For steady generalized Beltrami flow, we have  and since it is also planar we have . Introduce the stream function
Integration of  gives . So, complete solution is possible if it satisfies all the following three equations
A special case is considered when the flow field has uniform vorticity . Wang (1991) gave the generalized solution as
assuming a linear function for . Substituting this into the vorticity equation and introducing the separation of variables  with the separating constant  results in
The solution obtained for different choices of  can be interpreted differently, for example,  represents a flow downstream a uniform grid,  represents a flow created by a stretching plate,  represents a flow into a corner,  represents an Asymptotic suction profile etc.