## Saturday, February 23, 2013

### BBC Sport and Potential Flow theory

It is a fact, sadly unacknowledged, that BBC Sport's default background animation represents a doublet from Potential Flow theory.

Potential Flow theory is a branch of aerodynamics in which flows are idealised as being inviscid and irrotational. This means, respectively, that there is no friction resistance to shear between adjacent layers of fluid, and there is no vorticity. Hence, Potential Flow theory does not recognise the existence of boundary layers adjacent to solid objects.

Now, there is, within aerodynamics, a distinction between circulation and rotation, which has the potential (if you'll excuse the term) to confuse. In a flow with circulation, you can integrate the velocity vector around a closed loop and obtain a non-zero value. In a rotational flow, the vorticity field is non-zero.

In a Potential Flow (guaranteed, by definition, to be irrotational), if the region of space occupied by the fluid is simply connected topologically-speaking, (entailing that any loop can be smoothly deformed to a point) then the flow will have zero circulation. However, if the region is not simply connected, then the irrotational flow can possess circulation. The presence of solid objects in a fluid prohibits the region of space occupied by the fluid from being simply connected, (in 2-dimensional terms, at least), hence Potential Flows around solid objects can possess circulation.

This loophole (if you'll excuse the term) within Potential Flow theory enables one to represent the circulatory flow around wing sections. Because the equations of Potential Flow theory are linear, one can superpose several solutions of the theory to obtain other solutions. To represent the flow around a cylinder, for example, one superposes a uniform flow with a so-called doublet. The latter provides the stagnation points to the flow at the leading and trailing points of the cylinder.

To represent the circulatory flow around a wing section one basically just adds a free vortex to the superposition.

Hence, despite the BBC's apparent aversion to covering all the Grands Prix in a Formula One season, aerodynamics is clearly a subject close to their heart.