Compressible Turbulent Convection
Heat transport and scaling laws at extreme Rayleigh numbers.
My doctoral research investigated compressible turbulent convection at extreme Rayleigh numbers. We performed direct numerical simulations and compared compressible convection with Rayleigh–Bénard and periodic convection, reaching $Ra=10^{16}$ in two dimensions and $Ra=10^{13}$ in three dimensions.
A fully compressible turbulent-convection simulation from the original project gallery.
What we did
We separated the local vertical convective heat flux,
\[F_z(\mathbf{x}) = \rho u_z T_{\mathrm{sa}},\]into its positive and negative contributions. The Nusselt number can then be written schematically as
\[Nu = 1 + \sqrt{Ra\,Pr}\left(\langle F_z^+\rangle + \langle F_z^-\rangle\right).\]Although $\langle F_z^+\rangle$ and $\lvert\langle F_z^-\rangle\rvert$ are individually large, the thermal plates make them nearly cancel. We found that their imbalance decreases approximately as $Ra^{-0.20}$. Consequently,
\[Nu \sim Ra^{1/2}Ra^{-0.20} \sim Ra^{0.30},\]which explains the persistence of classical heat-transport scaling rather than a transition to the $Ra^{1/2}$ ultimate regime.
This work formed my Ph.D. thesis, Compressible turbulent convection at extreme Rayleigh numbers, which received the Outstanding PhD Thesis Award from IIT Kanpur in 2026.
Read the PNAS paper, read the thesis, or explore the related papers on the publications page.