Fully planarized of Pekeris, ACCAD and Shkollar flow

Pekeris, Accad and Shkollar (PAS) dynamo (Pekeris et al. [7]) is one of the earliest successful kinematic dynamos. PAS dynamo has convergent solution at relatively low magnetic Reynolds number. Bachtiar, Ivers and James (BIJ) (Bachtiar et al. [2]) tried to planarized the PAS flow in order to produce a planar velocity dynamo. BIJ claim that it is impossible to planarize PAS flow using their formula. In this paper, we discuss why PAS flow cannot be planarized in detail. We also propose a modified PAS flow so that it can be planarized and still have a similar structure. We believe that our results are important for future works.