Nonlinear Rossby adjustment in a channel: beyond Kelvin waves
Nonlinear Rossby adjustment in a channel: beyond Kelvin waves
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通道中的非线性罗斯贝调整：超越开尔文波
DOI：
10.1017/s0022112089002119
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发表时间：
1989
影响因子：
3.7
通讯作者：
E. Johnson
中科院分区：
文献类型：
--
作者：
A. Hermann;P. Rhines;E. Johnson
利用轮廓动力学方法，研究了重力和旋转作用下自由面高度不连续的非线性平流平差。当线性波动调整在宽（[Gt] 1罗斯比半径）通道中建立了内部射流和边界流后，流体在两个通道壁上沿通道向下涌动，而不仅仅是支持通道下开尔文波的那一面壁上。低位势涡度流体楔状侵入这一壁面，以及这种流体鼻状侵入另一壁面，有助于逆转先前存在的气流中相对涡度的迹象。对于较窄的通道，低位涡度流体的相干边界捕获结构在一个壁上喷射，并在其母流体之前喷射。当涡旋平流将最大值移到左侧时，电流最初倾向于集中在“右侧”壁上（北半球支持下通道开尔文波的壁上）。最终，流体在下游的任何地方冲刷，甚至穿过宽阔的通道，留下线性调整的上游状态作为最终状态。发生这种情况所需的时间随着通道宽度呈指数增长。线性理论中小振幅边界流的宽度等于Rossby的变形半径，但这里我们发现速度场和位涡场的变化宽度在很大的空间和时间范围内偏离了这个尺度。小振幅时有效的轮廓动力学解与大振幅时浅水方程的积分的比较显示出很大的相似性。边界摩擦强烈地修正了这些结果，产生更接近线性波调整状态的场。观测到的特征包括那些暗示海岸捕获重力流的特征。给出了边界附近涡度锋演化的解析结果，为数值实验提供了支持。
Nonlinear advective adjustment of a discontinuity in free-surface height under gravity and rotation is considered, using the method of contour dynamics. After linear wave-adjustment has set up an interior jet and boundary currents in a wide ([Gt ] one Rossby radius) channel, fluid surges down-channel on both walls, rather than only that wall supporting a down-channel Kelvin wave. A wedgelike intrusion of low potential vorticity fluid on this wall, and a noselike intrusion of such fluid on the opposite wall, serve to reverse the sign of relative vorticity in the pre-existing currents. For narrower channels, a coherent boundary-trapped structure of low potential vorticity fluid is ejected at one wall, and shoots ahead of its parent fluid. The initial tendency for the current to concentrate on the ‘right-hand’ wall (the one supporting a down-channel Kelvin wave in the northern hemisphere) is defeated as vorticity advection shifts the maximum to the left-hand side. Ultimately fluid washes downstream everywhere across even wide channels, leaving the linearly adjusted upstream condition as the final state. The time necessary for this to occur grows exponentially with channel width. The width of small-amplitude boundary currents in linear theory is equal to Rossby's deformation radius, yet here we find that the width of the variation in velocity and potential vorticity fields deviates from this scale across a large region of space and time. Comparisons of the contour dynamics solutions, valid for small amplitude, and integration of the shallow-water equations at large amplitude, show great similarity. Boundary friction strongly modifies these results, producing fields more closely resembling the linear wave-adjusted state. Observed features include those suggestive of coastally trapped gravity currents. Analytical results for the evolution of vorticity fronts near boundaries are given in support of the numerical experiments.