论文标题
旋转分层流向准地藻动力学的不相关性
Non-convergence of the rotating stratified flows toward the quasi-geostrophic dynamics
论文作者
论文摘要
在强分层和快速旋转方面，已使用了准斜角方程（QG）方程来捕获旋转分层的Boussinesq流动的渐近动力学。在本文中，当旋转 - 分层比固定为统一性或倾向于在渐近状态下足够缓慢地统一时，我们确定了这种近似值的无效性：旋转分层的Boussinesq流动与相应的QG流量之间的差异严格远离零，独立于旋转和地层的强度。相比之下，我们还表明，当旋转 - 分层率固定为统一或足够快地收敛到统一以外的数字时，会收敛发生。作为推论，我们计算收敛速率的下限，该速率随着旋转分层比为统一性而吹动。
The quasi-geostrohpic (QG) equation has been used to capture the asymptotic dynamics of the rotating stratified Boussinesq flows in the regime of strong stratification and rapid rotation. In this paper, we establish the invalidity of such approximation when the rotation-stratification ratio is either fixed to be unity or tends to unity sufficiently slowly in the asymptotic regime: the difference between the rotating stratified Boussinesq flow and the corresponding QG flow remains strictly away from zero, independently of the intensities of rotation and stratification. In contrast, we also show that the convergence occurs when the rotation-stratification ratio is fixed to be a number other than unity or converges to unity sufficiently fast. As a corollary, we compute a lower bound of the convergence rate, which blows up as the rotation-stratification ratio goes to unity.
