Transition from transient Theis wells to steady Thiem wells

Simple analytical calculations of groundwater flow around wells usually employ the Thiem well formula for steady calculations and the Theis formula for transient calculations. The superposition principle can be used with both formulas and even for combinations of both formulas. It is generally assumed that flow converges to a steady state when the boundary conditions remain constant for a long time. However, the heads in Theis's formula do not converge to steady heads for large times, although the (specific) discharges do converge to those of the steady Thiem well. This undesirable behaviour of the Theis solution can be compensated by means of a new function: the ring well. The ring well is a combination of Theis's well and Glover's well (solution for a transient well in a circular island). A second function, uniform recharge during a time interval, is needed to assure that the heads converge at a specific level. The functions also allow an analytical transition with Theis wells between any two steady states consisting of Thiem wells. The functions do not have a wide range of practical applications but they increase insight into the relationship between the two main functions in groundwater flow.