A new instability for finite Prandtl number rotating convection with free‐slip boundary conditions

A new instability for finite Prandtl number rotating convection with free-slip boundary conditions

Rolls in finite Prandtl number rotating convection with free-slip top and bottom boundary conditions are shown to be unstable with respect to small angle perturbations for any value of the rotation rate. This instability is driven by the horizontal mean flow whose estimation requires a special singular perturbation analysis. PACS numbers: 47.27.Te, 47.20.Bp, 47.32.-y, 47.20.-Lz

Oscillatory Convection in Rotating Spherical Shells: Low Prandtl Number and Non-Slip Boundary Conditions

A five-degree model, which reproduces faithfully the sequence of bifurcations and the type of solutions found through numerical simulations of the three-dimensional Boussinesq thermal convection equations in rotating spherical shells with fixed azimuthal symmetry, is derived. A low Prandtl number fluid of σ = 0.1 subject to radial gravity, filling a shell of radius ratio η = 0.35, differentiall...

On the onset of low-Prandtl-number convection in rotating spherical shells: non-slip boundary conditions

Accurate numerical computations of the onset of thermal convection in wide rotating spherical shells are presented. Low-Prandtl-number (σ ) fluids, and non-slip boundary conditions are considered. It is shown that at small Ekman numbers (E), and very low σ values, the well-known equatorially trapped patterns of convection are superseded by multicellular outer-equatorially-attached modes. As a r...

Bifurcation of Infinite Prandtl Number Rotating Convection

We consider infinite Prandtl number convection with rotation which is the basic model in geophysical fluid dynamics. For the rotation free case, the rigorous analysis has been provided by Park [15, 16, 17] under various boundary conditions. By thoroughly investigating We prove in this paper that the solutions bifurcate from the trivial solution u = 0 to an attractor ΣR which consists of only on...

Logarithmic Bounds for In nite Prandtl Number Rotating Convection