Deterministic Turbulence

"Turbulence is the most important unsolved problem of classical physics" (Richard Feynman) due to its high non-linearity and chaotic behaviour. Therefore, it has been widely accepted that turbulence is not repeatable even with identical initial and boundary conditions (i.e. the butterfly effects). Recently, however, a Russian research group led by Prof Kachanov (Visiting Researcher of this proposal) observed a certain set of repeatable flows in a very late stage of laminar-to-turbulent transition, which can be considered as turbulence as far as its statistics are concerned. These are called deterministic turbulence. Unlike "ordinary" turbulence, the deterministic turbulence allows us to predict the exact time and location of turbulence events that take place in the flow. One can also go back the flow history to see the cause of turbulence events. This provides an exciting opportunity for turbulence research that has not been possible before. Here we propose to utilise the deterministic turbulence to better understand the turbulent boundary-layer structures with a view to develop an innovative strategy for turbulence control and optimise existing flow control techniques.

Turbulence dominates a large number of fluid processes which affect the daily lives of all members of society. Turbulence is responsible for losses, and therefore low efficiencies, in fluid transport systems such as pumps and pipelines, and in propulsion systems such as gas-turbine and reciprocating engines. At the same time turbulence affects the combustion process by altering both the local concentrations of reactants and, in multi-phase flows, the contact surface area between the phases. Conversely turbulence is exploited to improve mixing of fluids and, for some flows, to reduce aerodynamic drag, unsteady loads and aero-acoustic noise footprint. The pursuit of understanding of turbulence over the past two centuries has been driven by the benefits of being able accurately to predict turbulence, and more recently of the opportunities to manipulate turbulence to reduce its deleterious consequences or to enhance its beneficial effects.
The deterministic turbulence project aims to build a new understanding of the development of turbulence, and opportunities for its control, by creating predictable, deterministic turbulent flows and then studying their response to a range of stimuli. The potential impact of the project is therefore enormous.
Firstly, a successful project outcome will mean the opening of new avenues of research into this fluid phenomenon. A simple analogy is that of a laboratory rat which was found to show completely repeatable but still complex behaviour to a range of complex environmental stimuli. The opportunities to understand the details of the biological mechanisms linking stimulus to response would be enormously greater than those arising from statistically significant, but still variable, behaviours. So it would be with deterministic turbulence: not a case of coherent structures traceable to a particular input, but an apparently complete turbulent cascade with a repeatable time history.
Secondly, the likely outcome of such studies will be the development of improved semi-empirical models for complex characteristics of turbulence, such as the pressure-strain correlation, the apparent limits on shear-stress anisotropy and the often unpredictable delayed response of turbulence to changes in certain strain fields. At present the computation of turbulent flows of practical significance is restricted to Reynolds-averaged approaches which are known to be poor at predicting many characteristics, not least the unsteady response of turbulent flows which is of importance in the study of fluid-structure interactions, aero-acoustic flows and environmental flows. Higher-order methods such as Direct Numerical Simulation are too expensive to be applied to complex or large-scale configurations, so fundamental lessons must be learned from simulation model problems and then used to refine lower order methods, often via matched hybrid solutions such as large- and detached-eddy models. Anything which simplifies or at least clarifies the modelling challenge is therefore likely to have a direct pull-through into the standard turbulence model correlations used in industry-standard CFD codes.
Thirdly, a better understanding of the response of turbulence to actuation will improve considerably the effectiveness of any number of turbulence control schemes currently under investigation, whether of the body-forcing type (plasmas), fluid injection type (synthetic jets) or more futuristic (oscillating walls). These devices have attracted considerable interest and investment from the aerospace community over recent decades, because of the major impact of turbulence on aircraft aerodynamic efficiency, and a breakthrough in the understanding of turbulence could significantly advance the entry-into-service dates of such control strategies.