## Turbulence

Owing to its complexity, turbulence is among the most fascinating states of a fluid. It represents a paradigmatic problem from the class of strongly driven non-equilibrium systems. Turbulence plays a key role in the dynamics of our oceans and our atmosphere and is of central importance for many engineering applications including mixing, combustion as well as wind energy conversion. In our work, we combine computational, dynamical and statistical methods in a simulation-assisted theoretical approach.

- D. G. Vlaykov, M. Wilczek,
- M. Wilczek, C. Meneveau, Pressure Hessian and viscous contributions to the velocity gradient statistics based on Gaussian random fields, J. Fluid Mech. 756, 191 (2014) [J. Fluid Mech.]
- M. Wilczek, Y. Narita, Wavenumber-frequency spectrum for turbulence from a random sweeping hypothesis with mean flow, Phys. Rev. E 86, 066308 (2012) [Phys. Rev. E]
- R. Friedrich, A. Daitche, O. Kamps, J. Lülff, M. Voßkuhle , M. Wilczek, The Lundgren-Monin-Novikov Hierarchy: Kinetic Equations for Turbulence, Com. Ren. Phy. 13, 929 (2012) [Com. Ren. Phy.]

## Going with the flow: particles in turbulence

Particle-laden flows arise in many engineering applications, the atmospheric sciences (e.g. clouds) and the marine sciences (e.g. microplastics dispersion, plankton blooms). The Lagrangian (particle-based) view of turbulence is particularly insightful and challenging, because particles sample the complexity of turbulence in space and time. In our work we investigate fundamental aspects of Lagrangian turbulence as well as the dynamics of active and passive particles in turbulence with applications to cloud physics and mixing of micro-organisms in the ocean.

- C.C. Lalescu, M. Wilczek, How tracer particles sample the complexity of turbulence, New J. Phys. 20, 013001 (2018) [New J. Phys]
- C.C. Lalescu, M. Wilczek,
Acceleration statistics of tracer particles in filtered turbulent fields.*J. Fluid Mech.**847*, R2 (2018) [J. Fluid Mech.] - R.E. Breier, C.C. Lalescu, D. Waas, M. Wilczek, M.G. Mazza, Emergence of phytoplankton patchiness at small scales in mild turbulence, PNAS 115, 12112 (2018) [PNAS] [featured in Physics World]
- J.M. Lawson, E. Bodenschatz, C.C. Lalescu, M. Wilczek, Bias in particle tracking acceleration measurement, Exp. Fluids 59, 172 (2018) [Exp. Fluids]

## Active Fluids

Active fluids are a rapidly evolving research field inspired by the biophysics of dense suspensions of motile cells. Their polar and hydrodynamic interactions give rise to the emergence of meso-scale vortex patterns reminiscent of two-dimensional turbulence. Active fluids are only interesting to study in their own right, but are useful in designing and building microfluidic devices and may lead to the development of novel meta-materials. Continuum descriptions of this phenomenon combine aspects from pattern formation with nonlinear advection of Navier-Stokes type. Active turbulence is the ideal testbed for novel methods that combine tools from nonlinear dynamics and pattern formation with the statistical mechanics of turbulence, which we develop in our group.

- M. James, W.J.T. Bos, M. Wilczek,
Turbulence and turbulent pattern formation in a minimal model for active fluids, Phys Rev. Fluids 3, 061101(Rapid Communication) (2018)[PRF] - M. James, M. Wilczek,
Vortex dynamics and Lagrangian statistics in a model for active turbulenceEPJE 41, 21 (2018) [EPJE]**,**

## Atmospheric flows & wind energy conversion

The understanding of atmospheric boundary layers plays a crucial role for climate research but also for technological applications such as wind energy conversion. For wind energy, atmospheric turbulence plays a key role: strong wind fluctuations impose significant structural fatigue loads on wind turbines which can lead to failure. Integrating the unsteady wind energy into a decentralized power grid poses further challenges with respect to power grid stability. In our work, we combine statistical modeling and computer simulations to better understand and predict turbulence in the atmosphere and in wind farms.

- L. Lukassen, R. Stevens, C. Meneveau, M. Wilczek, Modeling space-time correlations of velocity fluctuations in wind farms, Wind Energy 21:474–487 (2018)[Wind Energy]
- H. Ronellenfitsch, J. Dunkel, M. Wilczek,
Optimal Noise-Cancelling Networks, Phys. Rev. Lett. 121, 208301 (2018)[arxiv] [PRL] [Featured in Physics] - M. Wilczek, R. Stevens, C . Meneveau, Spatio-temporal spectra in the logarithmic layer of wall-turbulence: large-eddy simulations and simple models, J. Fluid Mech. 769, R1 (2015) [J. Fluid Mech.]
- M. Wilczek, R. Stevens, C . Meneveau, Height-dependence of spatio-temporal spectra of wall-bounded turbulence - LES results and model predictions, J. Turb 16(10), 937-949 (2015) [J. Turb]
- M. Wilczek, R. Stevens, Y. Narita, Charles Meneveau, A wavenumber-frequency spectral model for atmospheric boundary layers, J. Phys.: Conf. Ser. 524, 012104 (2014) [IOP]

## Convection

In many natural settings, such as the Earth's core or atmosphere, fluid flow is driven by a thermal gradient. In the prototypical situation in which the flow is heated from below and cooled from above, convection can arise. Sufficiently far from its onset, the convective flow becomes turbulent. From the viewpoint of fundamental turbulence research turbulent convection is one of the most interesting systems to study due to the complex interaction of large-scale flow patterns and turbulent fluctuations. In our group, we aim at disentangling this dynamics as well as at establishing rigorous statistical formulations of turbulent convection.

- K. Petschel, S. Stellmach, M. Wilczek, J. Lülff, U. Hansen, Dissipation Layers in Rayleigh-Bénard convection: A unifying view, Phys. Rev. Lett 110, 114502 (2013) [Phys. Rev. Lett]
- K. Petschel, S. Stellmach, M. Wilczek, J. Lülff, U. Hansen, Kinetic energy transport in Rayleigh-Bénard convection, J. Fluid Mech. 773: 395-417 (2015) [J. Fluid Mech.]
- J. Lülff, M. Wilczek, R. Stevens, R. Friedrich, D. Lohse, Turbulent Rayleigh-Bénard convection described by projected dynamics in phase space, J. Fluid. Mech. 781, 276-297 (2015) [J. Fluid Mech.]

## High-performance computing & scientific visualization

In our group we are actively developing high-performance simulation tools for complex systems. Our specialty is the development of parallel algorithms for nonlinear partial differential equations. An illustrative example are our state-of-the art simulations of fully developed turbulence with more than 200 billion degrees of freedom by means of pseudo-spectral methods (see welcome page). Our in-house developed codes are typically parallelized by employing hybrid MPI and OpenMP parallelization schemes to ensure efficient scaling up to tens of thousands of cores.