Turbulence is one of the last unsolved problems in classical physics. It is omnipresent in nature and technology, and many of today’s societal problems are deeply connected with turbulence, from ocean flow and mixing in the ocean, melting of glaciers, pollution in the atmosphere or in the ocean, climate, processing of fluids in the industry, transport in pipelines, etc. Turbulence has been approached from various sides, namely from statistical and theoretical physics, from mechanical or chemical engineering, from the applied mathematics point of view, and from the practitioner’s point of view, who works in oceanography or geophysics. All of these approaches have their justification and their strengths, but also their limitations.

Going back to Kolmogorov, there has been the paradigm in the more fundamental turbulence community of one universal state of homogeneous isotropic turbulence. In the last 15 years or so it has become more and more clear that this is not the case and that there can be several different states of turbulence, with transitions between these states. The transitions between the different states normally are of subcritical nature, just as the transition from laminar pipe or channel flow to turbulent pipe of channel flow. There, the origin of the subcritical nature is the nonnormality of the operator, combined with the nonlinearity of the Navier-Stokes equation. The nonnormality is intimately related to the local shear of the flow. All this also holds for turbulent flow, where one locally also has strong shear.

One example of a transition between different turbulent states is the transition between classical Rayleigh- Bénard turbulence and ultimate Rayleigh-Bénard turbulence. The transition leads to considerably enhanced heat transport. Viewing this transition in the nonnormal-nonlinear context has resolved various controversies in the field and further intensified the interest in the Rayleigh-Bénard convection and related thermally driven turbulent systems such as horizontal convection, vertical convection, internally heated convection or buoyancy-driven systems such as stratified inclined duct flow. However, the fully developed turbulence community traditionally had been disconnected from the community focusing on the transition from laminar to turbulent flow. One objective of the workshop is to bring together these two communities for their mutual benefit, resulting in the transfer of experimental, numerical, and theoretical methods and defining new joint problems.

Other examples of transitions between different turbulent states have been observed in the von Karman flow and Taylor-Couette flow. Also Rayleigh-Bénard turbulence knows further transitions, namely the one from zonal flow to flow with convection rolls or from turbulent flow with n convection rolls to that with n+1 or n-1 convection rolls. Questions to ask on all these systems with multiple turbulent states are: How to trigger a transition? What is the hysteretic character of the transition? What are the transport properties (heat, mass, momentum) of the different states? What are the lifetimes of the states, depending on the control parameters? Do local disturbances to one state grow and finally overwhelm the global flow structure and lead to a transition or do they die out?

The lecturers are all renowned scientists having worked on the transition to turbulence and on fully developed turbulence. All of them are Fellows of the American Physical Society. They have backgrounds in mathematics, physics, and mechanical engineering.