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Schematic of a typical setup used for experiments.
Thin film interference used to visualize the turbulent flow generated in a soap film. Here is a movie version.
Soap films and two-dimensional turbulence (石鹸薄膜と二次元乱流)
Soap films and two-dimensional turbulence (石鹸薄膜と二次元乱流)
Two-dimensional (2D) turbulence is the simplest paradigm for understanding large-scale atmospheric or oceanic turbulence, which at very large scales are approximately two-dimensional because of their small aspect ratio [1]. Besides its relevance to terrestrial flows, two-dimensional turbulence is interesting in its own right: the reduction in dimension adds a constraint on the vorticity, which leads to new physics not present in its three-dimensional counterpart. Two-dimensional flows can be realized in the laboratory using soap bubbles, which are extremely thin (microns) compared with their other dimensions (typically cm). By feeding soapy water into a soap bubble stretched on a frame, a flowing, two-dimensional channel flow is formed. I have used this setup to look at many things:
deviations from the standard theory of 2D turbulence [2]
information content (in the sense of Shannon) of turbulence [3]
minimal statistical modeling of turbulence [4]
mean velocity profiles of two-dimensional channel flow [5]
anisotropic turbulence [6]
and more recently some theoretical work on simplifying the derivation of a key diagnostic of turbulent flows (the third-order structure function) [7].
References:
[1] Davidson, P., "Turbulence: an introduction for scientists and engineers." Oxford University Press, USA, 2015.
Schematic of the transition to turbulence in pipe flow, along with representative experimental time series. If disturbances to the laminar flow remain small, the flow can remain laminar to infinite Reynolds numbers (Re). If finite-amplitude perturbations are added, which any imperfect pipe invariably has, laminar flow first yields to "puffs" (1600 < Re < 2250), then slugs (Re > 2250). If the perturbations are continuous, fully turbulent flow ensues, but if the perturbations are finite in time, then slugs persist.
The transition to turbulence in pipe flow (パイプ流における乱流遷移)
The transition to turbulence in pipe flow (パイプ流における乱流遷移)
All flows are laminar at low flow velocities and turbulent at high flow velocities. In pipe flows, at intermediate velocities, there is a transition wherein plugs of laminar flow alternate along the pipe with “flashes” of a type of fluctuating, non-laminar flow that remains poorly understood. Flashes were first observed by Osborne Reynolds in the 19th century [1]. Flashes are now categorized into the low Reynolds number (Re) "puffs", which although they remain of fixed size as they travel downstream, they can spontaneously die or fission into two statistically identical puffs. At higher Re (> 2250), puffs give way to "slugs", which expand inexorably as they travel downstream. My work on transitional pipe flow began by taking up a question that had eluded us from Reynolds' time: what is the friction during the transition? Reynolds sought "laws of resistance", and while he succeeded for laminar and turbulent flow, he admittedly failed for the "complex" transition. Using extensive experiments and simulations, we showed for the first time that the friction in flashes is actually the same as for turbulent flow [2]. More recently, we have gone further to show that the velocity fluctuations inside of flashes conforms to the same universal behavior predicted by Kolmogorov for turbulent flow at large Re [3], thereby extending this widely used framework beyond the expected domain of its validity and furnishing an important link between flashes and turbulence [4]. We have also discovered some important problems in a classic work on slugs [5], and by re-examining these issues have highlighted the rich Re-dependence of transitional flows [6].
References:
[1] Reynolds, O., An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Proceedings of the Royal Society of London, 35(224-226):84–99, 1883.
[2] Cerbus, R. T., Liu, C. C., Gioia G., & Chakraborty P. (2018). Laws of Resistance in Transitional Pipe Flows. Physical Review Letters, 120(5), 054502. Featured on PhysOrg: “In the pipeline: A solution to a 130-year old problem”
[3] Kolmogorov, A. N., The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR, 30(4):299–303, 1941.
[5] Wygnanski, I. J. & Champagne, F. H. 1973 On transition in a pipe. Part 1. the origin of puffs and slugs and the flow in a turbulent slug. J. Fluid Mech. 59 (02), 281–335.
Landslide runout (土砂崩れの到達距離)
Landslide runout (土砂崩れの到達距離)
A main objective in landslide research is to predict how far they will travel, as every year they claim thousands of lives and leave behind lasting ecological hazards. Landslides are complex, and a complete understanding of landslides in principle requires accounting for all of these parameters. A systematic study of each one is difficult if not impossible for natural landslides, and the vast variety of parameters has even led to landslides and avalanches with very different material and parameter values to be treated as distinct systems, even if the basic geometry and physics appears to be similar.
The result of both the experimental and parallel numerical study was that a relevant parameter absent in prevalent theories of landslide runout was the landslide grain size. We made a radical improvement on our ability to predict landslide runout by using systematic laboratory experiments of granular flow with a simplified landslide geometry combined with a scaling analysis. We found that additionally accounting for the granular nature of the flow through the constituent grain size, and correctly accounting for the fall height, reveals a striking correlation of normalized runout with landslide size which when combined with field data extends to several orders of magnitude [7]. We thus united seemingly disparate fields such as small-scale laboratory granular experiments, landslides, and snow avalanches, and dramatically enhanced runout prediction for dense flows. Our work alleviates the need for special theories and removes some of the mystery clouding the discussion of these fascinating, if extremely dangerous, phenomena.
We also showed what are the limits to the size of laboratory granular landslides that can be used to study large-scale natural landslides. The origin of this size (and height) limitation is air drag on the individual grains [8].
Plots of runout using the traditional (a) and our improved (b)-(c) normalizations. (a) The traditional plot of runout gives the (false) impression that small-scale laboratory granular landslides, large-scale ice avalanches, large-scale rock avalanches, and other landslides are all disparate phenomena. (b) Correctly accounting for the fall height H already yields a drastic improvement. By coloring the data points according to the grain size distribution's "skewness" (S), we see that the granularity also plays a role. (c) Runout normalized to correctly account for both fall height H and grain size distribution skewness S. Now all the data collapse onto a single curve.
References:
This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 793507.
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