Non-Boussinesq gravity currents propagating on different bottom slopes
Journal
Journal of Fluid Mechanics
Journal Volume
741
Pages
658-680
Date Issued
2014
Author(s)
Dai, A.
Abstract
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 = (ρ1 - ρ0)/ρ0, with ρ1 and ρ0 the densities of the heavy and light ambient fluids, respectively. We showed that a 3=2 power-law, (xf +x0) 3/2 + K3/2M B'01/2(t + t10), 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, B'0 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 = K2VB'02/3A1/30 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°. © Cambridge University Press 2014.
Type
journal article