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11 december 2018

Approved FOM programme

Number 142.
Title Towards ultimate turbulence (ULT)
Executive organisational unit BUW
Programme management Prof.dr. D. Lohse
Duration 2013-2018
Cost estimate M€ 2.4

In contrast to a decade-old paradigm, highly turbulent flow is strongly influenced and determined by boundaries. An increasing amount of evidence suggests that different states of turbulent flow exist, separated by sharp transitions and bifurcations. This evidence makes it difficult to extrapolate results from lab-scale experiments to industrial, geophysical, or astrophysical flows. We want to examine experimentally, numerically, and theoretically if different states of turbulence exist, how they are triggered, and the nature of the transitions between them. We focus on turbulence in closed systems, namely on Rayleigh-Benard (RB) and Taylor-Couette (TC) turbul  ence. In these paradigmatic systems – thermally or shear driven, respectively – the interplay between boundary layers and bulk is particularly important. We especially want to understand the transition towards the so-called ultimate turbulent state, which for extremely strong driving has recently been found in both systems and was interpreted as an indication of the breakdown of laminar-type boundary layers.

The objectives of the proposal thus are:

  1. To explore when there are different states of turbulence and how transitions between them occur. To study the role of boundary layers and how they interact with the bulk flow. What determines the state of the turbulent flow? What are the apt observables to characterize these states? Can one trigger a transition??

  2. To explore the ultimate regime of RB and TC turbulence, to understand the boundary layer – bulk interaction in this regime and the transition towards this regime.

  3. To push direct numerical simulations towards the ultimate turbulence regime in both TC and RB flow, which will allow for a one-to-one comparison between DNS and experiments.

Background, relevance and implementation
Turbulent flow is omnipresent. It is the standard type of flow for air and water at scales above the microscale. The strength of turbulence is defined by the Reynolds number, Re; the ratio between inertial and viscous forces. In geophysical, oceanographic, or astrophysical turbu­lence, Re is typically 1010 and larger. Neither in lab-scale experiments, nor in direct numerical simulations are these numbers attainable. One has to somehow extrapolate the results from lab-scale experiments and simulations at lower Re to these large values. Such an extrapolation becomes meaningless if a transition from a turbulent state at low Re to another turbulent state at high Re occurs, or when different states coexist at the same Re. So, one must understand if there is a transition to another state and what the properties of the flow are below and above such a transition.
The focus of the programme is on RB and TC turbulence, for many reasons: (i) They are mathematically well-defined by the (extended) Navier-Stokes equations with their respective boundary conditions; (ii) for these closed systems exact global balance relations between driving and dissipation can be derived; (iii) they are experimentally accessible with high precision, due to simple geometries and high symmetries; (iv) for possible transitions between different states, boundaries and boundary layers play a salient role, which are prominently present in these systems. RB and TC turbulence are thus ideal systems to study the interaction between boundary layers and bulk; and (v) a close analogy exists of RB and TC flow with pipe flow, which from a technological point of view may be the most important turbulent flow. Insight into the interaction between boundary layers and bulk in RB and TC turbulence will shed more light on the pipe flow problem. To achieve these objectives, we have to advance the level of experimental measurements and numerical simulations on RB and TC turbulence, to allow for one-to-one comparisons.

The final evaluation will be based on the self-evaluation report initiated by the programme leader and is foreseen for 2019.

Please find a research highlight that was achieved in 2013 within this FOM programme here.