The unsteady growth of a viscous fluid plume beneath a rigid upper lid is investigated. Two-dimensional (planar) flow is assumed, through a fissure in the horizontal lower boundary. Initially, the fluid exiting the bottom is assumed to form a semi-circular region, but rises as time progresses, and spreads across the upper boundary. The problem is modelled using Boussinesq theory, and solved using a time-dependent spectral method. These numerical solutions are also compared with the results of a simpler inviscid asymptotic solution. Results are indicated for different input fluid speeds and fissure widths.