Turbulent motions enhance the diffusion of large-scale flows and temperature gradients. Such is often parameterized by coefficients turbulent viscosity ( $\nu _{t}$ ) thermal diffusivity $\chi that are analogous to their microscopic counterparts. We compute imposing sinusoidal velocity gradients on a flow measuring response system. also confirm our results using experiments where imposed allowe...

We prove a new upper bound on the vertical heat transport in Rayleigh-Bénard convection of the form c Ra 1 3 (lnRa) 2 3 under the assumption that the ratio of Prandtl number over Rayleigh number satisfies Pr Ra ≥ c0 where the non-dimensional constant c0 depends on the aspect ratio of the domain only. This new rigorous bound agrees with the (optimal) Ra 1 3 bound (modulo logarithmic correction) ...

The dynamo instability is investigated in the limit of infinite magnetic Prandtl number. In this limit the fluid is assumed to be very viscous so that the inertial terms can be neglected and the flow is enslaved to the forcing. The forcing consist of an external forcing function that drives the dynamo flow and the resulting Lorentz force caused by the back reaction of the magnetic field. The fl...

The transition to convection in a zero Prandtl number fluid with stress-free and perfectly conducting boundaries differs significantly from finite Prandtl number convection, giving rise to a three-dimensional pattern. Two possible scenarios are described and compared with recent numerical simulations by Thual Ii]. The Prandtl number of a fluid can approach zero in one of two ways either because...

We use DNS to study the effect of Prandtl number on mixing in weakly density stratified Kelvin-Helmholtz (KH) billows at low to moderate Reynolds numbers. The time evolution of the density field of the flow and the mixing are significantly influenced by the Prandtl number. By increasing the Prandtl number, the final amount of mixing increases for Reynolds that are too low to sustain three-dimen...

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...