Variations in Wave Energy and Amplitudes along the Energy Dispersion Paths of Nonstationary Barotropic Rossby Waves

Abstract

The variations in the wave energy and the amplitude along the energy dispersion paths of the barotropic Rossby waves in zonally symmetric basic flow are studied by solving the wave energy equation, which expresses that the wave energy variability is determined by the divergence of the group velocity and the energy budget from the basic flow. The results suggest that both the wave energy and the amplitude of a leading wave increase significantly in the propagating region that is located south of the jet axis and enclosed by a southern critical line and a northern turning latitude. The leading wave gains the barotropic energy from the basic flow by eddy activities. The amplitude continuously climbs up a peak at the turning latitude due to increasing wave energy and enlarging horizontal scale (shrinking total wavenumber). Both the wave energy and the amplitude eventually decrease when the trailing wave continuously approaches southward to the critical line. The trailing wave decays and its energy is continuously absorbed by the basic flow. Furthermore, both the wave energy and the amplitude oscillate with a limited range in the propagating region that is located near the jet axis and enclosed by two turning latitudes. Both the leading and trailing waves neither develop nor decay significantly. The jet works as a waveguide to allow the waves to propagate a long distance.

摘要

Rossby波能量传播路径在大气遥相关等领域已得到了广泛的应用。但求解波作用守恒方程(或波能方程)需要已知沿波能量频散路径的群速度散度。而计算沿波射线的群速度散度存在一定的困难性(主要是由于波射线路径以外的群速度不可知),这限制了波能方程求解。根据波能方程,波能量随波射线的变化由两部分组成,一部分是群速度的散度,表示波能量的聚集或发散;另一部分是和基本流的能量交换,表示波动获得或失去能量。本文根据前人研究的结果,创新性地提出了计算沿波射线群速度散度的计算方法,进而分析了波能量和振幅沿波射线的变化,由此讨论了正压非定常Rossby波的发展和衰减。结果表明:在急流轴以南由临界纬度和转向纬度包围的传播区域内,初始时刻的导波会在向北传播的过程中存在一个显著发展的阶段,相应的波能和振幅均显著增加,波能的增加主要来自于涡旋活动输送的来自基本流的正压能量;当波射线转向南传播时,存在一个阶段,波能量将不断被基本流所吸收,波振幅和波能量均会显著减小,波动将会衰减。在急流轴附近,存在由两个转向纬度包围的波导区域,在这一区域内,波射线会在两个转向纬度之间交替转向并向前传播,波能量和波振幅均不会显著变化,波动既不显著发展也不显著衰减,波能可以实现长距离传播。利用这一新方法,能够求解波能量和振幅的变化规律,从而为深入理解正压Rossby波的传播和发展提供了新的手段。