两种类型中尺度涡旋Rossby波的相速度及其物理机制

PHASE SPEEDS OF TWO KINDS OF MESO-SCALE VORTEX ROSSBY WAVE AND THEIR PHYSICAL MECHANISMS

本文使用正压浅水方程组以及纬向切变基流下二维中尺度横波型扰动的Bouss-inesq近似方程组,分析了这种沿着基本气流方向传播的中尺度扰动的波动传播物理过程。研究结果表明,中尺度涡旋Rossby波划分为两种类型。由于纬向基本气流的方向的二阶水平切变或者基本气流的垂直涡度在南北方向的变化(β*因子)所导致的涡旋Rossby波称之为第一类涡旋Rossby波(正压涡旋Rossby波),它产生的根本原因是β*因子的作用。这种第一类涡旋Rossby波相对于基本气流-U0是单向传播的,其传播方向则与β*因子的正负符号有关。基本气流在垂直方向上的风速切变对于中尺度横波型的扰动起着不稳定的作用。如果考虑基流的二次垂直切变时,可以得到第二类涡旋Rossby波(斜压涡旋Rossby波)的相速度表达式,第二类涡旋Rossby波产生的物理根源是基本流场的风速-U的二次垂直切变或者基本流场y方向的平均涡度在空间z方向上的不均匀性(亦即β**因子)。第二类涡旋Rossby波相对于基本气流-U0也是单向传播的,其相速度与纬向波数k有关,能量是频散的,在纬向x方向存在群速度。在基本流场的风速-U存在二次垂直切变时,横波型不稳定可能是混合的涡旋Rossby-重力波的不稳定;而当基本流场的风速-U仅仅存在线性切变,不存在二次垂直切变时,此时根本不存在涡旋Rossby波,横波型扰动的不稳定则仅仅是重力惯性波的不稳定。最后利用横波型扰动的总涡度守恒方程对第二类涡旋Rossby波形成的物理机制做出了解释。

In the context of a system of barotropic shallow-water equations and Boussinesq approximate equations for two-dimensional meso-scale transversal wave disturbance in zonally sheared base flow, study is performed of the physical process of the meso disturbance propagation along the flow,indicating that such vortex Rossby waves （VRW） are separated into two kinds. The first kind VRW （the barotropic VRW） is produced owing to the second-order horizontal shear in the flow or due to the meridional change in vertical vorticity of the flow,i, e. ,the effect of β＊ as its central cause. This kind VRW travels unidirectionally with respect to base flow ^-Uo, depending on the plus or minus sign of β＊. The vertical windspeed shear of the base flow causes the transversal disturbance to be unstable. And the consideration of a secondorder vertical shear of ^-U will lead to the expression for phase speed of VRW of second kind （the baroclinic VRW）. This kind VRW has its physical mechanism lying in the second-order vertical shear of wind speed ^-U in the base flow or inhomogeneity of y-axis mean vorticity in the z direction,i, e. , the effect of β＊＊. The second kind of VRW propagates unidirectionally with respect to ^-Uo ,with its phase speed related to zonal wavenumber,its energy is dispersive and group velocity occurs in the x direction. When mean windspeed ^-U in the base flow experiences a second-order shear in vertical, the instability of transversal disturbance is likely to be that of mixed VRW and gravity ,wave. When ^-U experiences linear shear with no second-order shear in vertical available, no VRW happens at all, so that in this case the instability of transversal disturbance is that of internal inertial gravity waves only. Finally,the equation of total vorticity conservation for transversal disturbance is used to explain the physical mechanism for generating VRW of second kind.