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**:
- “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)
- R. Bolgiano, J. Geophys. Res. 64, 2226 (1959).
- 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
Email: mkv@iitk.ac.in |