A life-cycle of nonlinear baroclinic waves represented by a simple 3-D spectral model

In this study, a life-cycle experiment for baroclinic disturbances is carried out for Simmons and Hoskins’ 45° jet by integrating a three-dimensional spectral primitive equation model. The utility of the spectral representation in the vertical direction is examined for a fully nonlinear well-established phenomenon. The energy evolution and corresponding energy transformation are analyzed in the framework of the baroclinic-barotropic decomposition of atmospheric energy. According to the result, the initial perturbations of n = 6 grow exponentially drawing zonal baroclinic energy. This early evolution is reasonably described by linear baroclinic instability of the 45° jet. Both of baroclinic energy and barotropic energy of n = 6 increase simultaneously since the unstable mode maintains its consistent structure to grow. The energy flow is characterized as from zonal baroclinic energy via eddy baroclinic energy to eddy barotropic energy. These energy transformations are also synchronized since they are proportional to the eddy energy levels in the linear framework. When the waves reach the finite amplitude, the barotropic conversion increases, tranferring eddy barotropic energy toward zonal barotropic energy. It is shown by the result that the zonal barotropic energy increases when the waves decay, and the zonal jet is accelerated so that the structure becomes more barotropic. It is found by this study that the important baroclinic—barotropic interactions are coupled with baroclinic instability rather than the barotropic conversion. The results are consistent with previous studies. Therefore, we confirm also that the vertical spectral representation is applicable to simulate the nonlinear phenomenon.