09:00  09:30

opening  JanMichael Rost, director of the MPIPKS and the scientific coordinators

09:30  10:10

Predrag Cvitanović
(Georgia Institiute of Technology)
A spatiotemporal zeta function for transitional turbulence?
We address the long standing problem of how to describe, by means of discrete symbolic dynamics, the spatiotemporal chaos (or turbulence) in spatially extended, strongly nonlinear field theories.
One way to capture the essential features of turbulent motions is offered by coupled map lattice models, in which the spacetime is discretized, with the dynamics of smallscale spatial structures modeled by maps attached to lattice sites. The discretization that we study, the "spatiotemporal cat," has a remarkable feature that its every solution is uniquely encoded by a linear transformation from the corresponding finite alphabet symbol lattice. A spatiotemporal window into system dynamics is provided by a finite block of symbols, and the central question is to determine the likelihood of a given block's occurrence. As spatiotemporal states that share the same subblocks shadow each other exponentially well within the corresponding spatiotemporal windows, the dynamical zeta functions are now sums over spacetime tori, rather than timeperiodic orbits.
In the spatiotemporal formulation of turbulence there is no evolution in time, there are only a repertoires of admissible spatiotemporal patterns. In other words: throw away your integrators, and look for guidance in clouds' repeating patterns.

10:10  10:30

Valerio Lucarini
(University of Reading)
Global Stability Properties of the Climate: Melancholia States, Invariant Measures, and Phase Transitions
For a wide range of values of the incoming solar radiation, the Earth features at least two attracting states, which correspond to competing climates. The warm climate is analogous to the present one; the snowball climate features global glaciation and conditions that can hardly support life forms. Paleoclimatic evidences suggest that in past our planet flipped between these two states. The main physical mechanism responsible for such instability is the icealbedo feedback. In a previous work, we defined the Melancholia states that sit between the two climates. Such states are embedded in the boundaries between the two basins of attraction and feature extensive glaciation down to relatively low latitudes. Here, we explore the global stability properties of the system by introducing random perturbations as modulations to the intensity of the incoming solar radiation. We observe noiseinduced transitions between the competing basins of attractions. In the weak noise limit, large deviation laws define the invariant measure and the statistics of escape times. By empirically constructing the instantons, we show that the Melancholia states are the gateways for the noiseinduced transitions. In the region of multistability, in the zeronoise limit, the measure is supported only on one of the competing attractors. For low (high) values of the solar irradiance, the limit measure is the snowball (warm) climate. The changeover between the two regimes corresponds to a first order phase transition in the system. The framework we propose seems of general relevance for the study of complex multistable systems. At this regard, we relate our results to the debate around the prominence of contigency vs. convergence in biological evolution. Finally, we propose a new method for constructing Melancholia states from direct numerical simulations, thus bypassing the need to use the edgetracking algorithm.

10:30  11:10

Coffee break

11:10  11:30

Mahesh M. Bandi
(Okinawa Institute of Science and Technology Graduate University)
Fluctuations in flight

11:30  11:50

Jakub Zakrzewski
(Jagiellonian University)
Models for multielectron ionisation
I will present in the hopefully accessible way to the audience of various background the work accomplished together with Bruno Eckhardt on restricted dimensionality models of multielectron ionisation of atoms and molecules, starting with classical models and reaching full quantum mechanical simulations of dynamics.

12:00  13:00

Lunch break

13:00  13:30

Informal discussions

13:30  13:50

Beverley McKeon
(California Institute of Technology)
Some implications of selfsimilarity in canonical wall turbulence
There has been much recent progress with regards to characterizing selfsimilar behavior in wall turbulence in experiments, in simulation, and in the mean and instantaneous forms of the NavierStokes equations. Indeed, this is a topic about which Bruno thought deeply. Here, we identify commonalities and differences between these observations, and draw some conclusions concerning the requirements for selfsimilarity and selfsustaining processes in wall turbulence. Recent developments with respect to resolvent analysis are exploited to identify lowrank representations of these processes, their signatures and their limitations in physical and spectral space. We close with a discussion of some outstanding challenges related to the existence, selfsustenance and modeling of selfsimilar solutions and structures in the canonical flows.

13:50  14:10

Jianjun Tao
(Peking University)
Formation mechanism of Lobe and Cleft at the front of sand storm
Lobes and clefts are the primary structures formed at the fronts of sand storms and other meteorological gravity currents. Though the velocity field and the density field are coupled, the present numerical simulations and stability analyses of the gravity currents show that the local RayleighTaylor instability (RTI) at the density interface can determine the position and the original spanwise wave number of the strongest perturbations. Consequently, a RTI model is proposed without considering any information of the flow field, and includes only the fluids’ properties (Grashof number and Prandtl number). The predictions of the RTI model, i.e. the original dominating spanwise wave number of the Boussinesq current substantially depends on the Prandtl number and has a 1/3 scaling law with the Grashof number, are confirmed by the threedimensional numerical simulations and the experiments. Furthermore, by applying the turbulent eddy viscosity, the turbulent Schmidt number, and the sand storm density measured at Qingtu Lake in the RTI model, it is shown that the dominating spanwise wavelength predicted by the RTI model agrees qualitatively with the lobes’ scale observed at the front of sand storm.

14:10  14:30

Yongyun Hwang
(Imperial College London)
A minimal quasilinear approximation of turbulent channel flow
Townsend's model of attached eddies for boundary layers is revisited within a quasilinear approximation. The velocity field is decomposed into a mean profile and fluctuations. While the mean is obtained from the nonlinear equations, the fluctuations are modelled by replacing the nonlinear selfinteraction terms with an eddyviscositybased turbulent diffusion and stochastic forcing. Under this particular approximation, the resulting fluctuation equations remain linear, and it allows one to use superposition of their solutions for the calculation of Reynolds stress as in the original attached model. By leveraging this feature, the stochastic forcing is determined selfconsistently by solving an optimisation problem which minimises the difference between the Reynolds shear stresses from the mean and fluctuation equations, subject to a constraint that the averaged Reynolds shearstress spectrum is sufficiently smooth in the spatial wavenumber space. The proposed quasilinear approximation is subsequently applied to turbulent channel flow in a range of friction Reynolds number from Re_tau=500 to Re_tau=20,000. The best result is obtained when the Reynolds stress is calculated by considering two leading POD (proper orthogonal decomposition) modes, which further filters out the modelling artifact caused by the unphysical stochastic forcing. In this case, the resulting turbulence intensity profile and energy spectra exhibit exactly the same qualitative behaviour as DNS data throughout the entire wallnormal location, while reproducing the early theoretical predictions of the original attached eddy model within a controlled approximation to the NavierStokes equations.
*This is the work done with Bruno just before he passed away.

14:30  14:50

Björn Hof
(Institute of Science and Technology Austria)
From periodic orbit solutions to fully turbulent flow
In recent years detailed experiments combined with advances in dynamical systems theory and statistical mechanics have allowed much progress in our understanding of the transition to turbulence in linearly stable shear flows. I will summarize part of this work and highlight open questions and future directions.

14:50  15:10

Dwight Barkley
(University of Warwick)
A fluid mechanic's analysis of the teacup singularity
In 1926 Einstein published a short paper explaining the meandering of
rivers. He famously began the paper by discussing the secondary flow generated
in a stirred tea cup  the flow now widely known to be responsible for the
collection of tea leaves at the center of a stirred cup of tea. In 2014, Luo
and Hou presented detailed numerical evidence of a finitetime singularity in
a rotating, incompressible, inviscid flow. The key driving mechanism of that
singularity is the secondary teacup flow. The present work is not aimed at
proving the existence of a singularity in this flow, nor is it aimed at
generating more highly resolved numerical evidence for the singularity than
already exists. Rather, I will assume that the flow simulated by Luo and Hou
genuinely develops a singularity. My goal is to understand, from a
fluidmechanics perspective, why.

15:10  15:50

Coffee break

15:50  16:10

Raphael Gerlach
(Paderborn University)
The unstable manifold of edge states
In the last few years classical set oriented numerical methods for the approximation of invariant sets of finite dimensional dynamical systems have been extended to the infinite dimensional setting. This novel approach is based on embedding techniques that allow to a compute onetoone image of the invariant set in a finite dimensional space. After a brief review of the setoriented continuation method for the computation of unstable manifolds I will apply this algorithm to a fluid dynamics problem: The transition to turbulence in parallel shear flows is connected with the existence of a lowerdimensional manifold in state space that distinguishes between the basin of attraction of the laminar fixed point and initial conditions leading to turbulent flow. Relative attractors on this manifold, socalled edge states have therefore at least one unstable direction. Here, we calculate and visualize the unstable manifold of such an edge state in channel flow.

16:10  16:30

Jeff Moehlis
(University of California)
Phase Space Analysis in Neural Systems

16:30  16:50

Alexander Morozov
(University of Edinburgh)
Purely elastic turbulence in parallel shear flows
Newtonian fluids are known to exhibit hydrodynamic instabilities and/or transition
to turbulence at large enough Reynolds numbers. Recently it has been discovered
that in simple shear flows (like pressuredriven flows in a pipe or between two
plates) there exist the socalled coherent structures which organize the turbulent
dynamics close to the laminarturbulent transition. In that region, their dynamics
are lowdimensional and can be described by a few (order ten) wellchosen degrees of
freedom.
On the other hand, complex fluids, in general, and polymer solutions, in particular,
do not flow like Newtonian fluids. Their flows exhibit instabilities at very low Reynolds
numbers which are driven not by inertia, but rather by anisotropic elastic stresses.
Further increase of the flow rate results in a truly chaotic flow  the socalled
purely elastic turbulence. The mechanism of this new type of chaotic motion is poorly
understood.
In this talk I will discuss our recent attempts to generalise the Newtonian theory of
the transition to turbulence to the purely elastic case. We identify the relevant
coherent structures and construct a viscoelastic selfsustaining process that can
organise flow dynamics close to the transition.

16:50  17:10

Yohann Duguet
(LIMSICNRS, Orsay Cedex)
The collapse of the Edge
The “Edge” is the state space manifold of codimension 1 separating the basins of attraction of the laminar and the turbulent state. Its definition and identification are relatively straightforward in bistable systems, and less trivial in systems where turbulence is transient. It is of interest to understand what the notion of separatrix becomes in the presence of an additional linear instability of the laminar state, i.e. when turbulence is the only attractor of the system. Such a situation arises in many highReynolds number shear flows such as plane Poiseuille flow or the Blasius flow, or more simply in imperfect subcritical flows.
In this talk I will review the status of edge tracking for the Blasius flow and the practical difficulties encountered in simulations. A new threedimensional model will be used to illustrate the global bifurcation responsible for the gradual disappearance of the Edge
as the Reynolds number is increased.

17:10  17:30

Kerstin Avila
(University of Bremen)
Experimental observation of Duffing dynamics in liquid sloshing
In nature and in engineering, periodic forcing leads often to nonlinear resonances which are challenging to model and predict. We show that the sloshing of water in a rectangular container driven by harmonic horizontal excitation is accurately described by the Duffing equation. The system exhibits a bent response curve with strong hysteresis (increasing with the driving amplitude), transitions occurring at $90^\circ$phaselag, as well as periodthreemotion. At large driving amplitudes highly nonlinear effects like competition between states and wave breaking, cause deviations from the Duffing dynamics and call for the development of more advanced models.

17:30  17:50

Marc Avila
(University of Bremen)
Drop breakup in homogeneous isotropic turbulence
The formation and breakup of drops in turbulent flows is of key importance in chemical, mechanical and aerospace engineering, but their physical mechanisms and time scales remain poorly understood. We investigate drop breakup in homogeneous isotropic turbulence with direct numerical simulations, thereby resolving all temporal and spatial scales. A new GPU code solving the Cahn–Hilliard–Navier–Stokes equations enables the simulation of thousands of independent cases and a detailed analysis of the breakup process. We find that drop breakup is a memoryless process, whose rate depends on the Weber number. Our results allow estimating the evolution of dropsize distributions in the dilute regime and can be used to parametrize populationbalance equations.

17:50  18:30

Informal discussions

18:30  19:30

Dinner

19:30  21:00

Poster session
