Relationship between singular modes of blocking flow and high-frequency eddies

To investigate the maintenance mechanism of the blocking flow, we performed a numerical experiment using a barotropic spectral model on the sphere. The model is linearized about two types of realistic basic flows. One is a blocking flow near Alaska (blocking flow case) and the other is a zonal how in the North Pacific (zonal flow case). The model is integrated in time with prescribed high-frequency eddies which are generated in the Far East and propagate eastward along the northern flank of the jet stream. After several days of time integration, time mean vorticity flux divergence is calculated. Then, the resulting vorticity flux divergence field is used as the eddy vorticity forcing to compute the second-order flow induced by eddies. It is found that the induced second-order flow intensifies the blocking for the blocking flow case, and that this is not the case for the zonal flow case. To clarify the reason for the difference between the induced second-order flows, we carried out the singular value decomposition (SVD) of the matrix of the barotropic vorticity equation linearized about the basic flows. For the blocking how case, spatial distributions of the leading singular modes show blocking patterns which are similar to the blocking in the basic flow. It is found that these modes are effectively excited by the eddy vorticity forcing, and enhance the blocking in the basic flow. On the other hand, for the zonal flow case, leading singular modes do not show blocking patterns. These results indicate that blocking flows tend to have easily excited modes that can reinforce the block, and high-frequency eddies could maintain blocking by exciting these modes. The dependency of results of the experiment on the location of high-frequency eddies is also shown. It indicates the limitation of the model to investigate the high-frequency eddies feedback.