二维β平面湍流：双级串与纬向射流
Two-Dimensional $β$-plane Turbulence: Dual Cascade and Zonal Jets
AI总结：
该研究推导了β平面近似下受科里奥利力的二维纳维-斯托克斯方程的平均两点关联函数，补充了小尺度结果，阐明科里奥利力不影响熵和能量传递速率但促进纬向结构形成，证明依赖KHM关系的新表述。
AI中文摘要：
我们在β平面近似下受科里奥利力作用、处于统计稳态的受迫耗散二维纳维-斯托克斯方程中，推导了平均两点关联函数的精确新颖表达式。该恒等式与所谓的地转平衡相关：它通过两点关联函数将科里奥利力的效应与压力梯度关联起来。此外，我们给出了充分条件，在此条件下，大空间尺度下平均三阶结构函数的渐近行为遵循无科里奥利力时二维湍流的普适三阶律。这补充了我们之前关于小空间尺度的结果。综合来看，我们的结果清晰阐明了科里奥利力在β平面湍流中的作用：一方面，熵和能量的球平均传递速率不受科里奥利力影响；另一方面，科里奥利力通过改变能量的空间分布、促进纬向结构的形成，对大尺度各向异性组织产生贡献。该证明依赖于卡门-豪沃思-莫宁（Karman-Howarth-Monin, KHM）关系的新表述；对于地转平衡，我们采用了KHM关系的新颖反对称投影，在此投影下仅压力项和科里奥利项保留；对于级串律，我们证明科里奥利力对平均经典KHM关系的贡献在任意尺度下均恒等于零。
英文摘要：
We derive an exact and novel expression for an averaged two-point correlation function in the statistically stationary, forced-dissipative two-dimensional Navier-Stokes equations subject to the Coriolis force under the beta-plane approximation. This identity is related to the so-called geostrophic balance: it connects the effect of the Coriolis force to the pressure gradient through a two-point correlation function. Additionally, we provide sufficient conditions under which the asymptotics of the averaged third-order structure function at large spatial scales follow the universal third-order law of two-dimensional turbulence in the absence of the Coriolis force. This complements our previous results on small spatial scales. Together, our results provide a clear picture of the role of the Coriolis force in beta-plane turbulence. On the one hand, the spherically averaged rates of enstrophy and energy transfer are not affected by the Coriolis force. On the other hand, the Coriolis force contributes to anisotropic large-scale organization by altering the spatial distribution of energy and promoting the formation of zonal structures. The proof relies on a new formulation of the Karman-Howarth-Monin relation. For the geostrophic balance, we use a novel antisymmetric projection of the KHM relation under which only the pressure and Coriolis terms survive. For the cascade laws, we show that the Coriolis contribution to the averaged classical KHM relation vanishes identically at any scale.
