## 6.2A picture of turbulence

In turbulent ﬂow, the ﬂuid follows irregular curved paths, known as eddies. Eddies are generally illustrated by curved arrows, which does little to reveal the true nature of turbulence.

Instead, we can build a picture of turbulence from: photographs and videos from experiments, examples from engineering and everyday experiences; and, from images and animations from detailed computer simulations.

Generally, we see a mass of intertwined, ﬂow structures of many diﬀerent sizes. The structures move and rotate continuously. Through interactions with one another and the main ﬂow ﬁeld, they change shape and size rapidly.

The structures indicate regions of vorticity in the ﬂuid, as deﬁned in Sec. 2.11 . It is vorticity, not velocity, which is often used to describe turbulence. For example, Davidson2 describes turbulence as “a spatially complex distribution of vorticity which advects itself in a chaotic manner”, and a turbulent eddy as “a blob, tube or sheet of vorticity and the associated ﬂow.”

### Vorticity generation

Vorticity is primarily generated at solid boundaries and can be categorised as “fast” or “slow”.3 Fast generation is localised to regions of relative acceleration between the solid and ﬂuid, e.g. at the leading edge in ﬂow over a semi-inﬁnite ﬂat plate or at the lip at the exhaust of the air cannon in Sec. 2.11 .

Slow generation occurs over longer sections of boundary surface, e.g. the wall of a pipe with internal ﬂuid ﬂow. It is caused by the tangential pressure gradient at the surface.

Since vorticity is mostly generated at solid boundaries, we can try to imagine the how vortex structures might evolve. Consider a layer of a viscoelastic ﬂuid on a ﬂat surface — something like a sticky adhesive or putty. When shear is applied, the material tends to rotate rather than slide horizonatally.

Sections of material can break oﬀ and form tubes which roll across the surface. They tend to extend along their length and bend under uneven shear.

When we apply shear by hand, we can feel that the rotation is initiated within the uneven points, e.g. around the ﬁnger joints. In a similar way, the onset of turbulence is sensitive to surface roughness with the transition from laminar to turbulent ﬂow occurring at higher for smoother surfaces.

2Peter Davidson, Turbulence: an introduction for scientists and engineers, 2004.
3Bruce Morton, The generation and decay of vorticity, 1984.

Notes on CFD: General Principles - 6.2 A picture of turbulence