论文标题
从半段程序中以无限prandtl数字旋转对流的界限
Bounds for rotating convection at infinite Prandtl number from semidefinite programs
论文作者
论文摘要
在数值的情况下计算多型和环形动能的边界和热传输的边界，以在无限的prandtl数字上旋转对流，而无应力和无应力边界。该计算中调用的约束在问题变量中是线性或二次的，并导致了半决赛程序的制定。边界的行为是固定泰勒数在固定的泰勒数字上的函数，其方式与数量的数量相同。对于对流发作的瑞利数量小于临界雷利数的瑞利数量为零，它们的速度迅速增加，而瑞利数字刚开始的瑞利数字迅速增加，并且在较大的雷利数字上增加了速度较慢。如果对瑞利数字的依赖性通过幂律近似，则一个人的瑞利数字的界限比从实际的nusselt数字依赖性依赖于大型但有限的prandtl数字，从而获得了较大的指数。在对流开始时线性不稳定模式的波长似乎是边界中相关的长度比例。
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 computation are linear or quadratic in the problem variables and lead to the formulation of a semidefinite program. The bounds behave as a function of Rayleigh number at fixed Taylor number qualitatively in the same way as the quantities being bounded. The bounds are zero for Rayleigh numbers smaller than the critical Rayleigh number for the onset of convection, they increase rapidly with Rayleigh number for Rayleigh numbers just above onset, and increase more slowly at large Rayleigh numbers. If the dependencies on Rayleigh number are approximated by power laws, one obtains larger exponents from bounds on the Nusselt number for Rayleigh numbers just above onset than from the actual Nusselt number dependence known for large but finite Prandtl number. The wavelength of the linearly unstable mode at the onset of convection appears as a relevant length scale in the bounds.
