arXiv subjects

Bruno Eckhardt

Publications and source records attributed to Bruno Eckhardt.

At least 55 records · Page 3Linked to original sources

arXiv2014

Periodically bursting edge states in plane Poiseuille flow

We investigate the laminar-turbulent boundary in plane Poiseuille flow by the method of edge tracking. In short and narrow computational domains we find for a wide range in Reynolds number that all states in the boundary converge to a period orbit with a period of the order of $10^{3}$ time units. The attracting states in these small domains are periodically extended in the spanwise and streamwise direction, but always localized to one side of the channel in the normal direction. In short and wide domains the edge states are localized in the spanwise direction. The periodic motion found in the small domains then induces a large variety of dynamical activity. The findings are very similar to the ones in the asymptotic suction boundary layer.

physics.flu-dyn↗

arXiv2014

Long wavelength instability of coherent structures in plane Couette flow

We study the stability of coherent structures in plane Couette flow against long-wavelength perturbations in wide domains that cover several pairs of coherent structures. For one and two pairs of vortices, the states retain the stability properties of the small domains, but for three pairs new unstable modes are found. They are shown to be connected to bifurcations that break the translational symmetry and drive the coherent structures from the spanwise extended state to a modulated one that is a precursor to spanwise localized states. Tracking the stability of the orbits as functions of the spanwise wave length reveals a rich variety of additional bifurcations.

physics.flu-dyn↗

arXiv2013

Periodic orbits near onset of chaos in plane Couette flow

We track the secondary bifurcations of coherent states in plane Couette flow and show that they undergo an incomplete periodic doubling cascade that ends with a crisis bifurcation. We introduce a symbolic dynamics for the orbits and show that the ones that exist fall into the universal sequence described by Metropolis, Stein and Stein for unimodal maps. The periodic orbits cover much of the turbulent dynamics in that their temporal evolution overlaps with turbulent motions when projected onto a plane spanned by energy production and dissipation.

physics.flu-dyn↗

arXiv2013

Increasing lifetimes and the growing saddles of shear flow turbulence

In linearly stable shear flows turbulence spontaneously decays with a characteristic lifetime that varies with Reynolds number. The lifetime sharply increases with Reynolds number so that a possible divergence marking the transition to sustained turbulence at a critical point has been discussed. We present a mechanism by which the lifetimes increase: in the system's state space, turbulent motion is supported by a chaotic saddle. Inside this saddle a locally attracting periodic orbit is created and undergoes a traditional bifurcation sequence generating chaos. The formed new 'turbulent bubble' is initially an attractor supporting persistent chaotic dynamics. Soon after its creation it collides with its own boundary, by which it becomes leaky and dynamically connected with the surrounding structures. The complexity of the chaotic saddle that supports transient turbulence hence increases by incorporating the remnant of a new bubble. As a a result, the time it takes for a trajectory to leave the saddle and decay to the laminar state is increased. We demonstrate this phenomenon in plane Couette flow and show that characteristic lifetimes vary non-smoothly and non-monotonically with Reynolds number.

nlin.CD↗

arXiv2013

Complexity of localised coherent structures in a boundary-layer flow

We study numerically transitional coherent structures in a boundary-layer flow with homogeneous suction at the wall (the so-called asymptotic suction boundary layer ASBL). The dynamics restricted to the laminar-turbulent separatrix is investigated in a spanwise-extended domain that allows for robust localisation of all edge states. We work at fixed Reynolds number and study the edge states as a function of the streamwise period. We demonstrate the complex spatio-temporal dynamics of these localised states, which exhibits multistability and undergoes complex bifurcations leading from periodic to chaotic regimes. It is argued that in all regimes the dynamics restricted to the edge is essentially low-dimensional and non-extensive.

physics.flu-dyn↗

arXiv2013

Edge states for the turbulence transition in the asymptotic suction boundary layer

We demonstrate the existence of an exact invariant solution to the Navier-Stokes equations for the asymptotic suction boundary layer. The identified periodic orbit with a very long period of several thousand advective time units is found as a local dynamical attractor embedded in the stability boundary between laminar and turbulent dynamics. Its dynamics captures both the interplay of downstream oriented vortex pairs and streaks observed in numerous shear flows as well as the energetic bursting that is characteristic for boundary layers. By embedding the flow into a family of flows that interpolates between plane Couette flow and the boundary layer we demonstrate that the periodic orbit emerges in a saddle-node infinite-period (SNIPER) bifurcation of two symmetry-related travelling wave solutions of plane Couette flow. Physically, the long period is due to a slow streak instability which leads to a violent breakup of a streak associated with the bursting and the reformation of the streak at a different spanwise location. We show that the orbit is structurally stable when varying both the Reynolds number and the domain size.

physics.flu-dyn↗

arXiv2012

Intermittent boundary layers and torque maxima in Taylor-Couette flow

Turbulent Taylor-Couette flow between counter-rotating cylinders develops intermittently fluctuating boundary layers for sufficient counter-rotation. We demonstrate the phenomenon in direct numerical simulations for radius ratios η=0.5 and 0.71 and propose a theoretical model for the critical value in the rotation ratio. Numerical results as well as experiments show that the onset of this intermittency coincides with the maximum in torque. The variations in torque correlate with the variations in mean Taylor vortex flow which is first enhanced for weak counter-rotation, and then reduced as intermittency sets in. To support the model, we compare to numerical results, experiments at higher Reynolds numbers, and to Wendt's data.

physics.flu-dyn↗

arXiv2012

Direct Numerical Simulations of Local and Global Torque in Taylor-Couette Flow up to Re=30.000

The torque in turbulent Taylor-Couette flows for shear Reynolds numbers Re_S up to 3x10^4 at various mean rotations is studied by means of direct numerical simulations for a radius ratio of η=0.71. Convergence of simulations is tested using three criteria of which the agreement of dissipation values estimated from the torque and from the volume dissipation rate turns out to be most demanding. We evaluate the influence of Taylor vortex heights on the torque for a stationary outer cylinder and select a value of the aspect ratio of Γ=2, close to the torque maximum. The connection between the torque and the transverse current J^ωof azimuthal motion which can be computed from the velocity field enables us to investigate the local transport resulting in the torque. The typical spatial distribution of the individual convective and viscous contributions to the local current is analysed for a turbulent flow case. To characterise the turbulent statistics of the transport, PDF's of local current fluctuations are compared to experimental wall shear stress measurements. PDF's of instantaneous torques reveal a fluctuation enhancement in the outer region for strong counter-rotation. Moreover, we find for simulations realising the same shear Re_S>=2x10^4 the formation of a torque maximum for moderate counter-rotation with angular velocities ω_o\approx-0.4ω_i. In contrast, for Re_S<=4x10^3 the torque features a maximum for a stationary outer cylinder. In addition, the effective torque scaling exponent is shown to also depend on the mean rotation state. Finally, we evaluate a close connection between boundary-layer thicknesses and the torque.

physics.flu-dyn↗

arXiv2011

From travelling waves to mild chaos: a supercritical bifurcation cascade in pipe flow

We study numerically a succession of transitions in pipe Poiseuille flow that leads from simple travelling waves to waves with chaotic time-dependence. The waves at the origin of the bifurcation cascade possess a shift-reflect symmetry and are both axially and azimuthally periodic with wave numbers κ = 1.63 and n = 2, respectively. As the Reynolds number is increased, successive transitions result in a wide range of time dependent solutions that includes spiralling, modulated-travelling, modulated-spiralling, doubly-modulated-spiralling and mildly chaotic waves. We show that the latter spring from heteroclinic tangles of the stable and unstable invariant manifolds of two shift-reflect-symmetric modulated-travelling waves. The chaotic set thus produced is confined to a limited range of Reynolds numbers, bounded by the occurrence of manifold tangencies. The states studied here belong to a subspace of discrete symmetry which makes many of the bifurcation and path-following investigations presented technically feasible. However, we expect that most of the phenomenology carries over to the full state-space, thus suggesting a mechanism for the formation and break-up of invariant states that can sustain turbulent dynamics.

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

Localised edge states nucleate turbulence in extended plane Couette cells

We study the turbulence transition of plane Couette flow in large domains where localised perturbations are observed to generate growing turbulent spots. Extending previous studies on the boundary between laminar and turbulent dynamics we determine invariant structures intermediate between laminar and turbulent flow. In wide but short domains we find states that are localised in spanwise direction, and in wide and long domains the states are also localised in downstream direction. These localised states act as critical nuclei for the transition to turbulence in spatially extended domains.

physics.flu-dyn↗

arXiv2008

Quantum model for double ionization of atoms in strong laser fields

We discuss double ionization of atoms in strong laser pulses using a reduced dimensionality model. Following the insights obtained from an analysis of the classical mechanics of the process, we confine each electron to move along the lines that point towards the two-particle Stark saddle in the presence of a field. The resulting effective two dimensional model is similar to the aligned electron model, but it enables correlated escape of electrons with equal momenta, as observed experimentally. The time-dependent solution of the Schrödinger equation allows us to discuss in detail the time dynamics of the ionization process, the formation of electronic wave packets and the development of the momentum distribution of the outgoing electrons. In particular, we are able to identify the rescattering process, simultaneous direct double ionization during the same field cycle, as well as other double ionization processes. We also use the model to study the phase dependence of the ionization process.

physics.atom-ph↗

arXiv2008

Laminar-turbulent boundary in plane Couette flow

We apply the iterated edge state tracking algorithm to study the boundary between laminar and turbulent dynamics in plane Couette flow at Re=400. Perturbations that are not strong enough to become fully turbulent nor weak enough to relaminarize tend towards a hyperbolic coherent structure in state space, termed the edge state, which seems to be unique up to obvious continuous shift symmetries. The results reported here show that in cases where a fixed point has only one unstable direction, as for the lower branch solution in in plane Couette flow, the iterated edge tracking algorithm converges to this state. They also show that choice of initial state is not critical, and that essentially arbitrary initial conditions can be used to find the edge state.

physics.flu-dyn↗

arXiv2008

Lifetime statistics in transitional pipe flow

Several experimental and numerical studies have shown that turbulent motions in circular pipe flow near transitional Reynolds numbers may not persist forever, but may decay. We study the properties of these decaying states within direct numerical simulations for Reynolds numbers up to 2200 and in pipes with lengths equal to 5, 9 and 15 times the diameter. We show that the choice of the ensemble of initial conditions affects the short time parts of lifetime distributions, but does not change the characteristic decay rate for long times. Comparing lifetimes for pipes of different length we notice a linear increase in the characteristic lifetime with length, which reproduces the experimental results when extrapolated to 30 diameters, the length of an equilibrium turbulent puff at these Reynolds numbers.

physics.flu-dyn↗

arXiv2008

Mixing effectiveness depends on the source-sink structure: Simulation results

The mixing effectiveness, i.e., the enhancement of molecular diffusion, of a flow can be quantified in terms of the suppression of concentration variance of a passive scalar sustained by steady sources and sinks. The mixing enhancement defined this way is the ratio of the RMS fluctuations of the scalar mixed by molecular diffusion alone to the (statistically steady-state) RMS fluctuations of the scalar density in the presence of stirring. This measure of the effectiveness of the stirring is naturally related to the enhancement factor of the equivalent eddy diffusivity over molecular diffusion, and depends on the Peclet number. It was recently noted that the maximum possible mixing enhancement at a given Peclet number depends as well on the structure of the sources and sinks. That is, the mixing efficiency, the effective diffusivity, or the eddy diffusion of a flow generally depends on the sources and sinks of whatever is being stirred. Here we present the results of particle-based simulations quantitatively confirming the source-sink dependence of the mixing enhancement as a function of Peclet number for a model flow.

physics.flu-dyn↗

arXiv2007

How does flow in a pipe become turbulent?

The transition to turbulence in pipe flow does not follow the scenario familiar from Rayleigh-Benard or Taylor-Couette flow since the laminar profile is stable against infinitesimal perturbations for all Reynolds numbers. Moreover, even when the flow speed is high enough and the perturbation sufficiently strong such that turbulent flow is established, it can return to the laminar state without any indication of the imminent decay. In this parameter range, the lifetimes of perturbations show a sensitive dependence on initial conditions and an exponential distribution. The turbulence seems to be supported by three-dimensional travelling waves which appear transiently in the flow field. The boundary between laminar and turbulent dynamics is formed by the stable manifold of an invariant chaotic state. We will also discuss the relation between observations in short, periodically continued domains, and the dynamics in fully extended puffs.

physics.flu-dyn↗

arXiv2007

Comment on 'Critical behaviour in the relaminarization of localized turbulence in pipe flow'

This is a comment on arXiv:physics/0608292, subsequently published in Phys Rev Lett, 98, 014501 (2007), in which Willis and Kerswell study in direct numerical simulations the statistics of turbulent lifetimes in pipe flow. They suggest that their data for six different Reynolds numbers support a divergence of the lifetime near a Reynolds number of about 1870. However, their conclusion is not compelling: a re-analysis of their data shows that it is also compatible with an exponentially increasing lifetime.

physics.flu-dyn↗

arXiv2007

Suppression of correlated electron escape in double ionization in strong laser fields

The effect of the Pauli exclusion principle on double ionization of He atoms by strong, linearly polarized laser pulses is analyzed. We show that correlated electron escape, with electron momenta symmetric with respect to the field polarization axis, is suppressed if atoms are initially prepared in the metastable state 3S. The effect is a consequence of selection rules for the transition to the appropriate outgoing two-electron states. We illustrate the suppression in numerical calculations of electron and ion momentum distributions within a reduced dimensionality model.

physics.atom-ph↗