Let the length scales be normalized with the plate length  and the velocity scale by the free-stream velocity ; then the only parameter in the problem is the Reynolds number . Let the origin  of the coordinate system be located at the trailing edge of the plate. Further let  be the non-dimensional velocity components,  be the non-dimensional pressure field and  be the non-dimensional stream function such that  and . For shortness of notation, let us introduce the small parameter . The coordinate for horizontal interaction and for the three decks can then be defined by
As  (or ), the solution should approach the asymptotic behaviour of the Blasius solution, which is given by
where  is the Blasisus function which satisfies  subjected to . As  (or ), the solution should approach the asymptotic behaviour of the Goldsteins near wake, which is given by
where  and . The Goldstein's inner wake solution is not needed here.