We investigate the long-time evolution of flow structures and the kinetic-potential energy exchange in rotating stratified turbulence, which is of great significance in geophysical flows. Numerical simulations of forced three-dimensional homogeneous rotating stratified turbulence in transient state with different Froude numbers are performed. Numerous small vortices spread in the flow, besides a cyclone and an anticyclone that fill up the domain after a very long time. Cyclonic vortices, though being less numerous than anticyclonic vortices, grow faster, thus becoming comparable to the domain scale at an earlier time. When the strength of stratification is varied, we find that in the case with weak stratification, the intensity of global kinetic-potential energy exchange is nearly constant in earlier times, while it oscillates in time at later times. Moreover, for the simulation with weak stratification, the areas of intense kinetic-potential energy exchange tend to concentrate in segmented cylinders. In contrasts, when the strength of stratification is comparable to that of rotation, the areas of intense kinetic-potential energy exchange populate the flow as quadrupoles. For both simulations with stratification, the intense kinetic-potential energy exchange is found to be associated with the cyclonic structures. A possible relation between the sign of ${\omega }_z$ and the spatial distribution of the density field $\theta$ is proposed, and the conditional average $\langle \partial \theta /\partial z|{\omega }_z\rangle$ is found to be almost time-invariant throughout most of the domain.

中文翻译：

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强迫旋转分层湍流中的流动结构和动力学势交换

我们研究了旋转分层湍流中流动结构的长期演化和动能交换，这在地球物理流动中具有重要意义。对瞬态下具有不同弗劳德数的强迫三维均匀旋转分层湍流进行了数值模拟。在很长一段时间后，除了旋流器和反旋风器外，还有许多小涡流在流中扩散。旋风涡旋的数量虽然比反旋风涡旋的数量少，但增长得更快，因此在更早的时间变得与磁畴规模相当。当分层强度变化时，我们发现在分层较弱的情况下，全球动能交换的强度在早期几乎是恒定的，而它会在以后的时间中振荡。此外，对于分层较弱的模拟，强烈的动能交换区域倾向于集中在分段圆柱体中。相反，当分层强度可与旋转强度相媲美时，强烈的动能交换区域将流作为四极杆填充。对于这两个具有分层的模拟，都发现强烈的动能交换与旋风结构有关。符号之间的可能关系 激烈的势能交换区域以四极杆的形式填充流动。对于这两个具有分层的模拟，都发现强烈的动能交换与旋风结构有关。符号之间的可能关系 激烈的势能交换区域以四极杆的形式填充流动。对于这两个具有分层的模拟，都发现强烈的动能交换与旋风结构有关。符号之间的可能关系${\omega }_{ž}$ 和密度场的空间分布 $\theta$ 被提出，并且条件平均值 $〈\partial \theta /\partial ž|{\omega }_{ž}〉$ 发现在整个域的大部分时间几乎都是不变的。