Related papers: Large Prandtl Number Asymptotics in Randomly Force…
We consider the Boussinesq approximation for Rayleigh-B\'{e}nard convection perturbed by an additive noise and with boundary conditions corresponding to heating from below. In two space dimensions, with sufficient stochastic forcing in the…
We derive an improved rigorous bound on the space and time averaged temperature $<T>$ of an infinite Prandtl number Boussinesq fluid contained between isothermal no-slip boundaries thermally driven by uniform internal heating. A novel…
The Rayleigh number $Ra$ dependence of the Nusselt number $Nu$ in turbulent Rayleigh--B\'enard convection is numerically investigated for a moderate and low Prandtl number, $Pr=0.7$ and $0.021$, respectively. Here we specifically address…
We prove a new rigorous upper bound on the vertical heat transport for B\'enard-Marangoni convection of a two- or three-dimensional fluid layer with infinite Prandtl number. Precisely, for Marangoni number $Ma \gg 1$ the Nusselt number $Nu$…
New bounds are proven on the mean vertical convective heat transport, $\overline{\langle wT \rangle}$, for uniform internally heated (IH) convection in the limit of infinite Prandtl number. For fluid in a horizontally-periodic layer between…
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…
The non-hydrostatic, quasigeostrophic approximation for rapidly rotating Rayleigh-B\'enard convection admits a class of exact `single mode' solutions. These solutions correspond to steady laminar convection with a separable structure…
This paper examines the effects of energetic consistency in Fourier truncated models of the 3D Boussinesq-Coriolis (BC) equations as a case-study towards improving the realism of convective processes in climate models. As a benchmark we…
Conditions for the onset of nonpenetrative convection in a horizontal Boussinesq fluid layer subject to a step change in temperature are studied using propagation theory. A wide range of Prandtl numbers and two different kinematic boundary…
We are concerned with infinite Prandtl number Rayleigh--B\'enard convection with Navier-slip boundary conditions. The goal of this work is to estimate the average upward heat flux measured by the nondimensional Nusselt number $Nu$ in terms…
Thermal convection in an inclined layer between two parallel walls kept at different fixed temperatures is studied for fixed Prandtl number Pr=1.07. Depending on the angle of inclination and the imposed temperature difference, the flow…
We prove a conjecture in fluid dynamics concerning optimal bounds for heat transportation in the infinite Prandtl number limit. Due to a maximum principle property for the temperature exploited by Constantin-Doering and Otto-Seis, this…
In turbulent Rayleigh-B\'enard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by Rayleigh number. In experiments, one measures…
Thermal convection driven by internal heat sources and sinks was recently shown experimentally to exhibit the mixing-length, or "ultimate", scaling-regime: the Nusselt number $Nu$ (dimensionless heat flux) increases as the square-root of…
We study Rayleigh B\'enard convection based on the Boussinesq approximation. We are interested in upper bounds on the Nusselt number $\mathrm{Nu}$, the upwards heat transport, in terms of the Rayleigh number $\mathrm{Ra}$, that…
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…
In the quest to understand the basic universal features of compressible convection, one would like to disentangle genuine consequences of compression from spatial variations of transport properties. In the present work, we consider a very…
We consider the three-dimensional magnetohydrodynamics (MHD) equations in the presence of a spatially degenerate stochastic forcing as a model for magnetostrophic turbulence in the Earth's fluid core. We examine the multi-parameter singular…
Bounds for the poloidal and toroidal kinetic energies and the heat transport are computed numerically for rotating convection at infinite Prandtl number with both no slip and stress free boundaries. The constraints invoked in this…
Measurements of the Nusselt number $Nu$ and of temperature variations $\Delta T_b$ in the bulk fluid are reported for turbulent Rayleigh-B\'enard convection of a cylindrical sample. They cover the Rayleigh-number range $10^{9} \alt Ra \alt…