviour in a 1+1-dimensional model for double ionization in strong fields

Building on insights about the classical pathways to double ionization in strong laser fields we here propose a 1+1-dimensional model that captures essentials of the 3-d potential landscape and allows efficient studies of the process in reduced dimensions. The reduction to one degree of freedom for each electron is obtained by confining their motion to lines at an angle of pi/6 with respect to the field axis; the justification for this choice is that upon variation of the electric field the Stark saddles move along the same lines. In this way we obtain a low-dimensional representation in which symmetric electron escape is possible. As a demonstration of the advantages of this model we confirm numerically the equivalent of the Wannier threshold behaviour for constant electric field and identify several classes of trajectories that can contribute to the ionization process.

physics.atom-ph↗

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↗

arXiv2004

Non-sequential double ionization of molecules in a strong laser field

We consider the final stage of double ionization of $\rm O_2$ molecules by short linearly polarized laser pulses. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons from a molecule takes place are identified. The analysis of the saddles and numerical simulations of the ionization indicate that to observe clear signatures of simultaneous electron escape in double ionization of $\rm O_2$ molecules stronger and much shorter laser pulses than those used in the recent experiment [E. Eremina, {\it et al}, Phys. Rev. Lett. {\bf 92}, 173001 (2004)] should be applied.

physics.atom-ph↗

arXiv2004

Lagrangian tracers on a surface flow: the role of time correlations

Finite time correlations of the velocity in a surface flow are found to be important for the formation of clusters of Lagrangian tracers. The degree of clustering characterized by the Lyapunov spectrum of the flow is numerically shown to be in qualitative agreement with the predictions for the white-in-time compressible Kraichnan flow, but to deviate quantitatively. For intermediate values of compressibility the clustering is surprisingly weakened by time correlations.

nlin.CD↗

arXiv2004

Non-sequential double ionization of molecules

Double ionization of diatomic molecules by short linearly polarized laser pulses is analyzed. We consider the final stage of the ionization process, that is the decay of a highly excited two electron molecule, which is formed after re-scattering. The saddles of the effective adiabatic potential energy close to which simultaneous escape of electrons takes place are identified. Numerical simulations of the ionization of molecules show that the process can be dominated by either sequential or non-sequential events. In order to increase the ratio of non-sequential to sequential ionizations very short laser pulses should be applied.

physics.atom-ph↗

arXiv2004

Homogeneous shear turbulence

The addition of suitable volume forces to the Navier-Stokes equation allows to simulate flows in the presence of a homogeneous shear. Because of the explicit form of the driving the flows are accessible to rigorous mathematical treatment and to accurate quantitative modelling in their global properties. The statistics of the fluctuations provide insight into generic behaviour of non-equilibrium systems and into the presistence of anisotropies at small scales. Correlation functions can be used to identify dominant large scale dynamical processes that are relevant for most of the momentum transport across the shear. The numerical studies of homogeneous shear flows complement analytical and experimental investigations and contribute to bridging the gap between ideal homogeneous isotropic turbulence and the more realistic heterogeneous turbulence.

nlin.CD↗

arXiv2004

Sensitive dependence on initial conditions in transition to turbulence in pipe flow

The experiments by Darbyshire and Mullin (J. Fluid Mech. 289, 83 (1995)) on the transition to turbulence in pipe flow show that there is no sharp border between initial conditions that trigger turbulence and those that do not. We here relate this behaviour to the possibility that the transition to turbulence is connected with the formation of a chaotic saddle in the phase space of the system. We quantify a sensitive dependence on initial conditions and find in a statistical analysis that in the transition region the distribution of turbulent lifetimes follows an exponential law. The characteristic mean lifetime of the distribution increases rapidly with Reynolds number and becomes inaccessibly large for Reynolds numbers exceeding about 2200. Suitable experiments to further probe this concept are proposed.

physics.flu-dyn↗

arXiv2003

Energy dissipation in body-forced plane shear flow

We study the problem of body-force driven shear flows in a plane channel of width l with free-slip boundaries. A mini-max variational problem for upper bounds on the bulk time averaged energy dissipation rate epsilon is derived from the incompressible Navier-Stokes equations with no secondary assumptions. This produces rigorous limits on the power consumption that are valid for laminar or turbulent solutions. The mini-max problem is solved exactly at high Reynolds numbers Re = U*l/nu, where U is the rms velocity and nu is the kinematic viscosity, yielding an explicit bound on the dimensionless asymptotic dissipation factor beta=epsilon*l/U^3 that depends only on the ``shape'' of the shearing body force. For a simple half-cosine force profile, for example, the high Reynolds number bound is beta <= pi^2/sqrt{216} = .6715... . We also report extensive direct numerical simulations for this particular force shape up to Re approximately 400; the observed dissipation rates are about a factor of three below the rigorous high-Re bound. Interestingly, the high-Re optimal solution of the variational problem bears some qualitative resemblence to the observed mean flow profiles in the simulations. These results extend and refine the recent analysis for body-forced turbulence in J. Fluid Mech. 467, 289-306 (2002).

nlin.CD↗

arXiv2003

Fluctuations of energy injection rate in a shear flow

We study the instantaneous and local energy injection in a turbulent shear flow driven by volume forces. The energy injection can be both positive and negative. Extremal events are related to coherent streaks. The probability distribution is asymmetric, deviates slightly from a Gaussian shape and depends on the position in shear direction. The probabilities for positive and negative injection are exponentially related, but the prefactor in the exponent varies across the shear layer.

nlin.CD↗

arXiv2003

Asymmetric time correlations in turbulent shear flows

Cross correlations between normal and downstream velocity fluctuations in a turbulent shear flow are shown to carry information about the non-normal amplification process. The creation of spanwise modulated streaks by downstream vortices implies an asymmetry in temporal correlation functions. We verify this in numerical simulations in shear flows with $Re_λ\approx 100$.

nlin.CD↗

arXiv2003

Noise Correlations in Shear Flows

We consider the effects of a shear on velocity fluctuations in a flow. The shear gives rise to a transient amplification that not only influences the amplitude of perturbations but also their time correlations. We show that, in the presence of white noise, time correlations of transversal velocity components are exponential and that correlations of the longitudinal components are exponential with an algebraic prefactor. Cross correlations between transversal and downstream components are strongly asymmetric and provide a clear indication of non-normal amplification. We suggest experimental tests of our predictions.

nlin.CD↗

arXiv2003

Pathways to non-sequential multiple ionization in strong laser fields

The outgoing electrons in non-sequential multiple ionization in intense laser fields are strongly correlated. The correlations can be explained within a classical model for interacting electrons in the presence of the external field. Here we extend the previous analysis for two and three electrons to cases with up to eight electrons and identify the saddle configurations that guard the channels for non-sequential multiple ionization. For four and fewer electrons the electrons in the dominant configuration are equivalent, for six and more electrons this is no longer the case. The case of five electrons is marginal, with two almost degenerate transition configurations. The total number of configurations increases rapidly, from 2 configurations for three electrons up to 26 configurations for eight electrons.

quant-ph↗

arXiv2003

Passive fields and particles in chaotic flows

Two examples for the interplay between chaotic dynamics and stochastic forces within hydrodynamical systems are considered. The first case concerns the relaxation to equilibrium of a concentration field subject to both chaotic advection and molecular diffusion. The concentration field develops filamentary structures and the decay rate depends non-monotonically on the diffusion strength. The second example concerns polymers, modelled as particles with an internal degree of freedom, in a chaotic flow. The length distribution of the polymers turns out to follow a power law with an exponent that depends on the difference between Lyapunov exponent and internal relaxation rate.

nlin.CD↗

arXiv2002

Echoes in classical dynamical systems

Echoes arise when external manipulations to a system induce a reversal of its time evolution that leads to a more or less perfect recovery of the initial state. We discuss the accuracy with which a cloud of trajectories returns to the initial state in classical dynamical systems that are exposed to additive noise and small differences in the equations of motion for forward and backward evolution. The cases of integrable and chaotic motion and small or large noise are studied in some detail and many different dynamical laws are identified. Experimental tests in 2-d flows that show chaotic advection are proposed.

nlin.CD↗

arXiv2002

Clustering dynamics of Lagrangian tracers in free-surface flows

We study the formation of clusters of passive Lagrangian tracers in a non-smooth turbulent flow in a flat free-slip surface as a model for particle dynamics on free surfaces. Single particle and pair dispersion show different behavior for short and large times: on short times particles cluster exponentially rapidly until patches of the size of the divergence correlation length are depleted; on larger times the pair dispersion is dominated by almost ballistic hopping between clusters. We also find that the distribution of particle density is close to algebraic and can trace this back to the exponential distribution of the divergence field of the surface flow.

nlin.CD↗