两层正压流体涡旋中螺旋波的不稳定

THE SPIRAL WAVE INSTABILITY IN VORTEX OF TWO-LAYER BAROTROPIC FLUID

利用线性化的两层正压原始方程模型,对有水平和垂直切变基流的圆形涡旋中螺旋波的不稳定作了研究。结果表明,当基流失稳时,涡旋中不稳定扰动的厚度场、速度场在上、下两层都具有明显的螺旋结构,下层的螺旋结构要较上层复杂。基流垂直切变越大则越易失稳。失稳时上、下层扰动的配置接近反位相,故该螺旋波结构相应于斜压模。此时螺旋波上的扰动中心在切向是逆基流传播的,在径向则基本没有传播,而螺旋臂的整体运动缓慢。失稳的螺旋波其散度场要较涡度场明显,物理量的配置也大体符合重力惯性波的情况,故可认为其是重力惯性波的不稳定所致。本模型中该螺旋波的形态与实际热带气旋中的螺旋云(雨)带很相象。

In this paper, based on the linearized two-layer barotropic primitive equation model, the spiral wave instability is studied in a circular vortex with basic flow of horizontal and vertical shear. It is shown that the unstable disturbance fields of thickness, divergence and vorticity have obvious spiral structure in the top and low layers of the vortex, when the basic flow is destabilized. The spiral structure of thickness fields is the most obvious. The spiral structure in the low layer is more complex than in the top layer. In the model, the greater the vertical shear of basic flow is, the easier the destabilization of basic flow is. The phase of unstable disturbance in the top layer is almost inverse to that in the low layer, so the structure of the spiral wave is corresponding to baroclinic model. The propagation of disturbance centers in the spiral wave in the tangential direction is opposite to the basic flow and the disturbance centers almost do not propagate in the radial direction. The whole movement of the spiral arms is slower. It is obvious that the magnitude of divergence field is greater than that of vorticity and the allocation of these fields agree with the inertia-gravitational wave, so the occurrence of the spiral wave can be due to the instability of the inertia-gravitational wave. The shape of the spiral wave in the model is similar to the spiral cloud (rain) band in real tropical hurricanes.