Buoyancy-driven turbulent flows are often encountered in geophysics,
astrophysics, atmospheric and solar physics, and engineering. An
important unsolved problem in this field is how to quantify the
small-scale quantities, e.g., spectra and fluxes of kinetic energy
(KE) and potential energy (PE) of these flows. Using ideas of energy flux
in direct numerical simulation (DNS) and shell model simulation, we show
that the KE spectrum for stably stratified flows has -11/5 spectral
exponent, while Rayleigh-Bénard convection (RBC) has Kolmogorov's
-5/3 spectral exponent [1, 2, 3]. For RBC, we show the applicability of
Taylor's hypothesis in the presence of steady large-scale circulation
in a cubical geometry. Our simulations indicate that a cubical geometry
is better suited for spectral studies than a cylindrical one due to the
steady nature of large-scale circulation in a cube . We also show
a modified Bolgiano-Obukhov spectrum for the velocity field, and the
presence of internal gravity waves at large-scale in two-dimensional
stably stratified turbulence .
1. Kumar, Chatterjee, and Verma, Phys. Rev. E, 2014.
2. Kumar and Verma, Phys. Rev. E, 2015.
3. Verma, Kumar, and Pandey, New J. Phys., 2017
4. Kumar and Verma, under review, 2017.
5. Kumar, Verma, and Sukhatme, J. Turbul., 2017.