Experiments on gravity currents propagating on unbounded uniform slopes

Abstract

Gravity currents propagating on $12^\circ$, $9^\circ$, $6^\circ$, $3^\circ$ unbounded uniform slopes and on an unbounded horizontal boundary are reported. Results show that there are two stages of the deceleration phase. In the early stage of the deceleration phase, the front location history follows ${(x_f+x_0)}^2 = {(K_I B)}^{1/2} (t+t_{I})$, where $(x_f+x_0)$ is the front location measured from the virtual origin, $K_I$ an experimental constant, B the total buoyancy, t time and $t_I$ the t-intercept. In the late stage of the deceleration phase for the gravity currents on $12^\circ$, $9^\circ$, $6^\circ$ unbounded uniform slopes, the front location history follows ${(x_f+x_0)}^{8/3} = K_{VS} {{B}^{2/3} V^{2/9}_0 }{\nu }^{-1/3} ({t+t_{VS}})$, where $K_{VS}$ is an experimental constant, $V_0$ the initial volume of heavy fluid, $\nu$ the kinematic viscosity and $t_{VS}$ the t-intercept. In the late stage of the deceleration phase for the gravity currents on a $3^\circ$ unbounded uniform slope and on an unbounded horizontal boundary, the front location history follows ${(x_f+x_0)}^{4} = K_{VM} {{B}^{2/3} V^{2/3}_0 }{\nu }^{-1/3} ({t+t_{VM}})$, where $K_{VM}$ is an experimental constant and $t_{VM}$ the t-intercept. Two qualitatively different flow morphologies are identified in the late stage of the deceleration phase. For the gravity currents on $12^\circ$, $9^\circ$, $6^\circ$ unbounded uniform slopes, an ‘active’ head separates from the body of the current. For the gravity currents on a $3^\circ$ unbounded uniform slope and on an unbounded horizontal boundary, the gravity currents maintain an integrated shape throughout the motion. Results indicate two possible routes to the final stage of the gravity currents on unbounded uniform slopes.