Lagrangian transport by vertically confined internal gravity wavepackets
Lagrangian transport by vertically confined internal gravity wavepackets
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垂直受限内部重力波包的拉格朗日输运
DOI：
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发表时间：
2019
影响因子：
3.7
通讯作者：
B. Sutherland
中科院分区：
文献类型：
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作者：
T. S. Bremer;H. Yassin;B. Sutherland
我们研究水平调制，垂直限制（或引导），内部波包在分层，Boussinesq流体引起的流动。波包诱导欧拉流和斯托克斯漂移，它们共同决定被动示踪剂的拉格朗日输运。我们推导出描述任意稳定分层中波浪诱导流动的方程，并考虑四种特殊情况：两层流体、对称和非对称分段常数（“顶帽”）分层以及更能代表海洋的指数分层。在两层流体中，Stokes漂移处处为正，峰值在界面处，而欧拉流则为负，且随深度变化均匀。综合起来，净深度积分拉格朗日输运为零。如果一个层比另一个层浅，则波平均界面位移到该层中，使得该层中的欧拉流更负，而相对层中的欧拉流更正，使得深度积分欧拉输运在每一层中被抵消相同的量。相比之下，在连续分层中，由于斯托克斯漂移和欧拉流引起的深度积分传输各自为零，但是如果诱导流的水平相速度等于波包的群速度，则欧拉流是奇异的，从而在均匀分层中产生单个共振（McIntyre，J. Fluid Mech.，第60卷，1973年，第120页。801-811）。在大礼帽分层中，这种单一共振消失，取而代之的是当波包的水平群速度与高阶模式的水平相速度相匹配时发生的多重共振。此外，如果分层不是垂直对称的，那么欧拉诱导流变化为水平波数的平方反比的浅水波，相同的非对称两层的情况下。这种“红外灾难”也发生在指数分层的情况下，这表明显着向后近地表传输调制海洋内部模式的欧拉诱导流。数值模拟证实了这些理论预测。
We examine the flows induced by horizontally modulated, vertically confined (or guided), internal wavepackets in a stratified, Boussinesq fluid. The wavepacket induces both an Eulerian flow and a Stokes drift, which together determine the Lagrangian transport of passive tracers. We derive equations describing the wave-induced flows in arbitrary stable stratification and consider four special cases: a two-layer fluid, symmetric and asymmetric piecewise constant (‘top-hat’) stratification and, more representative of the ocean, exponential stratification. In a two-layer fluid, the Stokes drift is positive everywhere with the peak value at the interface, whereas the Eulerian flow is negative and uniform with depth for long groups. Combined, the net depth-integrated Lagrangian transport is zero. If one layer is shallower than the other, the wave-averaged interface displaces into that layer making the Eulerian flow in that layer more negative and the Eulerian flow in the opposite layer more positive so that the depth-integrated Eulerian transports are offset by the same amount in each layer. By contrast, in continuous stratification the depth-integrated transport due to the Stokes drift and Eulerian flow are each zero, but the Eulerian flow is singular if the horizontal phase speed of the induced flow equals the group velocity of the wavepacket, giving rise to a single resonance in uniform stratification (McIntyre, J. Fluid Mech., vol. 60, 1973, pp. 801–811). In top-hat stratification, this single resonance disappears, being replaced by multiple resonances occurring when the horizontal group velocity of the wavepacket matches the horizontal phase speed of higher-order modes. Furthermore, if the stratification is not vertically symmetric, then the Eulerian induced flow varies as the inverse squared horizontal wavenumber for shallow waves, the same as for the asymmetric two-layer case. This ‘infrared catastrophe’ also occurs in the case of exponential stratification suggesting significant backward near-surface transport by the Eulerian induced flow for modulated oceanic internal modes. Numerical simulations are performed confirming these theoretical predictions.