Logarithmic bounds for infinite Prandtl number rotating convection
نویسندگان
چکیده
Convection refers to fluid motion that is induced by buoyancy. In thermal convection buoyancy is due to temperature differences and one of the interesting questions is how much of the total heat transfer is due to convection. The natural measure of this quantity is the Nusselt number, N , and many experiments and numerical simulations have been performed to discern the relationship between N and the various parameters which describe the system. Much of this research has focused on the forcing parameter [1] [6], although it has been observed that rotation plays a nontrivial role as well [7]. The standard mathematical description of a convective system in a rotating frame of reference is based on the rotating Boussinesq equations for Rayleigh-Bénard convection (see, for example, Chandrasekhar [8]). This is a
منابع مشابه
On upper bounds for infinite Prandtl number convection with or without rotation
Bounds for the bulk heat transport in Rayleigh-Benard convection for an infinite Prandtl number fluid are derived from the primitive equations. The enhancement of heat transport beyond the minimal conduction value (the Nusselt number Nu) is bounded in terms of the nondimensional temperature difference across the layer (the Rayleigh number Ra) according to Nu ≤ c Ra where c < 1 is an absolute co...
متن کاملBound on vertical heat transport at large Prandtl number
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) ...
متن کاملHeat Transport in Rotating Convection
We derive upper bounds for the Nusselt number in innnite Prandtl-number rotating convection. The bounds decay algebraically with Taylor number to the conductive heat transport value; the decay rate depends on boundary conditions. We show moreover that when the rotation is fast enough the purely conductive solution is the globally and nonlinearly attractive xed point; the critical rotation rate ...
متن کاملBifurcation 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...
متن کامل