A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography
A Theoretical Model of Long Rossby Waves in the Southern Ocean and Their Interaction with Bottom Topography
复制标题
南大洋罗斯贝长波的理论模型及其与海底地形的相互作用
作者：
D. Marshall
假设位涡是浮力的线性函数，在存在任意底部地形的情况下，针对连续分层的行星地转海洋开发了长罗斯贝波的分析模型。其余的动力学由沿海面和海底的浮力物质守恒方程控制。平均稳态表面环流遵循 f 和 f / H 等值线的中间特征，其中 f 是科里奥利参数，H 是海洋深度；对于现实的层结和弱底流，这些特征大多是带状的，在主要地形特征上有弱偏转。推导出关于该平均状态的线性长罗斯贝波的方程。这些在质量上类似于两层海洋的长罗斯贝波动方程，关于静止状态线性化，除了波动方程中主导传播的表面特征遵循与平均表面流完全相同的路径。除了这种地形转向之外，还表明罗斯贝传播项的加权积分在 f / H 等值线包围的任何区域上消失，这已在两层模型中显示导致罗斯贝波“跳跃”穿过 f / H 等值线。最后，导出了非线性 Rossby 波动方程，作为 Rick Salmon 先前获得的结果的特化。这包括经典长罗斯比速度的固有向西传播（经过修改以考虑有限的海洋深度）以及深度平均流的多普勒频移。后者在南极绕极流中占主导地位，这与观测到的海面高度异常向东传播一致。
An analytical model of long Rossby waves is developed for a continuously-stratified, planetary geostrophic ocean in the presence of arbitrary bottom topography under the assumption that the potential vorticity is a linear function of buoyancy. The remaining dynamics are controlled by equations for material conservation of buoyancy along the sea surface and the sea floor. The mean, steady-state surface circulation follows characteristics that are intermediate to f and f / H contours, where f is the Coriolis parameter and H is the ocean depth; for realistic stratification and weak bottom currents, these characteristics are mostly zonal with weak deflections over the major topographic features. Equations are derived for linear long Rossby waves about this mean state. These are qualitatively similar to the long Rossby wave equations for a two-layer ocean, linearised about a state of rest, except that the surface characteristics in the wave equation, which dominate the propagation, follow precisely the same path as the mean surface flow. In addition to this topographic steering, it is shown that a weighted integral of the Rossby propagation term vanishes over any area enclosed by an f / H contour, which has been shown in the two-layer model to lead to Rossby waves “jumping” across the f / H contour. Finally, a nonlinear Rossby wave equation is derived as a specialisation of the result previously obtained by Rick Salmon. This consists of intrinsic westward propagation at the classical long Rossby speed, modified to account for the finite ocean depth, and a Doppler shift by the depth-mean flow. The latter dominates within the Antarctic Circumpolar Current, consistent with observed eastward propagation of sea surface height anomalies.
影响因子：
5.2
作者：
Klocker, Andreas;Marshall, David P.
通讯作者：
Marshall, David P.
影响因子：
3.5
作者：
Abernathey, Ryan;Marshall, John;Shuckburgh, Emily
通讯作者：
Shuckburgh, Emily
影响因子：
25.2
作者：
M. Meredith;P. Woodworth;T. Chereskin;D. Marshall;L. Allison;G. Bigg;K. Donohue;K. Heywood;C. Hughes;A. Hibbert;A. Hogg;H. Johnson;L. Jullion;B. King;H. Leach;Y. Lenn;M. M. Morales Maqueda-M.;D. Munday;A. N. Naveira Garabato;C. Provost;J. Sallée;J. Sprintall
通讯作者：
M. Meredith;P. Woodworth;T. Chereskin;D. Marshall;L. Allison;G. Bigg;K. Donohue;K. Heywood;C. Hughes;A. Hibbert;A. Hogg;H. Johnson;L. Jullion;B. King;H. Leach;Y. Lenn;M. M. Morales Maqueda-M.;D. Munday;A. N. Naveira Garabato;C. Provost;J. Sallée;J. Sprintall