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The resonance of topographically forced waves is studied using a quasi-geostrophic spectral model on the rotating sphere. The use of complete spectral expansions without truncation leads to the exact solutions of the nonlinear coupling equations by means of the random phase approximation and the projection operator techniques under the dissipation-vanishing limit. The energy transfer process between topographically forced wave ensemble and zonal mean flow is described.It is shown that the dynamical system loses stability and further bifurcation takes place when the topographic force has occurred. There are two sorts of equilibrium point in the resonance system. The unstable equilibrium is an isolated equilibrium point and, therefore, is hardly observed to occur. The stable equilibrium is an attractor set which is related to the phenomenon of blocking. 相似文献
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本文从球面非线性位涡方程出发,应用多重尺度法导出了三波共振的耦合方程.求得非线性耦合方程的通解可以用椭圆函数表示,因而扰动的能量及其变化是有界的.同时,还探讨了共振三波组的守恒律以及共振激发过程中能量的转换.指出在一定的初始条件下,非线性相互作用是可逆的;且就纬向波数谱而言,大波数模态的初始扰动能量在共振激发过程中可以完全转化为较小波数模态的能量.并揭示了旋转大气中非线性行星波动的孤立子性质. 相似文献
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本文应用多重尺度法研究了在旋转球面上正压大气中有限振幅扰动波包与纬向基本气流的非线性共振相互作用。首先,导出了同时包含色散效应和耗散效应的三波共振非线性耦合方程。然后,在零耗散极限和无规相位近似下,求得了不同模态波包的非线性共振耦合方程。并着重讨论了有限振幅扰动波包与纬向基本气流之间的能量输运过程。结果表明,在旋转球面上正压大气中的有限振幅扰动波包通过非线性共振相互作用能够激发出纬向基本气流,而且其能量最终都要输运给纬向基本气流,直至大气运动成为完全的带状环流为止。从而阐明了非线性共振相互作用是大气旋转适应过程的重要物理机制。 相似文献
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A barotropic spectral model is used to study the planetary-scale motions of an atmosphere whose wave ensemble modes are externally driven. Pertubations are induced by a barotropic analogue of thermal driving and by Ekman friction, bottom topography, and the vanished internal dissipation. The use of complete spectral expansions without truncation leads to that the nonlinear coupling equations between the low-index mode and the high-index mode are obtained by means of the random phase approximation and the projection operator techniques. The nonlinear coupling equations are entirely equivalent to the Volterra systems in ecology.In the phase-plane, the orbits of the nonlinear coupling equations are the family of closed curves, indicating a bound, and periodic motion. The qualitative behaviors of low-index and high-index modes as functions of time picture the motion of atmospheric flows, with exchanges of energy between the low-index mode and the high-index mode by nonlinear resonance interaction. It is sug 相似文献
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