Variable coefficient nonlinear systems,the Korteweg de Vries (KdV),the modified KdV (mKdV) and the nonlinear Schro¨dinger (NLS) type equations,are derived from the nonlinear inviscid barotropic nondivergent vorticity equation in a beta-plane by means of the multi-scale expansion method in two different ways,with and without the so-called yaverage trick.The non-auto-B¨acklund transformations are found to transform the derived variable coefficient equations to the corresponding standard KdV,mKdV and NLS equations.Thus,many possible exact solutions can be obtained by taking advantage of the known solutions of these standard equations.Further,many approximate solutions of the original model are ready to be yielded which might be applied to explain some real atmospheric phenomena,such as atmospheric blocking episodes.
Using monthly mean atmospheric re- analysis data and oceanic assimilation data product,the winter ocean-atmosphere interaction in middle and high latitude in Northwest Pacific was studied. Key regions were chosen to study the variations of Aleutian Low,the 500hPa westerly,the meriodional sea surface temperature (SST) gradient with three indices defined as Aleutian Low index,zonal index and meridional SST gradient between Kuroshio- influenced region and Oyashio-influenced region. The results show that when there is a deeper Aleu- tian Low accompanied by a stronger northerly wind in the western part of the Aleutian Low,the subpolar gyre of North Pacific is strengthened,the SST in the Oyashio-influenced region is decreased and the me- ridional SST gradient between Kuroshio-influ- enced region and Oyashio-influenced region is increased,which,in turn,will enhance the westerly jet in the upper troposphere due to thermal-wind relation. The strengthened westerly jet makes a favorable condi- tion for the deeper Aleutian Low over North Pacific beneath the left part of the jet exit region. Conse- quently,a positive feedback forms there.
