On the Three-Dimensional Residual Mean Circulation and Wave Activity Flux of the Primitive Equations
On the Three-Dimensional Residual Mean Circulation and Wave Activity Flux of the Primitive Equations
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DOI：
10.2151/jmsj.2010-307
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发表时间：
2010-06
影响因子：
3.1
通讯作者：
T. Kinoshita;Y. Tomikawa;Kaoru Sato
中科院分区：
文献类型：
--
作者：
T. Kinoshita;Y. Tomikawa;Kaoru Sato
转换后的欧拉平均（TEM）方程在研究大气波的产生和/或耗散如何驱动平均纬向环流方面是有用的。然而，TEM方程并不提供一个三维的运输视图。以前的一些研究将TEM方程系统扩展到三维，但通常是在准地转假设下进行的，这排除了重力波等小尺度现象。Miyahara最近导出了适用于重力波的三维波活动通量和相应的剩余环流。然而，他的提法有两个缺陷。首先，三维剩余平均环流不满足连续性方程。第二，欧拉平均流出现在平流项中，剩余环流出现在纬向动量方程的科里奥利力项中，而不是在TEM方程中。本研究在原始方程的基础上，克服了这些缺陷，发展了三维剩余平均环流和波活动通量的理论公式。在类似于TEM方程的假设下，证实了三维剩余平均环流与欧拉时间平均流和斯托克斯漂移之和一致，三维波动活动通量与波浪作用下物质表面的平均切向力一致。对三维波活动通量中的时均流切变等项给出了简单的物理意义。利用三维剩余平均环流导出了时间平均示踪剂输运方程。利用新公式对南半球平流层臭氧的三维输送进行了简单的案例研究。结果表明，科里奥利参数和强大的向极/向赤道斯托克斯漂移的产品也平衡的三维波活动通量的发散/收敛。
The transformed Eulerian-mean (TEM) equations are useful in examining how the generation and/or dissipation of atmospheric waves drives the mean meridional circulation. However, the TEM equations do not provide a three-dimensional view of the transport. Several previous studies extended the TEM equation system to three dimensions but usually under the quasi-geostrophic assumption, which excludes small-scale phenomena such as gravity waves. Miyahara recently derived three-dimensional wave activity flux and the corresponding residual circulation applicable to gravity waves. However, his formulation has two flaws. First, the three-dimensional residual mean circulation does not satisfy the continuity equation. Second, the Eulerian-mean flow appears in the advection terms and the residual circulation appears in the Coriolis force term of the zonal momentum equation, unlike in the TEM one. The present study developed theoretical formulae of a three-dimensional residual mean circulation and wave activity flux on the basis of primitive equations that overcome these flaws. It is confirmed that the three-dimensional residual mean circulation accords with the sum of the Eulerian time-mean flow and the Stokes drift and that the three-dimensional wave activity flux accords with the mean tangential forces across material surfaces corrugated by the waves under an assumption similar to the TEM equations. A simple physical meaning is given for the terms including the shear of time-mean flow in the three-dimensional wave activity flux. Moreover, the time mean tracer transport equation is derived using the three-dimensional residual mean circulation. A simple case study using the new formulae was made on the three-dimensional transport of stratospheric ozone in the Southern Hemisphere. It is shown that the product of the Coriolis parameter and the strong poleward/equatorward Stokes drifts also balances the divergence/convergence of the three-dimensional wave-activity flux.