IAENG Transactions on Engineering Sciences

Shallow-water solutions for gravity currents in non-rectangular cross-area channels

T. Zemach

Department of Computer Science, Tel-Hai College, Tel-Hai, Israel

ABSTRACT: We consider the propagation of a high-Reynolds-number gravity current at the bottom of a horizontal channel along the horizontal coordinate x. The bottom and top of the channel are at $z=0,H,$, and the cross-section is given by the general $-f_1(z)\le y\le f_2(z)$ for 0 ≤ z ≤ H. We use a one-layer, Boussinesq, Shallow-Water (SW) formulation to solve the time-dependent motion produced by release from rest of a fixed volume of fluid from a lock. The dependent variables are the position of the horizontal interface, $h(x,t)$, and the speed (averaged over the area of the current), $u(x,t)$. The ...