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Wave boundary layers in rotating stratified fluid and near-inertial oscillations

机译：旋转分层流体中的波边界层和近惯性振荡

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Theory of wave boundary layers (WBLs) developed by Reznik (J Mar Res 71: 253-288, 2013, J Fluid Mech 747: 605-634, 2014, J Fluid Mech 833: 512-537, 2017) is extended to a rotating stratified fluid. In this case, the WBLs arise in the field of near-inertial oscillations (NIOs) driven by a tangential wind stress of finite duration. Near-surface Ekman layer is specified in the most general form; tangential stresses are zero at the lower boundary of Ekman layer and viscosity is neglected below the boundary. After the wind ceases, the Ekman pumping at the boundary becomes a linear superposition of inertial oscillations with coefficients dependent on the horizontal coordinates. The solution under the Ekman layer is obtained in the form of expansions in the vertical wave modes. We separate from the solution a part representing NIO and demonstrate development of a WBL near the Ekman layer boundary. With increasing time t, the WBL width decays inversely proportional to and gradients of fields in the WBL grow proportionally to ; the most part of NIO is concentrated in the WBL. Structure of the WBL depends strongly on its horizontal scale L determined by scale of the wind stress. The shorter the NIO is, the thinner and sharper the WBL is; the short-wave NIO with L smaller than the baroclinic Rossby scale L (R) does not penetrate deep into the ocean. On the contrary, for L aeyen L (R) , the WBL has a smoother vertical structure; a significant long-wave NIO signal is able to reach the oceanic bottom. An asymptotic theory of the WBL in rotating stratified fluid is suggested.
机译：由Reznik（J Mar Res 71：253-288，2013，J Fluid Mech 747：605-634，2014，J Fluid Mech 833：512-537，2017）开发的波边界层（WBL）理论扩展到旋转分层流体。在这种情况下，WBL出现在由有限持续时间的切向风应力驱动的近惯性振荡（NIO）领域。以最通用的形式指定近表面埃克曼层；在埃克曼层的下边界处，切向应力为零，而在边界以下则忽略了粘度。风停止后，边界处的埃克曼泵浦变成惯性振荡的线性叠加，其系数取决于水平坐标。 Ekman层下的解以垂直波模式中的扩展形式获得。我们从解决方案中分离出一个代表NIO的部件，并演示在Ekman层边界附近的WBL的开发。随着时间t的增加，WBL的宽度与WBL成反比地衰减，并且WBL中的场梯度与W成正比地增长。 NIO的大部分集中在WBL。 WBL的结构在很大程度上取决于其水平尺度L，该水平尺度L由风应力的大小决定。 NIO越短，WBL越薄且越锐利； L小于斜压Rossby标度L（R）的短波NIO不会深入海洋。相反，对于L aey L（R），WBL具有更平滑的垂直结构；一个重要的长波NIO信号能够到达海底。提出了旋转分层流体中WBL的渐近理论。

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