Non-Boussinesq gravity currents propagating on different bottom slopes

Experiments on the non-Boussinesq gravity currents generated from an instantaneous buoyancy source propagating on an inclined boundary in the slope angle range 0∘ ≤ θ ≤ 9∘ with relative density difference in the range of 0.05 ≤ ε ≤ 0.17 are reported, where ε = (ρ ₁-ρ ₀)/ρ ₀ , with ρ ₁ and ρ ₀ the densities of the heavy and light ambient fluids, respectively. We showed that a $3/2$ power-law, (xf+x₀)3/2= KM3/2 B₀'1/2 (t+tI0) , exists between the front location measured from the virtual origin, (xf+x₀) , and time, t , in the early deceleration phase for both the Boussinesq and non-Boussinesq cases, where KM is a measured empirical constant, B₀' is the total released buoyancy, and tI0 is the t -intercept. Our results show that KM not only increases as the relative density difference increases but also assumes its maximum value at θ ≈ 6∘ for sufficiently large relative density differences. In the late deceleration phase, the front location data deviate from the $3/2$ power-law and the flow patterns on θ =6∘,9∘ slopes are qualitatively different from those on θ =0∘,2∘ . In the late deceleration phase, we showed that viscous effects could become more important and another power-law, (xf+x₀)²= KV² B₀'2/3 A1/3₀ ν -1/3 (t+tV0) , applies for both the Boussinesq and non-Boussinesq cases, where KV is an empirical constant, A₀ is the initial volume of heavy fluid per unit width, ν is the kinematic viscosity of the fluids, and tV0 is the t -intercept. Our results also show that KV increases as the relative density difference increases and KV assumes its maximum value at θ ≈ 6∘ .