ON GRAVITY CURRENTS OVER A POROUS FLOOR IN POWER-LAW CROSS-SECTION CHANNELS

The behavior of an inviscid gravity current which propagates over a horizontal porous floor in containers of power-law cross section (CS) is analysed by shallow-water theory. It is shown that the effect of the porous boundary can be incorporated by means of a parameter lambda which represents the ratio of the characteristic time of porous drainage to that of horizontal spread. The interesting cases correspond to small values of lambda; otherwise the current has drained before any significant propagation can occur. Typical solutions are presented for various values of the parameters and differences to the non-porous boundary currents are pointed out. The methodology is illustrated for flow in typical power-law CS containers f(z) = 0.5 + 0.5z(alpha) where alpha is positive constant.