Ambrish Pandey

Scaling of heat flux and energy spectrum for very large Prandtl number convection.

Under the limit of infinite Prandtl number, we derive analytical expressions for the large-scale quantities, e.g., Péclet number Pe, Nusselt number Nu, and rms value of the temperature fluctuations θ(rms). We complement the analytical work with direct numerical simulations, and show that Nu ∼ Ra(γ) with γ ≈ (0.30-0.32), Pe ∼ Ra(η) with η ≈ (0.57-0.61), and θ(rms) ∼ const. The Nusselt number is observed to be an intricate function of Pe, θ(rms), and a correlation function between the vertical velocity and temperature. Using the scaling of large-scale fields, we show that the energy spectrum E(u)(k) ∼ k(-13/3), which is in a very good agreement with our numerical results. The entropy spectrum E(θ)(k), however, exhibits dual branches consisting of k(-2) and k(0) spectra; the k(-2) branch corresponds to the Fourier modes θ[over ̂](0,0,2n), which are approximately -1/(2 nπ). The scaling relations for Prandtl number beyond 10(2) match with those for infinite Prandtl number.

Phenomenology of buoyancy-driven turbulence: recent results

In this paper, we review the recent developments in the field of buoyancy-driven turbulence. Scaling and numerical arguments show that the stably-stratified turbulence with moderate stratification has kinetic energy spectrum

Flow reversals in turbulent convection with free-slip walls

E_u(k) \sim k^{-11/5}

Transitional boundary layers in low-Prandtl-number convection

and the kinetic energy flux

Scalings of field correlations and heat transport in turbulent convection.

\Pi_u(k) \sim k^{-4/5}

Scaling of large-scale quantities in Rayleigh-Bénard convection

, which is called Bolgiano-Obukhov scaling. The energy flux for the Rayleigh-Benard convection (RBC) however is approximately constant in the inertial range that results in Kolmorogorvs spectrum (

Near isotropic behavior of turbulent thermal convection

E_u(k) \sim k^{-5/3}

Turbulent superstructures in Rayleigh-Bénard convection

) for the kinetic energy. The phenomenology of RBC should apply to other flows where the buoyancy feeds the kinetic energy, e.g. bubbly turbulence and fully-developed Rayleigh Taylor instability. This paper also covers several models that predict the Reynolds and Nusselt numbers of RBC. Recent works show that the viscous dissipation rate of RBC scales as

Similarities between 2D and 3D convection for large Prandtl number

\sim \mathrm{Ra}^{1.3}

On the applicability of low-dimensional models for convective flow reversals at extreme Prandtl numbers

, where