Book of Abstracts and Programs - uni-bremen.deBook of Abstracts and Programs The 5th Bremen Winter...

The 5th Bremen Winter School and SymposiumThe 5th Bremen Winter School and Symposium

Dynamical systems and fluidsDynamical systems and fluidsMarch 27-31 2017March 27-31 2017

Fachbereich Mathematik & InformatikFachbereich Mathematik & InformatikUniversität BremenUniversität Bremen

Book of AbstractsBook of Abstractsand Programsand Programs

The 5th Bremen Winter School and Symposium

Dynamical systems and fluids

March 27-31 2017Fachbereich Mathematik & Informatik

Universität Bremen

Funded by Collaborative Research CenterTRR 181

Energy Transfer in Atmosphere and Ocean

Contents

Programs.................................................................................1

List of Posters..........................................................................6

Abstracts..................................................................................8

Poster Abstracts....................................................................23

Participants............................................................................41

ORGANISING COMMITTEE

M. KeßeböhmerIvan OvsyannikovJens Rademacher

ADMINISTRATIVE CONTACT

Ebba Feldmann

Programs 1

Programs

Monday 27.03

09:00-10:30

Course: Edgar Knobloch (University of California Berkeley,USA)Rotating convection

10:50-12:20

Course: Mariana Haragus (Université de Franche-Comté, Besancon, France)Local bifurcations and reduction methods in reversible systems. Application to water-wave models

13:45-15:35

Course: Lev Lerman (Freie Universität Berlin)Hamiltonian dynamics and fluid motions

16:00-16:50

Discussion session

17:00-20:00

Poster session / Reception

2 Dynamical systems and fluids

Tuesday 28.03

09:00-10:30


10:50-12:20


13:45-14:15

Talk 1: Ksenia Guseva (Universität Oldenburg)Sedimentation of inertial particles in the presence of history force

14:25-14:55

Talk 2: Arturo Vieiro (Universitat de Barcelona, Spain)The splitting of separatrices associated to a Hamiltonian-Hopf bifurcation under the effect of a periodic forcing

15:05-15:35

Talk 3: Nikita Begun (Freie Universität Berlin)On the stability of weakly hyperbolic invariant sets

Programs 3

Wednesday 29.03

09:00-10:30


10:50-12:20


13:45-14:15

Talk 4: Gualtiero Badin (Universität Hamburg)Covariant coherent structures in two dimensional flow

14:25-14:55

Talk 5: Anton Savostianov (Durham University, UK)Smooth attractors for wave equation with fractional damping and fast growing nonlinearities

15:05-15:35

Talk 6: Michael Wilczek (Max Planck Institute for Dynamics and Self-Organization)Low dimensional models of fully developed turbulence

16:00-16:30

Exercise: Mariana Haragus (Université de Franche-Comté, Besancon, France)

18:00- Public lecture: Mariana Haragus (Université de Franche-Comté, Besancon, France)Waves and patterns in nature and experiments: a source of inspiration for mathematics


Thursday 30.03

09:00-10:30


10:50-12:20


13:45-14:15

Talk 7: Valerio Lucarini (University of Reading, UK)Melancholia states in the climate system: Exploring global instabilities and critical transitions

14:25-15:35

Exercise: Lev Lerman (Freie Universität Berlin)

16:00-16:30

Talk 8: Mattia Serra (ETH Zürich, Switzerland)Objective Eulerian Coherent Structures in Complex Dynamical Systems

17:00-20:00

Discussion session

Programs 5

Friday 31.03

09:00-10:30


10:50-11:20

Talk 9: Jim Thomas (Courant Institute of Mathematical Sciences, New York, USA) Wave-vortex interactions in rotating shallow water

11:20-11:50

Talk 10: Xavier Leoncini (Aix-Marseille Université, Marseille, France)Particle dynamics in flows

11:50-12:20

Talk 11: Olga Shishkina (Universität Göttingen)Scalings and boundary layers in natural thermal convection

13:45-14:55

Plenary Lecture: Eduard Feireisl (Institute of Mathematics of the Czech Academy of Sciences, Czech Republic)Weak vs. strong solvability of problems in fluid mechanics

15:05-15:35

Closing discussion


List of Posters

Poster 1 Makrina Agaoglou (Aristotle University of Thessaloniki, Greece)Discrete breathers in PT-Symmetric nonlinear metamaterials

Poster 2 Giovanni Conti (Universität Hamburg)Covariant coherent structures in two dimensional flow

Poster 3 Tobias Haas (Universität Stuttgart)Failure of an amplitude equation

Poster 4 Paul Mannix (Imperial College London, UK)TBD

Poster 5 La Mi (Technion -- Israel Institute of Technology)Asymptotic based stabilization of a multi-tethered lighter-than-air system in uniform flow

Poster 6 Naoko Miyajima (Durham University)Determining modes of the 2D Navier-Stokes equations on the beta-plane

Poster 7 Florian Noethen (Universität Hamburg)A projector based convergence proof of the Ginelli algorithm for Covariant Lyapunov Vectors

Poster 8 Paul Ritter (Center of Applied Space Technology and Microgravity, University of Bremen)Simulation and modeling of localised invariant solutions in transitional pipe flow

Poster 9 Evgenii Ryzhov (Pacific Oceanological Institute of Far Eastern Branch of Russian Academy of Sciences, Vladivostok, Russia)Parametric instability of vortex systems in nonlinear flows

List of Posters 7

Poster 10 Matthew Salewski (Technische Universität Berlin)Symmetry reduction in model reduction

Poster 11 Jim Thomas (New York University)Wave-vortex interactions in rotating shallow water

Poster 12 Konstantin Trifonov (Lobachevsky State University of Nizhny Novgorod, Russia)Symplectic partially hyperbolic automorphisms of 4-dimensional

Poster 13 Gabin Urbancic (University of Bergen, Norway)Near-resonant internal wave triads

Poster 14 Panagiotis Vasilopoulos (National Technical University ofAthens, Greece)Infinite dimensional singular perturbation theory for the second order Maxwell - Bloch equations

Poster 15 Nicola Vassena (Freie Universität Berlin)Sensitivity of chemical reaction networks

Poster 16 Sergiy Vasylkevych (Universität Hamburg)Global well-posedness of the generalized LSG equations

Poster 17 Caroline Ziegler (Technische Universität München)Lagrangian description of advection-diffusion and coherent sets


Abstracts

Course

Rotating convection

Edgar Knobloch*

In this series of lectures I will describe basic properties ofBoussinesq convection in a rotating horizontal layer, starting from theprimitive equations.

In lecture 1 I will discuss in the linear and weakly nonlineartheries for steady convection and for standing and traveling waves(for low Prandtl number convection) in the plane. I will discuss modi-fications when the domain is a rotating circular cylinder and the dis-tinction between body and wall modes.

In lecture 2 I will discuss spatially localized structures in this sys-tem.

In lecture 3 I will discuss the properties of geostrophic turbu-lence that is present at large Rayleigh numbers in the limit of lowRossby numbers (the rapid rotation limit).

* Email address: knobloch(at)berkeley.eduUniversity of California Berkeley, USA

mailto:[email protected]

Abstracts 9

Course

Local bifurcations and reduction methods inreversible systems. Application to water-wave

models

Mariana Haragus*

Starting with the simplest bifurcation problems arising for ordi-nary differential equations in one and two dimensions, the purpose ofthese lectures is to describe several tools from the theory of infinite-dimensional dynamical systems, allowing to treat more complicatedbifurcation problems, as for instance bifurcations arising in partial dif-ferential equations. Such tools are extensively used to solve con-crete problems arising in physics and natural sciences. We focus ontwo specific methods, namely the center manifold reduction and thenormal form theory. We illustrate these methods on different water-wave models.

* Email address: mariana.haragus(at)univ-fcomte.frUniversité de Franche-Comté, Besancon, France


Course

Hamiltonian dynamics and fluid motions

Lev Lerman*

Lecture 1. “Introduction to the dynamics of Hamiltonian sys-tems” In the lecture some background needed to understand whatHamiltonian systems are, the sources of their appearance in mathe-matics, their special structure and why they require special tools forthe study, the main geometric base for studying Hamiltonian sys-tems, which classes of Hamiltonian systems are more or less studiedby now.

Lecture 2. Soliton-type topics in Hamiltonian systems: homo-heteroclinic orbits and around them. I shall discuss possible types ofhomoclinic structures in Hamiltonian dynamics, how they depend onthe type of equilibria (periodic orbits, invariant tori), problems fromphysics leading to the study of such behavior.

Lecture 3. “Two-dimensional hydrodynamics and Hamiltoniansystems” Two-dimensional fluid motions can be described by the re-lated equation for the stream function. This function is a Hamiltonianof the system in the ideal two-dimensional hydrodynamics. Someother models from hydrodynamics leading to the study of Hamilton-ian systems (interaction of vortices, etc.). Elliptic PDEs which ariseas models of these Hamiltonians, patterns in such equations.

Lecture 4. “Advection and transport: applications of Hamiltoniandynamics.” We discuss briefly some models of the transport of pas-sive impurity along two-dimensional Hamiltonian flows, how thismodel arises and some conclusions that can be extracted from thisdescription.

* Email address: lermanl(at)mm.unn.ruFreie Universität Berlin

Abstracts 11

Plenary Lecture

Weak vs. strong solvability of problems in fluidmechanics

Eduard Feireisl*

We discuss the concept of weak or even measure valued solu-tion in fluid mechanics. We present a simple proof that all these gen-eralized solutions coincide as long as the problem admits a strongsolution (weak--strong uniqueness). Then we discuss possible appli-cations to problems of convergence of certain numerical schemes.

* Emal address: feireisl(at)math.cas.czInstitute of Mathematics of the Czech Academy of Sciences, Czech Republic


Talk 1

Sedimentation of inertial particles in the presence ofhistory force

Ksenia Guseva*

The motion of small inertial particles through a fluid is influencedby different hydrodynamic forces, described by the Maxey-Rileyequations. One of these forces is the Basset force — an integral overthe particle’s history. We analyse the effect of the history force on thesedimentation of inertial particles in a two-dimensional convectionflow and in a three-dimensional homogeneous isotropic turbulentflow in the presence of gravity. As a special case we investigate theproblem of settling of nearly neutrally buoyant particles, exemplifiedby marine snow. We find that the presence of the history force in oursystems leads to individual trajectories that strongly deviate fromwhat is observed without memory. In particular, in the presence ofgravity the effect of the Basset force is an extraordinarily slow con-vergence (proportional to ) towards an asymptotic settling veloc-ity of the center of mass of the particle ensemble. Finally, we discussthe application of the concept of snapshot attractors to understandthe extraordinary slow convergence due to long-term memory.

* Email address: ksenia.guseva(at)uol.deUniversität Oldenburg

Abstracts 13

Talk 2

The splitting of separatrices associated to aHamiltonian-Hopf bifurcation under the effect

of a periodic forcing

Arturo Vieiro*

We consider a Hamiltonian system given by a suitable trunca-tion of the normal form of the Hamiltonian-Hopf bifurcation plus aconcrete periodic non-autonomous perturbation having all harmon-ics. Our goal is to give some details on the behaviour of the splittingof the 2-dimensional separatrices. The theoretical results will becompared with direct computations of the invariant manifolds. A care-ful analysis of the associated Poincaré-Melnikov integral will providea description of the sequence of parameters corresponding tochanges on the dominant harmonics of the splitting function.

This is a joint work with E. Fontich and C. Simó.

* Email address: vieiro(at)maia.ub.esUniversitat de Barcelona, Spain


Talk 3

On the stability of weakly hyperbolic invariant sets

Nikita Begun*

The dynamical object which we study is a compact invariant setwith a suitable hyperbolic structure. Stability of weakly hyperbolicsets was studied by V. A. Pliss and G. R. Sell. They assumed that theneutral, unstable and stable linear spaces of the corresponding lin-earized systems satisfy Lipschitz condition. They showed that if aperturbation is small, then the perturbed system has a weakly hyper-bolic set , which is homeomorphic to the weakly hyperbolic set of the initial system, close to , and the dynamics on is close tothe dynamics on . At the same time, it is known that the Lipschitzproperty is too strong in the sense that the set of systems without thisproperty is generic. Hence, there was a need to introduce new meth-ods of studying stability of weakly hyperbolic sets without Lipschitzcondition. In this talk we will show that even without Lipschitz condi-tion there exists a continuous mapping such that .(Joint works with V. A. Pliss and G. R. Sell)

* Email address: begun(at)math.fu-berlin.deFreie Universität Berlin

Abstracts 15

Talk 4

Covariant coherent structures in two dimensionalflow

Gualtiero Badin*

A new method to describe hyperbolic patterns in two dimen-sional flows is proposed. The method is based on the Covariant Lya-punov Vectors (CLVs), which have the properties to be covariant withthe dynamics, and thus being mapped by the tangent linear operatorinto another CLVs basis, they are norm independent, invariant undertime reversal and can be not orthonormal. CLVs can thus give amore detailed information on the expansion and contraction direc-tions of the flow than the Lyapunov Vector bases, that are instead al-ways orthogonal.

We suggest a definition of Hyperbolic Covariant Coherent Struc-tures (HCCSs), that can be defined on the scalar field representingthe angle between the CLVs. We then study the connection betweenthe HCCSs and the Hyperbolic Lagrangian Coherent Structures(HLCSs), detected by a variational/geodesic theory.

We consider three examples: a simple autonomous Hamiltoniansystem, as well as the non-autonomous “double gyre” and Bickleyjet, to see how well the angle is able to describe particular patternsand barriers. We compare the results from the HCCSs with other de-tection methods such as the ridges of the Finite Time Lyapunov Ex-ponents (FTLEs) and the variational/geodesic theory for the HLCSs.Results show the capability of our method to capture a subset of theHLCSs characterized by orthogonality between the CLVs and theirappearance and disappearance in time. (Work in collaboration withGiovanni Conti)

* Email address: gualtiero.badin(at)uni-hamburg.deUniversität Hamburg


Talk 5

Smooth attractors for wave equation with fractionaldamping and fast growing nonlinearities

Anton Savostianov*

In this talk I would like to give a brief review of the results on theexistence of global attractors and their smoothness for dynamicalsystems generated by several models of nonlocally damped waveequations with critical nonlinearities. It appears that if the nonlinearityentering the equation grows faster than a certain threshold then theonly energy estimate is not enough to obtain even uniqueness of thesolutions. To go beyond the threshold we need extra regularity of thesolutions provided by so called Strichartz estimates, which are usu-ally obtained for the conservative systems. I will explain how thesetype of estimates can be transferred to our models. In turn, the ob-tained extra regularity allows to prove global well-posedness of theproblems under consideration and establish existence of smoothglobal attractors for the corresponding dynamical systems. If timepermits I will highlight the application of this approach to the socalled hyperbolic Cahn-Hilliard-Oono equation.

* Email address: anton.savostianov(at)u-cergy.frDurham University, UK

Abstracts 17

Talk 6

Low dimensional models of fully developedturbulence

Michael Wilczek*

Turbulence is a paradigm for a system with a huge amount ofstrongly interacting degrees of freedom. One hallmark of turbulentflows is the intrinsic non-Gaussianity of the velocity field. Probabilitydensity functions (PDFs) of velocity gradients, for example, exhibitbroad tails, indicating that extreme jumps in the velocity field are or-ders of magnitude more likely than if turbulence were Gaussian.Probing turbulent velocity fields on increasing scales, for example bymeans of velocity increment PDFs, reveals a breaking of statisticalself-similarity: the PDFs change shape as a function of scale, a phe-nomenon known as intermittency. The complexity of this problemcalls for simple, low-dimensional models to develop a better under-standing.

In this presentation we will shed light on this topic from two dif-ferent perspectives. The first part of the presentation will focus on thesmall scales of turbulence, which can be comprehensively capturedin terms of the velocity gradient tensor. We will introduce and discussa simple dynamical system for its statistical evolution and comparethe results to direct numerical simulations of fully developed turbu-lence.

In the second part of the presentation we will discuss how non-Gaussianity and intermittency can be captured in terms of phase cor-relations in Fourier space. We will present a simple phase-couplingmodel which qualitatively reproduces some feature observed in tur-bulence.

Both topics covered in this presentation demonstrate how meth-ods from nonlinear dynamics can help to better understand complexsystems like turbulent flows.

* Email address: michael.wilczek(at)ds.mpg.deMax Planck Institute for Dynamics and Self-Organization


Talk 7

Melancholia states in the climate system: Exploringglobal instabilities and critical transitions

Valerio Lucarini*

Multistability is a ubiquitous feature in systems of geophysicalrelevance and provides key challenges for our ability to predict a sys-tem's response to perturbations. Near critical transitions smallcauses can lead to large effects and - for all practical purposes - irre-versible changes in the properties of the system. The Earth climate ismultistable: present astronomical and astrophysical conditions sup-port two stable regimes, the warm climate we live in, and a snowballclimate, characterized by global glaciation. We first provide an over-view of methods and ideas relevant for studying the climate re-sponse to forcings and focus on the properties of critical transitions.Following an idea developed by Eckhardt and co. for the investiga-tion of multistable turbulent flows, we study the global instability giv-ing rise to the snowball/warm multistability in the climate system byidentifying the climatic edge state, a saddle embedded in the bound-ary between the two basins of attraction of the stable climates. Theedge state attracts initial conditions belonging to such a boundaryand is the gate facilitating noise-induced transitions between compet-ing attractors. We use a simplified yet Earth-like climate model con-structed by coupling a primitive equations model of the atmospherewith a simple diffusive ocean. We refer to the climatic edge states asMelancholia states. We study their dynamics, their symmetry proper-ties, and we follow a complex set of bifurcations. We find situationswhere the Melancholia state has chaotic dynamics. In these cases,the basin boundary between the two basins of attraction is a strangegeometric set with a nearly zero codimension, and relate this featureto the time scale separation between instabilities occurring onweather and climatic time scales. We also discover a new stable cli-matic state characterized by non-trivial symmetry properties.

* Email address: v.lucarini(at)reading.ac.ukUniversity of Reading, UK

Abstracts 19

Talk 8

Objective Eulerian coherent structures in complexdynamical systems

Mattia Serra*

We present a variational theory of Objective Eulerian CoherentStructure (OECS) in two-dimensional non-autonomous dynamicalsystems (Serra, M. and Haller, G., Chaos 26(5), 2016). OECSs un-cover the instantaneous skeleton of the overall dynamical system,acting as theoretical centerpieces of short-time trajectory patterns.We also show that OECSs are null-geodesics of appropriateLorentzian metrics. Exploiting the geometry of geodesic flows, wederive a fully automated procedure for the computation of OECSs. Asan illustration, we apply our results to satellite-derived ocean velocitydata, and submesoscale ocean surface velocity field reconstructedfrom high-frequency-radar measurements. (Joint work with GeorgeHaller)

* Email address: serram(at)ethz.chETH Zürich, Switzerland





Talk 9

Wave-vortex interactions in rotating shallow water

Jim Thomas*

In this talk I will present recent theoretical work examining vari-ous possible interactions between fast inertia-gravity waves and slowbalanced quasi-geostrophic motions in rotating shallow water sys-tem. Using multi-scale asymptotic analysis, a set of evolution equa-tions will be presented for the potential vorticity. These equationscapture the slow dynamics of the rotating shallow water to a higherdegree of accuracy than the lowest order approximate model - thequasi-geostrophic equation. These new asymptotic reduced models,whose validity is confirmed by numerical experiments, point out thatfast waves can energetically interact with slow balanced motions.The results from asymptotic models is complemented by a series ofhigh resolution numerical simulations of the rotating shallow waterequations in regimes not directly accessible by asymptotic analysis,such as characterizing turbulent wave-vortex interactions. The mainfindings of these simulations is that the presence of strong wavescan significantly impact the balanced motion. For instance, it is ob-served that wave activity can prevent vortex mergers and inversecascades, these being well known features of balanced models suchas the quasi-geostrophic equation.

* Email address: jt1939(at)nyu.eduNew York University

Abstracts 21

Talk 10

Particle dynamics in flows

Xavier Leoncini*

In this talk I will discuss the dynamics of particles advected inregular and chaotic flows. I will address the transport properties ofpassive tracers in various flows. For all studied cases, anomaloussuperdiffusive transport with a characteristic exponent is observed. The origin of the anomaly is explained by the phenome-non of stickiness around coherent structures in regular flows, and bythe presence of regular chaotic jets for the chaotic and “turbulent”ones. We shall as well show we may be able to localize three-dimen-sional coherent structures or how to improve mixing properties in cel-lular flows while keeping the cellular structure of the flow.

* Emal address: Xavier.Leoncini(at)cpt.univ-mrs.frAix-Marseille Université, Marseille, France


Talk 11

Scalings and boundary layers in naturalthermal convection

Olga Shishkina*

We consider three classical paradigmatic systems to study ther-mally driven flows: Rayleigh–Bénard convection, horizontal convec-tion and vertical convection. For these systems we discuss how themean convective heat transport and momentum transport, measuredby the Nusselt number (Nu) and Reynolds number (Re), respectively,scale with the main input parameters, which are the Rayleigh num-ber (Ra) and Prandtl number (Pr). Further we consider thermalboundary layers in natural convection and discuss the influence ofthe turbulent fluctuations and of a non-vanishing mean pressure gra-dient on the boundary layer structure.

* Email address: Olga.Shishkina(at)ds.mpg.deUniversität Göttingen

Poster Abstracts 23

Poster Abstracts

Poster 1

Discrete breathers in PT-Symmetric nonlinearmetamaterials

Makrina Agaoglou*

In this work we investigate a one-dimensional parity-time (PT)-symmetric magnetic metamaterial consisting of split-ring dimers hav-ing both gain and loss. Employing a Melnikov analysis we study theexistence and persistence of localized travelling waves and studytheir linear stability. We find conditions under which the homoclinicorbits persist using the homoclinic Melnikov Method. Our analyticalresults are found to be in good agreement with direct numerical com-putations.

* Email address: makrina_agao(at)hotmail.comAristotle University of Thessaloniki, Greece


Poster 2

Covariant coherent structures in two dimensionalflow

Giovanni Conti*

A new method to describe hyperbolic patterns in two dimen-sional flows is proposed. The new method is based on the CovariantLyapunov Vectors (CLVs), which have the properties to be covariantwith the dynamics, and thus being mapped by the tangent linear op-erator into another CLVs basis, they are norm independent, invariantunder time reversal and can be not orthonormal. CLVs can thus givea more detailed information on the expansion and contraction direc-tions of the flow than the Lyapunov Vector bases, that are instead al-ways orthogonal.

We suggest a connection between the Hyperbolic Covariant Co-herent Structures (HCCSs), that can be defined on the scalar fieldrepresenting the angle between the CLVs, and the Hyperbolic La-grangian Coherent Structures (HLCSs), detected by a variational/ge-odesic theory.

We investigate three models: a simple autonomous Hamiltoniansystem, as well as the non-autonomous “double gyre” and Bickleyjet, to see how well the angle is able to describe particular patternsand barriers. We compare the results from the HCCSs with other de-tection methods such as the ridges of the Finite Time Lyapunov Ex-ponents (FTLEs) and the variational/geodesic theory for the HLCSs.(Joint work with Gualtiero Badin)

* Email address: giovanni.conti(at)uni-hamburg.deUniversität Hamburg

Poster Abstracts 25

Poster 3

Failure of an amplitude equation

Tobias Haas*

The approximation by amplitude equations still plays an impor-tant role in the understanding of complex systems of PDEs, e.g. theKorteweg-de Vries (KdV) approximation of the water wave problem.In the last two decades many proofs of approximation results for for-mally derived amplitude equations were provided, but there aresome counterexamples where formally derived amplitude equationsdo not approximate solutions on a long time scale, too (e.g. [1]).These counterexamples usually use periodic boundary conditions.We want to give a counterexample without imposing periodic bound-ary conditions by showing that the (resonant) four wave interaction(FWI) system fails to describe the dynamics of some Boussinesqmodel.

References[1] Guido Schneider, Danish Ali Sunny, and Dominik Zimmermann,

The NLS Approximation Makes Wrong Predictions for the WaterWave Problem in Case of Small Surface Tension and SpatiallyPeriodic Boundary Conditions, Journal of Dynamics and Differ-ential Equations 27 (2015), no. 3, 1077–1099.

* Email address: tobias.haas(at)mathematik.uni-stuttgart.deUniversität Stuttgart


Poster 4

TBD

Paul Mannix*

TBD.

* Email address: p.mannix15(at)imperial.ac.ukImperial College London, UK

Poster Abstracts 27

Poster 5

Asymptotic based stabilization of a multi-tetheredlighter-than-air system in uniform flow

La Mi*

We investigate the self-excited oscillations of a multi-tetheredlighter-than-air system (LTAS) in uniform flow. We derive the equa-tions of motion for the LTAS which consists of an elastically re-strained spherical rigid-body that is augmented by a three-dimen-sional nonlinear wake oscillator model representing vortex-induced vibration (VIV). The resulting dynamical system consists ofeighteen coupled first-order equations ( ) that incorporate a stronggeometrically nonlinear elastic restoring force coupled to a mixedquadratic and cubic interaction for the self-excited wake. The formu-lation is validated by comparing the amplitude response of a fourtether configuration with a ninety degree initial tether inclination tothe limit-cycle magnitude of a single-tethered benchmark experimentwhich exhibited large VIV in the transverse direction. An asymptoticmultiple-scales analysis of a reduced-order configuration ( ) resultsin a set of slowly-varying evolution equations for the coupled trans-verse body-wake interaction. Analysis of the resulting steady-statealgebraic equations culminates with a parameter set that enablessignificant reduction of the LTAS transverse dynamics. This algebraicrelation provides a guideline on choice of control parameters for VIVamplitude reduction. Numerical analysis of a modified system withoptimal reduced mass and tether length is applied to the original system demonstrating its effectiveness.

* Email address: mila(at)technion.ac.ilTechnion -- Israel Institute of Technology





Poster 6

Determining modes of the 2D Navier-Stokesequations on the beta-plane

Naoko Miyajima*

It has been known since 1967 (F&P) that the solutions of the 2dNavier-Stokes equations are essentially determined by a finite num-ber of degrees of freedom.

Physical arguments and numerics suggest that a flow on a rotat-ing plane will become zonal with time. Al-Jaboori and Wirosoetisno(2011) proved that with the beta-plane approximation, flows becomemore zonal with stronger rotation and the global attractor reduces toa point at a large but finite rotation rate.

In this poster, I will show that with sufficiently fast rotation, onecan improve on the number of determining modes over that given byJones and Titi in 1993.

* Email address: naoko.miyajima(at)durham.ac.ukDurham University

Poster Abstracts 29

Poster 7

A projector based convergence proof of the Ginellialgorithm for Covariant Lyapunov Vectors

Florian Noethen*

Covariant Lyapunov Vectors detect directions of asymptoticgrowth rates to small linear perturbations of solutions in a dynamicalsystem. During the last few years, several algorithms to compute theCLVs emerged and were used in a broad range of applications. Oneof the most popular algorithms was developed by Ginelli and relieson the concept of a stationary Lyapunov basis.

In my current research, I correct and extend existing conver-gence results for the stationary Lyapunov basis as in Ginelli's algo-rithm. Using orthogonal projections, I am able to handle the case of adegenerate Lyapunov spectrum. Ultimately, those new results willyield a complete convergence proof of the Ginelli algorithm.

* Email address: florian.noethen(at)uni-hamburg.deUniversität Hamburg


Poster 8

Simulation and modeling of localised invariantsolutions in transitional pipe flow

Paul Ritter*

Turbulent spots surrounded by laminar flow are a characteristicfeature of transitional shear flows. Yet there is no theory explainingtheiremergence and dynamics with respect to the equations of mo-tion. One possible approach uses the framework of dynamical sys-temstheory trying to identify exact invariant solutions to the govern-ing equations. These are thought to partition phase space via homo-and heteroclinic connections between their stable and unstable di-rections, thus providing a scaffold for the turbulent dynamics.

Since the transition to turbulence involves localised structures,their successful description also requires localised solutions. In thiswork, extensive direct numerical simulations of localised periodic or-bits in pipe flow for Reynolds numbers between 1500 and 5000 werecarried out.

As for turbulent localised spots the up- and downstream frontswere found to decay exponentially towards the laminar profile. Thisallows to model the heads and tails of the localised solutions by thelinearised Navier-Stokes equations [1, 2]. Combined with a modalansatz for the velocity- and pressure field, the model was able to pre-dict the drift speed of the solutions and radial velocity profiles as afunction of Reynolds number, azimuthal wavenumber and the slopeof the spatial decay towards laminar flow.

Hence, this study should provide insight into the relationship be-tween the kinematics and structure of localised spots and more gen-erally into the physics of localisation and the eventual relaminarisa-tion or spreading of the turbulent spots. (Joint work with Stefan Zam-mert, Bruno Eckhardt and Marc Avila)

* Email address: paul.ritter(at)zarm.uni-bremen.deCenter of Applied Space Technology and Microgravity, University of Bremen

Poster Abstracts 31

Figure 1. Structure of the investigated localised edge states obtained fromDNS at 3000 with (a) twofold (LB2), (b) threefold (LB3) rotational symmetry.The central image depicts isosurfaces and cross-sections of axial velocity.The upper right shows the upstream front of the same state (appears shorterdue to perspective). Shown is the perturbation velocity with the laminar flowsubtracted. Red (blue) streaks are faster (slower) than base flow. In order tohighlight the tail- and head-region, the isovalues have been chosen small:

. The axial extent of the shown isosurfaces is .

References[1] Brand, E. and Gibson, J.F.: A doubly localized equilibrium solu-

tion of plane Couette flow. Journal of Fluid Mechanics 750, p.R3, 2014

[2] Zammert, S. and Eckhardt, B.: Streamwise-lStreamwise decayof localized states in channel flow. Physical Review E 94 (4), p.041101, 2016


Poster 9

Parametric instability of vortex systems in nonlinearflows

Evgenii Ryzhov*

We study the dynamics of an elliptic vortex evolving in an oscil-latory nonlinear flow consisting of shear and rotational components.If the external flow is stationary, the elliptic vortex can perform threetypes of motion: oscillation, rotation, infinite elongation. In addition, itcan be motionless if positioned at a stationary point in the corre-sponding phase space. Certain stationary points in the correspond-ing phase space are hyperbolic, which makes them susceptible toexternal perturbations. Once perturbed the corresponding vortex dy-namics features a multitude of irregular dynamical phenomena in-cluding flipping between different canonical states.

* Email address: ryzhovea(at)poi.dvo.ruPacific Oceanological Institute of Far Eastern Branch of Russian Academy of Sciences, Vladivostok, Russia

Poster Abstracts 33

Poster 10

Symmetry reduction in model reduction

Matthew Salewski*

Model reduction takes a high-dimensional system, for example asystem of PDEs, to a system of much smaller dimension in order toimprove the computational efficiency without a substantial loss of ac-curacy. Transport-dominated dynamical systems however continue towithstand current methods of model reduction, and call for newstrategies. Here we present the application of symmetry reduction tomodel reduction. Removing the effect of continuous-parameter trans-formation groups from the solution space results in dynamics wherethe transport is diminished, or even removed, which can improve thefidelity of the models. In fact, systems which support transport phe-nomena, moving fronts and waves, often have translation invariance.We demonstrate reduced basis models using symmetry reduction forsome standard systems exhibiting transport phenomena. Further-more, we demonstrate symmetry reduction without equivariance ofthe vector field, further extending the reach of the application tomodel reduction.

* Email address: salewski(at)math.tu-berlin.deTechnische Universität Berlin





Poster 11

Wave-vortex interactions in rotating shallow water

Jim Thomas*

In this poster I will present recent theoretical work examiningvarious possible interactions between fast inertia-gravity waves andslow balanced quasi-geostrophic motions in rotating shallow watersystem. Using multi-scale asymptotic analysis, a set of evolutionequations will be presented for the potential vorticity. These equa-tions capture the slow dynamics of the rotating shallow water to ahigher degree of accuracy than the lowest order approximate model -the quasi-geostrophic equation. These new asymptotic reduced mod-els, whose validity is confirmed by numerical experiments, point outthat fast waves can energetically interact with slow balanced mo-tions. The results from asymptotic models is complemented by a se-ries of high resolution numerical simulations of the rotating shallowwater equations in regimes not directly accessible by asymptoticanalysis, such as characterizing turbulent wave-vortex interactions.The main findings of these simulations is that the presence of strongwaves can significantly impact the balanced motion. For instance, itis observed that wave activity can prevent vortex mergers and in-verse cascades, these being well known features of balanced mod-els such as the quasi-geostrophic equation.

* Email address: jt1939(at)nyu.eduNew York University

Poster Abstracts 35

Poster 12

Symplectic partially hyperbolic automorphismsof 4-dimensional

Konstantin Trifonov*

We study partially hyperbolic symplectic automorphisms of a 4-dimensional torus generated by integer unitary symplectic matricies.Before only hyperbolic torus maps were mainly studied, the investi-gations of partially hyperbolic automorphisms started rather recentlyand there are still many open questions. In this paper, we constructexamples of partially hyperbolic symplectic maps on the four-dimen-sional torus with various dynamics. In particular, we construct suchmap on the torus which has transitive one-dimensional foliationsgenerated by the eigendirections corresponding to eigenvalues lyingoff the unit circle. In order to construct such an example, the theoryof irreducible polynomials with integer coeffcients and some proper-ties of invariant subspaces of the related integer unitary matrices areexploited.

* Email address: kostya_31_08(at)mail.ruLobachevsky State University of Nizhny Novgorod, Russia





Poster 13

Near-resonant internal wave triads

Gabin Urbancic*

Exact phase-locked internal wave triads have been extensivelystudied due to their role in nonlinear energy transfer across the inter-nal wave spectrum. It is observed that near-resonant triads can alsoexist with surprising strength in a numerical simulation of tidal flowover an oceanic shelf break. Understanding this process is pivotal tounderstanding the local structure of the internal wave field.

* Email address: gabin.urbancic(at)gmail.comUniversity of Bergen, Norway

Poster Abstracts 37

Poster 14

Infinite dimensional singular perturbation theory forthe second order Maxwell - Bloch equations

Panagiotis Vasilopoulos*

We study the second order Maxwell - Bloch equations governinga two level laser in a ring cavity. For Class A lasers, these equationshave two widely separated time scales and form a singularly per-turbed, semilinear hyperbolic system with three distinct characteris-tics. We extend Menon - Haller's theory [G.Menon,Georgy Haller,SIAM J.MATH. ANAL.,Vol.33,No 2, pp315-346] to the second orderMaxwell - Bloch equations by proving the persistence of an arbitrarilysmooth slow manifold under an unbounded perturbation. The proof isobtained by a modified graph transform method.

* Email address: pvasilopmath(at)gmail.comNational Technical University of Athens, Greece


Poster 15

Sensitivity of chemical reaction networks

Nicola Vassena*

In living cells we can observe complex network systems such asmetabolic networks. Studying their sensitivity is one of the main ap-proach for understanding the dynamics of these biological systems.The study of sensitivity is based on knocking out an enzyme whichcatalyzes the reaction and the responses in the concentrations ofchemicals or their fluxes are observed. However, due to the com-plexity of the systems, it has been unclear how the network struc-tures determine the responses of the systems. We study the networkresponse to perturbations of a reaction rate j* and describe whichother reaction rates j’ respond by nonzero reaction flux, at steadystate. Nonzero responses of j’ to j* are called flux-influence of j* on j’.The main and most important aspect of this analysis lies in the reac-tion graph approach, in which the chemical reaction networks aremodeled by a directed graph. We emphasize that the analysis doesnot require numerical input: the require data is the network structureonly. We follow an approach by Fiedler and Mochizuki, inspired by pi-oneering works of Feinberg.

* Email address: nicovax540(at)zedat.fu-berlin.deFreie Universität Berlin




Poster Abstracts 39

Poster 16

Global well-posedness of the generalized LSGequations

Sergiy Vasylkevych*

Generalized LSG equations is a family of balance models for ro-tating shallow water flow that includes and LSG equations derivedby R. Salmon and their generalization by the authors. Each model inthe family can be formulated as an advection equation of a scalar po-tential vorticity by a 2D horizontal velocity, where the nonlinear PV in-version operator is given implicitly through a cascade of ellipticPDE’s.

We prove existence and uniqueness of global classical solutionsto the generalized large-scale semigeostrophic equations with peri-odic boundary conditions. The results are, under the physical restric-tion that the initial potential vorticity is positive, as strong as thoseavailable for the Euler equations of ideal fluid flow in two dimensions.

Our results are based on careful estimates and optimization ofexponents in Galiardo-Nirenberg inequalities, which show that, al-though the potential vorticity inversion is nonlinear, bounds on thepotential vorticity inversion operator remain sublinear. This permitsthe adaptation of an argument based on elliptic theory, proposedby Yudovich in 1963 for proving existence and uniqueness of weaksolutions for the two-dimensional Euler equations to our particularnonlinear situation.

This is a joint work with M. Oliver and M. Çalik

* Email address: sergiy.vasylkevych(at)uni-hamburg.deUniversität Hamburg


Poster 17

Lagrangian description of advection-diffusion andcoherent sets

Caroline Ziegler*

Many fluid flows at the onset of turbulence exhibit regions whichdisperse slowly with time, so called coherent sets. There are twoways of looking at the fluid motion: The Eulerian space-time descrip-tion and the Lagrangian material description. We develop a La-grangian approach to advection-diffusion, which yields a diffusion-only equation. In this setting, coherent structures are almost-invariantsets under the material evolution equation, which can be detected bya spectral analysis of a suitably defined Laplace-Beltrami operator.

* Email address: ziegler(at)ma.tum.deTechnische Universität München




Participants 41

Participants

Makrina Agaogloumakrina_agao(at)hotmail.comAristotle University of Thessaloniki, Greece

p. 23

Chinenye Jane Anichinenye(at)aims.ac.zaAfrican Institute for Mathematical Sciences, South Africa

Gualtiero Badingualtiero.badin(at)uni-hamburg.deUniversität Hamburg

p. 15

Berry Bakkerb.bakker(at)vu.nlVU University Amsterdam

Nikita Begunbegun(at)math.fu-berlin.deFreie Universität Berlin

p. 14

Mallory Carlumallory.carlu(at)abdn.ac.ukUniversity of Aberdeen, Scotland

Giovanni Contigiovanni.conti(at)uni-hamburg.deUniversität Hamburg

p. 24

Eduard Feireislfeireisl(at)math.cas.czInstitute of Mathematics of the Czech Academy of Sciences, Czech Republic

p. 11

Robin FlohrRobin.Flohr(at)kit.eduKarlsruher Institut fuer Technologie (KIT)


Ryan Gohrgoh(at)bu.eduBoston University, USA

Ksenia Gusevaksenia.guseva(at)uol.deUniversität Oldenburg

p. 12

Adem Güngöradem.guengoer(at)fu-berlin.deFreie Universität Berlin

Tobias Haastobias.haas(at)mathematik.uni-stuttgart.deUniversität Stuttgart

p. 25

Mariana Haragusmariana.haragus(at)univ-fcomte.frUniversité de Franche-Comté, Besancon, France

p. 9

Christopher Higginss1676879(at)staffmail.ed.ac.ukUniversity of Edinburgh

Edgar Knoblochknobloch(at)berkeley.eduUniversity of California Berkeley, USA

p. 8

Xavier LeonciniXavier.Leoncini(at)cpt.univ-mrs.frAix-Marseille Université, Marseille, France

p. 21

Lev Lermannlermanl(at)mm.unn.ruLobachevsky University of Nizhny Novgorod, Russia

p. 10

Tsz Yan LeungT.Y.Leung(at)student.reading.ac.ukUniversity of Reading, UK

Participants 43

Valerio Lucariniv.lucarini(at)reading.ac.ukUniversity of Reading, UK

p. 18

Paul Mannixp.mannix15(at)imperial.ac.ukImperial College London, UK

p. 26

Gökce Tuba Masurg.masur(at)jacobs-university.deJacobs University

La Mimila(at)technion.ac.ilTechnion -- Israel Institute of Technology

p. 27

Naoko Miyajimanaoko.miyajima(at)durham.ac.ukDurham University

p. 28

Benson Muitebenson.muite(at)ut.eeUnivsersity of Tartu, Estland

Farrukh Naumanfarrukh.nauman(at)nbi.ku.dkNiels Bohr Institute, Copenhagen

Florian Noethenflorian.noethen(at)uni-hamburg.deUniversität Hamburg

p. 29

Ivan Ovsyannikoviovsyan(at)uni-bremen.deUniversität Bremen

Alex Owenao306(at)exeter.ac.ukExeter University, England


Gözde Özdeng.oezden(at)jacobs-university.deJacobs University

Artur Pruggeraprugger(at)informatik.uni-bremen.deUniversität Bremen

Jens Rademacherjdmr(at)uni-bremen.deUniversität Bremen

Paul Ritterpaul.ritter(at)zarm.uni-bremen.deCenter of Applied Space Technology and Microgravity, University of Bremen

p. 30

Evgenii Ryzhovryzhovea(at)poi.dvo.ruPacific Oceanological Institute of Far Eastern Branch of Russian Academy of Sciences, Vladivostok, Russia

p. 32

Matthew Salewskisalewski(at)math.tu-berlin.deTechnische Universität Berlin

p. 33

Anton Savostianovanton.savostianov(at)u-cergy.frDurham University, UK

p. 16

Mattia Serraserram(at)ethz.chETH Zurich

p. 19

Olga ShishkinaOlga.Shishkina(at)ds.mpg.deUniversität Göttingen

p. 22

Participants 45

Lars Siemerlsiemer(at)uni-bremen.deUniversität Bremen

Geoff Stanleygeoff.stanley(at)physics.ox.ac.ukUniversity of Oxford

Miriam Steinherrmiriamszr(at)gmail.comUniversität Bremen

Jim Thomasjt1939(at)nyu.eduNew York University

p. 20p. 34

Konstantin Trifonovkostya_31_08(at)mail.ruLobachevsky State University of Nizhny Novgorod, Russia

p. 35

Dennis Ulbrichdennisu(at)math.uni-bremen.deUniversität Bremen

Gabin Urbancicgabin.urbancic(at)gmail.comUniversity of Bergen, Norway

p. 36

Panagiotis Vasilopoulospvasilopmath(at)gmail.comNational Technical University of Athens, Greece

p. 37

Nicola Vassenanicovax540(at)zedat.fu-berlin.deFreie Universität Berlin

p. 38

Sergiy Vasylkevychsergiy.vasylkevych(at)uni-hamburg.deUniversität Hamburg

p. 39


Arturo Vieirovieiro(at)maia.ub.esUniversitat de Barcelona, Spain

p. 13

Amit Vurgaftvurgaftamit(at)gmail.comTechnion, Israel institute of technology

Michael Wilczekmichael.wilczek(at)ds.mpg.deMax Planck Institute for Dynamics and Self-Organization

p. 17

Jichen Yangjyang(at)uni-bremen.deUniversität Bremen

Ayse F. Yesilayse.yesil(at)epfl.chÉcole polytechnique fédérale de Lausanne EPFL

Caroline Zieglerziegler(at)ma.tum.deTechnische Universität München

p. 40

Lukas Zwirnerlukas.zwirner(at)ds.mpg.deMPI für Dynamik und Selbstorganisation in Göttingen

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