论文标题
区域和湍流组件之间的腹膜分配
Partition of enstrophy between zonal and turbulent components
论文作者
论文摘要
已经研究了针对二维压缩流的β平面模型的涡度（有序）和波浪（湍流）组成之间的胚胎分配。已经得出了对区域成分的最小值的分析估计。将能量，角动量，循环以及总肠唤起，作为最小化Zonal Enstrophy的限制。相应的变分原理具有不寻常的数学结构（主要是因为目标功能不是强制性形式），通过该结构，约束以有趣的方式奏效。能量限制产生了一组离散的纬向腹膜水平；每个级别由代表区域流量层压周期的特征值指定。然而，纬向腹部水平的值本身是仅角动量和循环的函数，独立于能量（和总肠）。取而代之的是，能量可以选择放松状态的“水平”（特征值）。放松是通过发出小规模波浪形的肠道而发生的，并继续延伸到通过能量缩放的非线性效应可以产生波浪状的腹膜。与数值模拟的比较表明，该理论给出了在松弛状态下的纬向膜的适当估计。
The partition of enstrophy between zonal (ordered) and wavy (turbulent) components of vorticity has been studied for the beta-plane model of two-dimensional barotropic flow. An analytic estimate of the minimum value for the zonal component has been derived. The energy, angular momentum, circulation, as well as the total enstrophy are invoked as constraints for the minimization of the zonal enstrophy. The corresponding variational principle has an unusual mathematical structure (primarily because the target functional is not a coercive form), by which the constraints work out in an interesting way. A discrete set of zonal enstrophy levels is generated by the energy constraint; each level is specified by an eigenvalue that represents the lamination period of zonal flow. However, the value itself of the zonal enstrophy level is a function of only angular momentum and circulation, being independent of the energy (and total enstrophy). Instead, the energy works in selecting the "level" (eigenvalue) of the relaxed state. The relaxation occurs by emitting small-scale wavy enstrophy, and continues as far as the nonlinear effect, scaled by the energy, can create wavy enstrophy. Comparison with numerical simulations shows that the theory gives a proper estimate of the zonal enstrophy in the relaxed state.
