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Turbulent thermal convection governs heat transport in systems ranging from stellar interiors to industrial heat exchangers. Two-dimensional Rayleigh-B\'enard convection serves as a paradigm for these flows, reproducing key features such as…
We analyse the nonlinear dynamics of the large scale flow in Rayleigh-B\'enard convection in a two-dimensional, rectangular geometry of aspect ratio $\Gamma$. We impose periodic and free-slip boundary conditions in the streamwise and…
Using direct numerical simulations of Rayleigh-B\'{e}nard convection (RBC) under free-slip boundary condition, we show that the normalized correlation function between the vertical velocity field and the temperature field, as well as the…
We consider Rayleigh-B\'enard convection in a layer of fluid between rough no-slip boundaries where the top and bottom boundary heights are functions of the horizontal coordinates with square-integrable gradients. We use the background…
Rigorous upper limits on the vertical heat transport in two dimensional Rayleigh-Benard convection between stress-free isothermal boundaries are derived from the Boussinesq approximation of the Navier-Stokes equations. The Nusselt number Nu…
We study the topology and the temporal dynamics of turbulent Rayleigh-Benard convection in a liquid metal with a Prandtl number of 0.03 located inside a box with a square base area and an aspect ratio of five. Experiments and numerical…
A quantitative theory is developed for the vertical mean temperature profile (MTP) in turbulent Rayleigh-Benard convection (RBC), which explains the recent experimental and numerical observations of a logarithmic law by Ahlers et al.(Phys.…
Recent investigations show that steady solutions share many features with turbulent Rayleigh--B\'enard convection (RBC) and form the state space skeleton of turbulent dynamics. Previous computations of steady roll solutions in…
Rayleigh-B\'enard convection in the turbulent regime is studied using statistical methods. Exact evolution equations for the probability density function of temperature and velocity are derived from first principles within the framework of…
We study the structure of the thermal boundary layer (BL) in Rayleigh-B\'enard convection for Prandtl number ($Pr$) 0.021 by conducting direct numerical simulations in a two-dimensional square box for Rayleigh numbers ($Ra$) up to $10^9$.…
A numerical investigation of an asymptotically reduced model for quasi-geostrophic Rayleigh-B\'enard convection is conducted in which the depth-averaged flows are numerically suppressed by modifying the governing equations. The Reynolds…
Two-dimensional direct numerical simulations are conducted for convection sustained by uniform internal heating in a horizontal fluid layer. Top and bottom boundary temperatures are fixed and equal. Prandtl numbers range from 0.01 to 100,…
We investigate the dynamics of triaxial collapse in terms of eigenvalues of the deformation tensor, the velocity derivative tensor and the gravity Hessian. Using the Bond-Myers model of ellipsoidal collapse, we derive a new set of equations…
Large-scale patterns, which are well-known from the spiral defect chaos regime of thermal convection at Rayleigh numbers $Ra < 10^4$, continue to exist in three-dimensional numerical simulations of turbulent Rayleigh-B\'{e}nard convection…
Direct numerical simulations of turbulent convection at high Rayleigh numbers in large aspect ratio cells are challenging because of the prohibitive computational resources required. One can achieve high Rayleigh numbers at affordable costs…
We study, using direct numerical simulations, the effect of geometrical confinement on heat transport and flow structure in Rayleigh-B\'enard convection in fluids with different Prandtl numbers. Our simulations span over two decades of…
Planetary and stellar convection, which are compressible and turbulent, remain poorly understood. In this paper, we report numerical results on the scaling of Nusselt number ($\mathrm{Nu}$) and Reynolds number ($\mathrm{Re}$) for extreme…
We consider the two-dimensional Rayeigh-B\'enard convection problem between Navier-slip fixed-temperature boundary conditions and present a new upper bound for the Nusselt number. The result, based on a localization principle for the…
In turbulent Rayleigh-B\'{e}nard (RB) convection, a transition to the so-called ultimate regime, in which the boundary layers (BL) are of turbulent type, has been postulated. Indeed, at very large Rayleigh number $Ra \approx…
Three-dimensional miscible Rayleigh--Taylor (RT) turbulence at small Atwood number and at Prandtl number one is investigated by means of high resolution direct numerical simulations of the Boussinesq equations. RT turbulence is a…