The efficiency of modern transportation is severely compromised by the prevalence of turbulent drag. The high level of turbulent skin-friction occurring, e.g., on the surface of an aircraft or the carriage of a high-speed train, is responsible for excess fuel consumption and increased carbon emissions. The environmental, political, and economic pressure to improve fuel efficiency and reduce carbon emissions associated with transportation means that reducing turbulent skin-friction drag is a pressing engineering problem.
For passenger jet aircraft, several strategies have been proposed, ranging from altering the morphology of the aircraft surface (e.g. introducing ridges or riblets, similar to the dentricles found on shark skin) [1,2] to introducing surface motion to oscillate the boundary layer and produce, in a way that is not yet clearly understood, a significant reduction in turbulent skin-friction . A problem with passive-control concepts is that the drag reduction tends to be modest (approx. 5-10%, typically, for riblets). This can be greatly improved with active open-loop control (such as with an oscillating surface), however the energy input required for actuation operation could undercut any fuel savings. A more promising, but at present speculative, system is active closed-loop flow control, in which actuators and sensors interact with turbulence on spatial and temporal scales comparable to those at which it is generated.
It is generally accepted that streak-like flow structures, existing very close to the wall, play a critical role in the cyclical generation of turbulence in wall-bounded flows [4-6]. Figure 1 shows a hydrogen-bubble visualisation of near-wall streaks alongside a low-order direct numerical simulation of a single streak mode. The idea of targeting and cancelling these near-wall streaks has been considered by several researchers (see, e.g., [2,5,6]) as a potential method for drastically reducing turbulence and the concomitant skin-friction drag. Simulations have successfully demonstrated such control [5,6] and also shown that the fluid power input is negligible relative to the saving from reduced drag . However, the minute spatial and temporal scales over which these streaks exist in normal cruise conditions present a daunting technical challenge for sensors and actuators.
The streaks are separated, on average, by a distance of 100 l+ (see, e.g., ) and are roughly 10 l+ in plan-view thickness, where l+ is the viscous length scale. It is realistic to expect, therefore, that a system capable of sensing and controlling such streaks individually — and capable of doing this as advecting streaks meander from side to side downstream — should have a resolution of the order of the viscous length scale itself, which, for a typical aircraft in cruise conditions, is 2-4 µm, depending on the location on the aircraft, its altitude and speed . So micro scale flow-control actuators and sensors will almost certainly be required.
Comparing the viscous length scale to the molecular mean free path of air at 10 km altitude (which is approx. 0.2 µm) provides the Knudsen number, Kn, that indicates the degree of departure from local thermodynamic equilibrium. For a closed-loop flow control application, we estimate Kn=0.05-0.1, which means the flow in and around the envisioned flow-control devices is in the transition between free-molecular and continuum flow. Accurately modelling this flow regime is not possible using current Navier-Stokes methods, and is too computationally expensive for direct simulation Monte Carlo (DSMC) simulation. Moreover, the mean-free path will be still larger at higher altitudes and in flow regions with local low pressure (e.g. wing upper surfaces).
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