Editorial | Published:

Big whorls, little whorls

Nature Physics volume 12, page 197 (2016) | Download Citation


An excursion into ecology and two sets of experiments lay the foundation for our Focus on Turbulence.

The connection between turbulence and predation was made as early as 1922, when Lewis Fry Richardson wrangled it into rhyming verse1 with the lines:

Big whorls have little whorls Which feed on their velocity, And little whorls have lesser whorls And so on to viscosity.

The poem, later granted wider circulation by James Gleick2, was a play on Augustus de Morgan's famous paraphrasing3 of Jonathan Swift:

Great fleas have little fleas Upon their backs to bite 'em, And little fleas have lesser fleas And so ad infinitum.

But the significance of the link lay dormant for some time, surfacing only late last year when Hong-Yan Shih and colleagues came up with a predator–prey model for turbulence, giving the analogy new meaning — and providing evidence in support of some long-held claims about Richardson's whorls.

The paper, which appears on page 245 as part of this month's Focus on Turbulence (see also the News & Views on page 204), reports numerical results that establish a clear link between the transition to turbulence and the universality class describing directed percolation. This idea dates back some thirty years to a conjecture made by Yves Pomeau that the transition to turbulence in shear flows might be understood in terms of an absorbing phase transition. Pomeau provides some historical perspective on this front with a Commentary on page 198.

On the heels of the contribution from Shih et al. came a pair of remarkable experimental findings from Masaki Sano and Keiichi Tamai (page 249) and, independently, from Grégoire Lemoult and co-workers (page 254). Although a number of theoretical and experimental studies have lent support to Pomeau's conjecture over the years, no published experimental work had yet confirmed the directed percolation picture. These groups have succeeded in doing so simultaneously, albeit in two vastly different experiments.

Both teams looked at the onset of the transition to turbulence in the shear flow of Newtonian incompressible fluids and found evidence for critical exponents consistent with directed percolation. But whereas Lemoult et al. studied flows driven by differential wall motion in a quasi-1D Couette flow geometry, both numerically and experimentally, Sano and Tamai took on 2D channel flow created by a pressure gradient.

Establishing that the transition to turbulence falls into a well-known universality class promises great things for our understanding of this puzzling behaviour. The parallels with other fields are perhaps just as exciting, as our Focus on Turbulence seeks to convey.


  1. 1.

    Weather Prediction by Numerical Process (Cambridge Univ. Press, 1922).

  2. 2.

    Chaos: Making a New Science (Viking Press, 1987).

  3. 3.

    A Budget of Paradoxes (Longmans, Green, and Co., 1872).

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