Sources of turbulence in F1

Whilst this season's F1 World Championship is shaping up into a fascinating pentahedral battle between Jenson Button, Lewis Hamilton, Sebastien Vettel, Mark Webber, and Fernando Alonso, the sport's underlying aerodynamic problems remain. The turbulent wake created by a Formula 1 car, and the loss of downforce induced in a following vehicle, continue to mitigate against good racing. The recommendations of the FIA's Overtaking Working Group, implemented for the 2009 season, were intended to both reduce downforce, and to reduce the amount of turbulence to which a following car's downforce-generating devices would be sensitive. These recommendations were, of course, promptly undermined by the development of double and multi-deck diffusers. Hence, the regulations for the 2011 season seek to improve the opportunities for overtaking by banning multi-deck diffusers, and by also introducing driver-adjustable rear wings.

Perhaps, however, the regulations could go still further, and to this end it's worth noting that the rear end of a Formula 1 car generates turbulence by several different mechanisms. Any wing profile will, of course, generate a turbulent wake, but more generally, any surface will possess a boundary layer, and when that boundary layer detaches, it will inevitably create turbulence. In addition, it may be that modern F1 aerodynamics create some degree of Kelvin-Helmholtz turbulent instability. If two parallel adjacent layers of airflow have different velocities, then the velocity shear will induce such turbulent instability. The different levels of a multi-deck diffuser may well create some degree of Kelvin-Helmholtz instability, unless they discharge their airflows at exactly the same velocity.

Note that this is a different source of turbulence from that created by wing section profiles, which induce turbulence because they require a circulatory airflow component to operate. To understand this, consider the idealised situation where the airflow around a wing is a superposition of (i) a uniform 'freestream' flow from left to right, where the streamlines are parallel straight lines, and (ii) a pure circulatory flow, where the streamlines are anti-clockwise concentric circles.

Taking the sum of the velocity vector fields for the uniform and circulatory flow at each point, the anti-clockwise circulation is added to the freestream velocity below the wing, and subtracted from it above. Hence, the airflow beneath the wing will be faster than that above, and in accordance with the Bernoulli principle, the pressure beneath the wing will be lower than that above. This pressure differential causes a net downward force. The presence of circulation is also consistent with the use of Newton's third law ('action equals reaction') to explain the creation of downforce, because the circulatory flow adds an upward component to the airflow in the wake of the wing, corresponding to the upward deflection of air, and a downward reaction force.

If multi-deck diffusers do indeed induce Kelvin-Helmholtz instability, then whilst this particular source of turbulence will be eliminated next year, the teams will continue to use the airflow over the rear deck and beam wing to help pull the airflow out of a single diffuser, and these airflows presumably have different velocities. If so, it will remain a source of Kelvin-Helmholtz turbulent instability, and will continue to mitigate against overtaking.

So why not ban beam wings?