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Zonal flow

Short critique of zonal flow in transitional turbulence

The interaction between turbulence and zonal flow has been proposed as the mechanism to account for the critical point in pipe flow [1]Link opens in a new window. I do not agree with this mechanism and below I summarize the three most essential reasons.

There are no published observations (experiments or DNS) of zonal flow in a turbulent puff.

There is only one published DNS of zonal flow in a pipe (Figure 1 of [1])Link opens in a new window, and that is from the core of a slug. The core of a slug is not the same as a puff. Notably, puffs vary rapidly in the streamwise direction. (See energy budgets from Song reproduce below.)

There are no published results showing that zonal flow plays any role in puff decay or puff splitting.

It must be understood that the critical point for the onset of turbulence in pipe flow arises from the competition between puff decay and puff splitting [2]Link opens in a new window. Hence it is essential to account for these processes.

Zonal flow has never been observed in a puff, and consequently it has not been shown to play any role in either the decay or splitting of puffs. More generally, zonal flow has not been shown to relaminarize turbulence.

The dynamics of transitional pipe flow can be explained using a simpler, broader theory.

There is a simpler, broader theory that accounts not only for the critical point, but all other large-scale features of pipe flow, without any need to invoke zonal flow. The theory is based on the well-established interaction between turbulence and the mean streamwise shear [3]Link opens in a new window[4]Link opens in a new window. The viewpoint is that the dynamics of transitional pipe flow are the generic consequence of the transition from excitability to bistability with a fluctuating excited state.

In the context of pipe flow, zonal flow is defined as azimuthal flow that is independent of the streamwise and azimuthal directions. It varies with radius and can change sign with radius. It is a fluctuating field whose temporal or ensemble mean is zero.

Below are energy budgets for a puff and slug (courtesy of Baofang Song). These clearly show that a puff is not a streamwise constant structure and not the same as the core of a slug. (The puff is at Re=2200 and the slug at Re=2600.)