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doi:10.1038/nindia.2017.139 Published online 15 November 2017

Supercomputers overturn 50-year-old conjecture of fluid physics

Arati Halbe

Researchers from the Indian Institute of Technology (IIT) Kanpur have found a way out of a long-unsolved problem in fluid mechanics with new studies1, 2 that characterise ‘buoyancy-driven flows’ more accurately, something that could overturn an age-old conjecture in the physics of fluids. New insights into fluid motion could improve marine and air travel and help create better weather prediction models, and even better air-conditioning for households.

Using large-scale numerical simulations on some of the best supercomputers of the world, Mahendra Verma and colleagues at IIT Kanpur ran a home-grown numerical code – TARANG – to create detailed simulations for buoyancy-driven flows. They observed that the buoyancy driven turbulent flow is better characterised by a model, first proposed by the Russian scientist Andrey Kolmogorov, instead of the model proposed by R. Bolgiano and Alexander Obukhov, as was previously believed.

Fluid motion is at the heart of our understanding of everything that involves motions of fluids – from flowing rivers to blowing winds or even a steaming cup of hot coffee. Turbulence occurs when there are chaotic changes in the pressure and flow velocity of a moving fluid. Turbulent motion can be seen on the surface as also interiors of the earth, planets, sun and stars. Buoyancy, the force that fluids exert on subjects immersed in them, also drives and influences flows. Flows influenced by buoyancy are called buoyancy driven flows.

“The atmosphere of earth has shear (difference in flow speeds at different locations) driven turbulence as well as buoyancy driven turbulence”, explains Jayawant Arakeri from the mechanical engineering department of Indian Institute of Science (IISc), Bengaluru.

The ‘unsolved’ problem

Is it possible to describe precisely the behaviour of a fluid undergoing turbulent flow, particularly its internal structure?

Russian mathematician Andrey Kolmogorov had proposed the first statistical model for hydrodynamic turbulence. The model suggests that energy cascades through the liquid from large scale to small scale at a constant rate. It does not seem to spell out the flow well as the energy transfer appears to reduce at smaller scales.

There are multiple types of buoyancy driven flows, and each shows a different behaviour3.

Verma and colleagues worked on two of them. In one case, a heavier, colder fluid was at the bottom of a container and a lighter, hotter fluid on top with no vertical movement. Such systems are called ‘stably stratified’ and their density and temperature change uniformly from bottom to top. The other system has the lighter, hotter fluid at the bottom and the heavier, colder fluid on top – the Rayleigh-Bènard convection.

The IIT team carried out high resolution numerical simulations for both, the stably stratified systems and Rayleigh-Bènard convection. They observed that stably stratified systems follow the Bolgiano-Obukov model but contrary to the earlier belief, Rayleigh-Bènard Convection followed the Kolmogorov model.

“This is a fundamental result. It is important to note that due to the detailed simulations carried out, all scales were resolved,” Arakeri says.

Verma’s team implemented their code on the supercomputers at King Abdullah University, Saudi Arabia’s Shaheen II and the supercomputer at Indian Institute of Science (IISc), Bengaluru. It was essential to analyse the flow equations for as small a volume as possible. The computation power required for the detailed simulation was enormous. Certain aspects of energy transfer in turbulent fluids could be established only because of the detailed, fine resolution computations, Verma says.

This analysis, he says, opens the door for future work on energy transfers in various forms of fluid flows.


References

1. Verma, M. K. et al. Phenomenology of buoyancy-driven turbulence: recent results. New J. Phys. 19, 025012 (2017) doi: 10.1088/1367-2630/aa5d63
2. Chatterjee, A. G. et al. Scaling of a Fast Fourier Transform and a pseudo-spectral fluid solver up to 196608 cores. J. Parallel Distributed Computing (2017) doi: 10.1016/j.jpdc.2017.10.014 
3. Kumar, A. et al. Energy spectrum of buoyancy-driven turbulence. Phys. Rev. E 90, 023016 (2014)