Unsteady Shallow Groundwater Flow Over a Curved Impermeable Boundary

The asymptotic method which produced the new Dressler equation for curved open channel hydraulic flow is employed here to obtain analogous equations for unsteady, two‐dimensional, free surface groundwater flow over an arbitrarily curved bed. The result is a pair of partial differential equations: the first linear, stemming from Darcy's Law, and the second nonlinear, expressing mass conservation. The hydraulic conductivity and porosity can be functions of position. The flow component above and parallel to the bed behaves as a vortex in the small with centrifugal acceleration but with no centrifugal term in the pressure. For the special case of a plane sloping bed our equations reduce to the Wooding‐Chapman extension of the Dupuit‐Forchheimer equations. Our two‐dimensional flow equations are generalized to a special case of a nonisotropic medium and to include the effect of a variable recharge rate. All the systems are parabolic, thus describing diffusion, and can be integrated numerically as readily as the simpler equations for plane beds.