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On 7 August 2019 the German physics community lost one of its leading members, Professor Bruno Eckhardt of the Philipps-Universität Marburg, from complications following surgery.

Bruno was a highly respected physicist and a pillar of the physics community. He studied physics at the University of Kaiserslautern and at Georgia Institute of Technology, and earned a PhD degree in 1986 from the University of Bremen in Germany for his work on chaotic dynamics in classical and quantum systems for which he received the 1987 Bremer Studienpreis. He defended his habilitation thesis at Philipps-Universität Marburg in Germany in 1992 on quantum chaos and periodic orbit quantization, and subsequently became a professor at the Carl von Ossietzky Universität Oldenburg. In 1996 he returned to Marburg as a professor of physics. Throughout his career, he held a number of visiting positions including those in Delft, Edinburgh and the University of Maryland.

In Marburg Bruno turned his attention to hydrodynamics, focusing on turbulence and particularly the transition to turbulence in shear flows. This transition is almost universally strongly subcritical, implying coexistence between turbulence and laminar flow. In some flows, such as plane Couette flow, the laminar state is linearly stable for all values of the Reynolds number, a dimensionless parameter specifying the strength of the shear relative to viscous diffusion. Despite this, turbulence is observed in experiments at rather well-defined Reynolds numbers. Bruno and his students and coworkers wrote a number of seminal papers on the properties of so-called edge states, states that lie on the boundary between the turbulent state and relaminarization. These states can be spatially extended or spatially localized and represent the structure of the optimal perturbation that will trigger the onset of turbulence at a given Reynolds number. Through this work Bruno developed a picture of turbulence in which he posited that the observed state consisted of bouncing between different types of time-independent and time-dependent states aka exact coherent structures, all corresponding to saddles in phase space, in a manner of a pinball machine, with the edge states providing a gate to relaminarization, i.e., sudden decay of the turbulent state. This picture has been very influential and has led to a focus on exact coherent structures in turbulent flows and their stability properties. It also led to a focus on the lifetime of turbulent "puffs" in pipe flow and the timescale for their growth and splitting, both as functions of the Reynolds number. This work in turn led to the identification of a critical Reynolds number at which these two timescales match that could be reliably associated with the transition to turbulence in pipe flow, a compelling picture of the transition akin to percolation, thereby confirming a suggestion made in the 1980's by Y. Pomeau.

Bruno's far-reaching contributions were recognized by a Leibniz prize of the German Science Foundation (2002), and election as a Fellow of the Institute of Physics (2004), the American Physical Society (2005) and the European Mechanics Society (2006).

Bruno is the author of the highly regarded monograph *Chaos* (Fischer, Frankfurt, 2004) that summarizes much of his understanding of classical and quantum chaos. He has published widely in the physics and mathematics literature; among his best known works is a paper on crowd-induced oscillations of the Millenium Bridge in London that were discovered on its opening day when crowds thronged the newly opened bridge (Nature 438, 43, 2005). His 1988 review on the *Quantum Mechanics of Classically Non-integrable Systems*, Physics Reports 163, 205-297, remains a sought-after reference.

Bruno also had a distinguished editorial career. He served on the boards of Physical Review E, Nonlinearity, Journal of Nonlinear Science, and the German language Physik Journal. As Associate Editor for Physical Review E, he was responsible for the fluid dynamics section; as Associate Editor of Nonlinearity he was highly effective and someone whose views I came to greatly value when I was Editor-in-Chief.

Over the last 10 years or so Bruno devoted much effort to the setting up of the Loewe Center for Synthetic Microbiology at the Philipps-Universität Marburg, a Center he directed for six years (2010-2016). He was also a member of the German Science Foundation's Senate and Joint Committee, and played leading roles in the governing bodies of both IUTAM and EUROMECH.

I last saw Bruno in June of this year, at the conference *From Pattern Formation to Turbulence* in Kloster Banz in Bavaria to celebrate the 60th birthday of Eberhard Bodenschatz. As usual Bruno gave a splendid talk focusing on his recent work with M. Linkmann, G. Boffetta and M.C. Marchetti on the formation of condensate-like structures in active-matter turbulence. He had also become interested in hurricanes and in his talk discussed his work on analyzing both recent and historical records of storms that developed into hurricanes and those that did not, with a view to developing a statistical picture of the conditions required for their formation. I had a long discussion with him after his talk about the similarities and differences between the hurricane problem, his work on the transition to turbulence and on my own work on the formation of condensates (aka large scale vortices) in geostrophic turbulence. We promised one another to keep discussing these problems but it was not be. I noticed that he had aged since our previous meeting but did not mention it.

Bruno was 59. He leaves his wife Kirsten, three daughters and a grandchild.

Obituary written by Edgar Knobloch, Department of Physics, University of California at Berkeley, 14 October 2019.

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