Axel Brandenburg

Biography. Axel Brandenburg is professor at Stockholm University and Nordita, where he is also currently the deputy director. He received his PhD at the University of Helsinki in 1990. After two postdocs at Nordita in Copenhagen and at the High Altitude Observatory at the National Center for Atmospheric Research in Boulder/Colorado he returned to Nordita as Assistant Professor and went in 1996 as full Professor of Applied Mathematics to the University of Newcastle upon Tyne. In 2000 he moved once again to Nordita, this time as full professor. He became professor at the Department of Astronomy in Stockholm when Nordita moved from Denmark to Sweden in 2007. He is currently holding an ERC Advanced Grant. Axel Brandenburg is working in the field of astrophysical fluid dynamics and has also an interest in selected topics of astrobiology. He is particularly interested in the question of magnetic field generation from turbulent motions with applications to the Sun and stars, accretion discs, galaxies, and the early Universe. He is also responsible for the maintenance of the Pencil Code, which is a public domain code (pencil-code.googlecode.com) for astrophysical fluid dynamics that is well suited for large clusters with distributed memory.

Numerical simulations of turbulent dynamos. Many astrophysical bodies (for example the Sun or the Milky Way) consist of hot ionized gas which is electrically conducting. Such flows are also turbulent. However, a purely hydrodynamic turbulent state can become unstable to the dynamo instability, so the final state becomes magnetized. Significant amounts of energy can then be converted to and dissipated through magnetic fields. Numerical simulations show a turbulent forward cascade in which the magnetic spectral energy is always slightly larger than the kinetic spectral energy. The ratio of kinetic to magnetic energy dissipation scales with the magnetic Prandtl number approximately to the 1/2 power, so at low magnetic Prandtl numbers, most of the energy is dissipated magnetically. This leaves much less energy in the rest of the kinetic energy cascade than at unit magnetic Prandtl numbers. Consequently, at given numerical resolution the viscosity can be lower than otherwise. Simulations show that for isotropically forced turbulence, the so-called small-scale dynamo exists at magnetic Prandtl numbers down to 0.01.

Next, I will discuss two quite different examples in which turbulent hydromagnetic flows can develop spatio-temporal structures on scales much larger and longer than those of the turbulence. The first example is what is sometimes referred to as a mean-field or large-scale dynamo, which requires finite helicity of the flow. Since magnetic helicity is conserved in the limit of high electric conductivity, it is driven preferentially to larger scales. This process can be modeled quantitatively in terms of averaged equations in which the magnetic diffusivity is renormalized and other new terms (e.g. the alpha effect) appear.

The second example is about a process that is now sometimes referred to as negative effective magnetic pressure instability. In this case the magnetic pressure gets renormalized and can become negative. This process is general and exists even in isotropic non-helical turbulence. However, when it is applied to a strongly stratified gas with an applied uniform magnetic field, an instability develops that leads to magnetic flux
concentrations on scales encompassing that of at least ten turbulent eddies. The physics behind this is straightforward: as the magnetic field is increased, it increases the magnetic pressure, but it also suppresses the turbulent pressure, and this effect can be stronger, rendering the total magnetic effect a negative one.

These two examples illustrate the general principle by which the consideration of averaged equations can lead to new insights with quantitative predictions that are then also borne out by direct numerical simulations. Other dramatic examples include the turbulent pumping of passive scalars and angular momentum transport even for rigid rotation. Applications to the Sun will be discussed.

Roberto Camussi 

Biography. Roberto Camussi is a professor of Fluid Dynamics at the University Roma Tre of Rome. He received his PhD in Theoretical and Applied Mechanics from the University “La Sapienza” of Rome in 1995. In the same year he became a researcher at the University Roma Tre where now he is full professor. He teaches courses on fluid dynamics, aerodynamics and propulsion as well as advanced courses on aeroacoustics for the Doctoral School of Engineering in Roma Tre. The leading themes of his present research activity are experimental aeroacoustics and data analysis, with specific applications in jet noise, fan noise and cavity noise. Other research interests include turbulent combustion, convective turbulence, naval propellers, wind turbines.

Application of time-frequency tools in aeroacoustics: identification of noise sources and theoretical modelling. The need for quieter aircraft, especially during take-off, requires a great theoretical effort to identify and control aerodynamic noise. Despite many decades of research, the physical mechanisms underlying the generation of noise, especially for propulsive jets,  are still vague and the techniques adopted to control the flow and abate noise are not yet established.

This lecture focuses on the application of time-frequency analysis (single and multi-variate wavelet transform) to clarify this puzzling problem.  Recent theoretical and experimental results concerning the identification of noise sources in turbulent shear flows will be briefly reviewed. Due to their relevance in the community noise problem, attention will be focussed on high Reynolds number jets and significant results obtained through the application of wavelet analysis to aeroacoustic data, including cases with flow control, will be presented. Theoretical implications, in particular related to the role played by instability waves, will be also considered.

A brief review of results obtained in other situations, including incompressible turbulent boundary layers, tip leakage flows and  propeller/rudder interactions, will be included in the lecture.

François Daviaud

Biography. Francois Daviaud is a researcher at the French Atomic Energy Commission (CEA), where he is also the director of the Condensed Matter Physics Laboratory in Saclay. He received his PhD in Physics at Pierre et Marie Curie University in 1990. His scientific interests deal with hydro- and magnetohydro-dynamics, chaos , turbulence and out of equilibrium systems.

Instability in developped turbulence. Phase transitions are ubiquitous in physical systems and generally associated with symmetry breaking. For example, ferromagnetic systems are well known to undergo a phase transition from paramagnetism to ferromagnetism at the Curie temperature Tc. This transition is associated with a symmetry breaking from the disordered paramagnetic— associated with a zero magnetization—toward the ordered ferromagnetic phase—associated with a finite magnetization. In the context of fluid dynamics, symmetry breaking also governs the transition to turbulence that usually proceeds, as the Reynolds number Re increases, through a sequence of bifurcations breaking successively the various symmetries allowed by the Navier-Stokes equations coupled to the boundary conditions. Finally, at large Reynolds number, when the fully developed turbulent regime is reached, it is commonly admitted that all the broken symmetries are restored in a statistical sense, the statistical properties of the flow not depending anymore on Re. However, both natural systems and recent experimental studies of turbulent flows have shown the possible existence of turbulent transitions between some “mean states”. Using the von Karman flow as a model turbulent experiment, we first show the sequence of bifurcations leading to chaos and turbulence and describe the characteristics of the turbulent states. We then study the transitions observed for different forcing conditions from Re =10^2 to Re = 10^6. (i) Supercritical transition: we report a divergence of the susceptibility to symmetry breaking at a critical Reynolds number Re = 4.10^4 revealing a phase transition, analogous to the para-ferromagnetic transition. This transition is furthermore associated with a change in the statistical properties and a peak in the amplitude of fluctuations of the instantaneous flow symmetry corresponding to intermittencies between spontaneously symmetry breaking metastable states. (ii) Subcritical transition: above Re = 10^4, the mean flow presents multiple turbulent solutions, the bifurcation between these states is highly subcritical and the system keeps a memory of its history. The transition exhibits very peculiar statistics. In the first case, we introduce the notion of instability of a turbulent von Karman flow, thanks to the monitoring of the spatio-temporal spectrum of the velocity fluctuations, combined with projection onto suitable Beltrami modes. It is shown that the turbulent time averaged flow, which is initially axi-symmetric, obeys a sequence of Eckhaus instabilities when the Reynolds number Re is varied from 10^2 to 10^6. This sequence results in non-axisymmetric modulations with increasing azimuthal wavenumber from 1 to 3. These modulations are stationary or nearly statistically stationary until Re ≈ 4 × 10^3. Above, they become periodic with an increasing frequency. We describe these modulations and show in particular that they are connected with coherent structures of the mixing shear layer In the second case, we study the influence of the energy injection on the steady turbulent states, at constant impeller speed, or at constant torque. We find that the different forcing conditions change the nature of the stability of the steady states and reveal dynamical regimes that bear similarities with low-dimensional systems. We suggest that this forcing dependence may be an out-of-equilibrium analogue of the ensemble inequivalence observed in long-range interacting statistical systems, and that it may be applicable to other turbulent systems.

Arne V. Johansson

Biography. Arne Johansson is professor in Mechanics, since 1991, at KTH and prior to that extra professor at KTH since 1986 (PhD 1983) and is director of the Linné FLOW Centre at KTH. AJ has a research group active in research focussed on simulation and modelling of turbulent flows including multiphase and reactive flows. AJ has published 78 papers in international peer reviewed journals (h-index 26) and is a member of the Swedish Royal Academy of Sciences since 2000. AJ was Secretary General for the Natural and Engineering Sciences  Council of the Swedish Research Council during the period 2004-2010 and is currently engaged in several research funding organizations in Sweden. AJ is the chairman of the international organizing committee for the TSFP symposium series.

DNS and modeling of structures, complexities, fibres and rotational effects in turbulent channel flow. DNS has developed into a powerful tool for studying the physics of fluid flows, and during the recent years we have been able to include many different types of complex physical phenomena, such as effects of density stratification, particles, reactions etc, and at the same time, take this endeavors into a range of interesting Reynolds numbers. It is still a struggle to develop really efficient tools for DNS of flows with complexities such as e.g. particles, fibres or reactions. Even the flow case of turbulent pipe flow still offers challenges due to the complexity introduced by the cylindrical geometry and the centerline (if polar coordinates are used). I will briefly touch upon a new strategy for high accuracy simulation of this case. In anew study of finite size fibres in turbulent channel flow we have been able to study four-way interactions and the specific effects of finite size of the fibres in their interaction with the wall and the near-wall flow. In this case we have chosen a Lattice-Boltzmann Method as the tool for the simulations and made use of the specific advantages of this method for this specific case. The case of channel or boundary layer flows with density stratification are of central importance for the understanding of atmospheric flows. The case of unstably stratified case offers the challenge of high levels of vertical mixing near the wall, which leaves spectral methods with Chebyshev polynomial representation in the wall-normal direction unsuitable treasonably high Reynolds numbers. Indeed, in all these cases we have the challenge to make use of the DNS results to construct better sub-grid scale models for LES, in order to reach Reynolds numbers of relevance for practical applications. I will describe some efforts in this direction.

Rich Kerswell

Biography. Rich Kerswell is a professor of Applied Mathematics at Bristol University, England. He received his PhD in Applied Mathematics from MIT in 1992, took up his first position at Newcastle University, England in the same year and moved to Bristol in 1996. He has broad scientific interests ranging from astrophysical and geophysical fluid mechanics through granular media to transition and turbulence.

Recurrent flows embedded in 2D turbulence. Ideas from dynamical systems have recently provided fresh insight into transitional and weakly turbulent flows where the system size is smaller than the spatial correlation length. Viewing such flows as a trajectory through a phase space littered with invariant (`exact’) solutions and their stable and unstable manifolds has proved a fruitful way of understanding such flows. It is therefore natural to ask whether any ideas attempting to rationalise chaos may have something to say about developed turbulence. One promising line of thinking in low-dimensional, hyperbolic dynamical systems stands out as a possibility – Periodic Orbit Theory. With this in mind, I will discuss long-time simulations of body-forced turbulence on a 2D torus with the purpose of extracting simple invariant sets or `exact recurrent flows’ embedded in this turbulence. Each recurrent flow represents a sustained closed cycle of dynamical processes which underpins the turbulence. These are used to reconstruct the turbulence statistics in the spirit of Periodic OrbitTheory.

Szymon P. Malinowski

Beverly J. McKeon

Biography. Beverley McKeon is Professor of Aeronautics and Associate Director of the Graduate Aerospace Laboratories at Caltech (GALCIT). Her research interests include interdisciplinary approaches to manipulation of boundary layer flows using morphing surfaces and fundamental investigations of wall turbulence at high Reynolds number. She was the recipient of a Presidential Early Career Award (PECASE) in 2009 and an NSF CAREER Award in 2008, and she currently serves as an editor of Experimental Thermal and Fluid Science.

A systems approach to wall turbulence. The potential impact of control of turbulence near walls, particularly in the context of the energy expenditure and emissions associated with overcoming turbulent skin friction, is well known. At the level of fundamental understanding, the ability to effect practical control in applications such as commercial air vehicles would imply a significant advance in understanding of the dynamics and scaling of turbulence. In recent work, we have described an approach to understanding the scaling behavior of wall turbulence based on a gain analysis of the resolvent formulation of the Navier-Stokes equations. The picture at each wavenumber/frequency combination is essentially that of linear dynamics of wavelike fluctuations around the turbulent mean velocity profile associated with the selective response of the resolvent, forced by nonlinear triadic interactions from other wavenumbers and frequencies. This formulation permits the treatment of wall-bounded turbulent flow using the elegant theoretical tools of systems theory, revealing information about how the system behaves as a whole, inclusive of the nonlinearity, but in tractable and compact form. In this talk, I will outline the underlying resolvent analysis and give examples of its post- and pre-dictive power with respect to observations of real wall turbulence, including scaling behavior of velocity fluctuations, coherent vortical structure and strategies for control.

 Haitao Xu

Biography. Haitao Xu is a researcher at Max Planck Institute for Dynamics and Self-Organization in Göttingen, Germany. Before coming to Germany, he received his PhD in 2003 from Cornell University and worked as a postdoc from 2003 to 2006 at Cornell. His research interest focuses on experimental investigation of Lagrangian properties of fluid turbulence and the dynamics of particles in turbulence.

Lagrangian single-particle statistics of fluid turbulence. For three-dimensional fluid turbulence, kinetic energy is supplied at large scales and then transferred to smaller scales until it is dissipated by viscosity. The well-known Kármán-Howarth-Kolmogorov equation establishes an exact relation between the rate of energy transfer (energy cascade), ε, and the third-order Eulerian velocity structure function in space:

⟨ {[u(x+r) − u(x)]}.(r/r)^3 ⟩ = −4/5 εr      (1)

where r is the distance between the two points separated by vector r at which the velocities u(x + r) and u(x) are measured simultaneously. This exact “4/5-law” has been the foundations of nearly all the subsequent theoretical and phenomenological work on Eulerian statistics of turbulence.
Lagrangian properties of turbulence, i.e., how turbulence looks like when traveling with fluid particles in the flow, have attracted increasing interest in the last two decades, due to a combination of theoretical breakthroughs and the rapid advances in experimental and numerical techniques. However, unlike in the cases of Eulerian statistics, there is no known exact result on inertial range Lagrangian single-particle statistics. It is commonly assumed that in the inertial range the dimensional scaling relation of the second-order Lagrangian velocity structure function holds:

D2(τ)=⟨δτv^2⟩=⟨[v(t+τ)−v(t)]^2⟩=C0ετ, (τη ≪τ ≪TL)       (2)

where v(t) is the velocity following a fluid particle in turbulence, C0 is assumed to be a universal dimensionless constant, τη and TL are the Kolmogorov and integral time scales of the flow, respectively. The reason that the second-order structure function D2(t) is treated specially is that there is no apparent intermittency correction on the scaling of τ in this dimensional argument. Considerable effort has been devoted to verify Eq. (2) or to identify the numerical values of C0. However, no convincing inertial scaling relation as predicted by Eq. (2) has been observed in state-of-the-art experimental and numerical simulation data.

Based on theoretical considerations and observations of experimental and numerical data, we argue that the dimensional scaling Eq. (2) might be fundamentally flawed. For example, if Eq. (2) holds, then the following will be true:

dD2/dτ=2⟨aδτv⟩=C0ε      (3)

in the inertial range. However, as shown in Figure 1, dD2/dτ observed from experiments and numerical simulations reaches maximum at approximately 2τη and then decreases nearly exponentially, without appreciable plateau range. Further investigation of the acceleration spectra obtained from numerical simulations indicate that a small correction on the scaling exponent given in Eq. (2) better fits the data: D2 ~ τ ^(1−μ) with μ ≈ 0.1.

This small correction, if it holds true at larger Reynolds numbers, implies that the choice of available parameters in the dimensional argument leading to Eq. (2) is incorrect. If ε is not the right parameter, then what is the alternative? A deeply related question is: How are Lagrangian single-particle statistics related to ε, the energy cascade through spatial scales? We will discuss these in the presentation.