Gravity plays an important role in atmospheric and geophysical flows. The flow is destabilized when heavier or colder fluid is on top of lighter or hotter one, often seen in thermal convection (left figure). But the flow is stabilized if lighter fluid sits on top of heavier fluid, for example in Earth’s atmosphere (right figure). The latter configuration, called stably stratified, can be made turbulent by an additional stirring of the fluid. Kumar, Chatterjee, and Verma (PRE, 2014) solved the physics of such flows using theoretical and numerical analysis.

In a typical fluid turbulence scenario, for example in a glass of milk stirred strongly by a spoon, the energy supplied by the spoon at the large scales cascades to the microscopic scales. During this process, a constant energy flux flows across various length scales of the system. However, for stably stratified flows, in 1959, Bolgiano and Obhukhov conjectured that buoyancy will convert the kinetic energy to the potential energy at all scales, thus decreasing the above kinetic energy flux. This feature makes the physics of buoyancy driven flows very different than pure fluid turbulence. Kumar et al. investigated this aspect using sophisticated theoretical and numerical tools, and found that Bolgiano and Obhukhov’s conjecture was indeed correct. Kumar et al.’s simulations provide the first numerical validation of Bolgiano and Obhukhov’s conjecture. The simulations were performed using home-made spectral solver TARANG on 1024x1024x1024 grid, which is one of the largest for such problems.

In early 1990’s, Bolgiano and Obhukhov’s conjecture was extended to thermal convection. Kumar et al. showed that for thermal convection, kinetic energy flux increases due to buoyancy, not decrease, thus invalidating the extension of Bolgiano and Obhukhov’s conjecture to thermal convection. Their numerical simulations show that a delicate balance of energetics in thermal convection leads to a energy distribution in thermal convection very similar to that of pure fluid turbulence.

Thus, Kumar et al. put forward a novel energy flux analysis that unravels the mystery of buoyancy driven turbulence.

Reference:

1. “Energy spectrum of buoyancy-driven turbulence”, Abhishek Kumar, Anando G. Chatterjee, and Mahendra K. Verma, Physics Dept., IIT Kanpur, Phys. Rev. E, 90, 023-16 (2014)

2. R. Bolgiano, J. Geophys. Res. 64, 2226 (1959).

3. A. N. Obukhov, Dokl. Akad. Nauk SSSR 125, 1246 (1959).

Contact:
Mahendra K. Verma
Department of Physics
IIT Kanpur

http://turbulence.phy.iitk.ac.in
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