High-Reynolds-number gravity currents over a porous boundary: shallow-water solutions and box-model approximations

The behaviour of an inviscid, lock-released gravity current which propagate s over a horizontal porous boundary in either a rectangular or an axisymmet ric geometry is analysed by both shallow-water theory and 'box-model' appro ximations. It is shown that the effect of the porous boundary can be incorp orated by means of a parameter lambda which represents the ratio of the cha racteristic time of porous drainage, tau, to that of horizontal spread, x(0 )/(g'h(0))(1/2), where x(0) and h(0) are the length and height of the fluid initially behind the lock and g' is the reduced gravity. The value of tau is assumed to be known for the fluid-boundary combination under simulation. The interesting cases correspond to small values of lambda; otherwise the current has drained before any significant propagation can occur. Typical s olutions are presented for various values of the parameters, and difference s to the classical current (over a non-porous boundary) are pointed out. Th e results are consistent with the experiments in a rectangular tank reporte d by Thomas, Marine & Linden (1998), but a detailed verification, in partic ular for the axisymmetric geometry case, requires additional experimental d ata.