# What does “eddy” mean in turbulence?

a newbie in turbulence study, very confused about the concept of eddy, I feel the word "eddy" having two meanings in fluid-mechanics maybe more and i'm not sure if i understand correctly.

1. a vision concept

we can say, in a flow, there is a large or small eddy in this region, in this meaning, eddy means rotating fluid material, we can say an eddy in this place an eddy in that place. if we draw streamlines, we can see approximately circular and approximately concentric streamlines visually.

1. Fourier component

we do a space Fourier transform(maybe time Fourier transform?) to a scalar or vector field, and we call the k-component an eddy with k-wavenumbers or an eddy with scale of 1/k. so in this meaning ,we can't say an eddy in a place or in a region, because a position has all eddies superimposed in the point.

so does both meaning exist? depending on the context? or just one meaning is correct? more meaning and understanding?

at last, same confusion about the word "vortices" and "whorls" which i think these two word should be the first meaning ie the visual concept but not very sure if i understand correctly.

• I doubt there is "a concept of eddy". I guess "eddy" is just a funny English word which the author used instead of more common synonyms. Sep 26, 2022 at 11:08
• There is a concept of eddy. Sep 26, 2022 at 12:19
• @KurtG. thanks, although not settled totally, still helps Sep 26, 2022 at 13:58

Terminology like "eddy" and "whirl/whorl" is quite loosely meant.

The true structures present in a flow are defined quantitatively via various correlation functions/filters that act on the velocity (and rarely, pressure) fields.

They are usually based on detecting concentrations of momentum (e.g. uniform moment zones), vorticity (vorticies), or kinetic energy. Many of these structures may not be visible to the human eye (even a human eye looking at velocity fields).

There exist many definitions for vorticies/whirls. A peak in vorticity doesn't necessarily mean that you will see some sort of swirling motion that you are used to imagining.

Another way eddies are talked about is when referring to length scales. An example is the "integral length scale" (which is often used to describe the "largest eddies" in a flow). It may be defined by taking the integral (ideally, to infinity) of e.g. the velocity autocorrelation function. You might never observe a "flow structure" exactly matching that length scale, but many "flow structures" will be seen fluctuating around that scale, so it is a meaningful and intuitive quantity.

When it comes to viewing turbulence in Fourier space, $$1/k$$ does indeed translate to a length scale. This doesn't mean you will observe shapes that exactly match that length scale, but rather that certain shapes will correlate with that length scale more than others (if you have a peak at $$k$$ in, say, your energy spectrum $$E(k)$$). Again it is statistical.