Statistically relevant conserved quantities for truncated quasigeostrophic flow
Statistically relevant conserved quantities for truncated quasigeostrophic flow
复制标题
截断准地转流的统计相关守恒量
DOI：
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发表时间：
2003
影响因子：
11.1
通讯作者：
A. Majda
中科院分区：
文献类型：
--
作者：
R. Abramov;A. Majda
平衡统计力学的思想的系统应用，导致有前途的战略，以评估在许多科学和工程问题的未解决的运动尺度。在过去的25年里，科学界一直在争论，在形式上无限的列表中，哪些守恒量与大尺度平衡统计行为在统计上相关。在这里，这个重要的问题是解决通过使用合适的离散数值近似地球物理流与许多保守的数量作为一个数值实验室。数值实验的结果，这些截断的地球物理流与地形在一个合适的制度。这些实验表明，除了常见的能量、环流和涡度拟能约束外，位涡的积分三次幂（积分二次幂）在大尺度下的粗粒平衡统计行为在该区域中具有统计相关性。此外，在本文所研究的例子中，位涡的积分高次幂大于3与大尺度平衡统计行为在统计上无关。
Systematic applications of ideas from equilibrium statistical mechanics lead to promising strategies for assessing the unresolved scales of motion in many problems in science and engineering. A scientific debate over more than the last 25 years involves which conserved quantities among the formally infinite list are statistically relevant for the large-scale equilibrium statistical behavior. Here this important issue is addressed by using suitable discrete numerical approximations for geophysical flows with many conserved quantities as a numerical laboratory. The results of numerical experiments are presented here for these truncated geophysical flows with topography in a suitable regime. These experiments establish that the integrated third power of potential vorticity besides the familiar constraints of energy, circulation, and enstrophy (the integrated second power) is statistically relevant in this regime for the coarse-grained equilibrium statistical behavior at large scales. Furthermore, the integrated higher powers of potential vorticity larger than three are statistically irrelevant for the large-scale equilibrium statistical behavior in the examples studied here.