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Experiments on gravity currents propagating on unbounded uniform slopes
Environmental Fluid Mechanics ( IF 2.2 ) Pub Date : 2020-07-29 , DOI: 10.1007/s10652-020-09758-2
Albert Dai , Yu-Lin Huang

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.



中文翻译:

重力流在无界均匀斜坡上传播的实验

报告了在\(12 ^ \ circ \)\(9 ^ \ circ \)\(6 ^ \ circ \)\(3 ^ \ circ \)无界均匀斜率和无界水平边界上传播的重力流。结果表明,减速阶段分为两个阶段。在减速阶段的早期,前端位置历史记录遵循\({(x_f + x_0)} ^ 2 = {(K_IB)} ^ {1/2}(t + t_ {I})\),其中\((x_f + x_0)\)是从虚拟原点测量的最前面的位置,\(K_I \)是一个实验常数,B是总浮力,t时间,而\(t_I \)t-截距。在\(12 ^ \ circ \)\(9 ^ \ circ \)\(6 ^ \ circ \)无界均匀斜率上的重力流减速阶段的后期,前位置历史遵循\( {{x_f + x_0)} ^ {8/3} = K_ {VS} {{B} ^ {2/3} V ^ {2/9} _0} {\ nu} ^ {-1/3}({ t + t_ {VS}})\),其中\(K_ {VS} \)是实验常数,\(V_0 \)是重流体的初始体积,\(\ nu \)运动粘度和\(t_ {VS} \)截距。在减速阶段的后期,重力电流为\(3 ^ \ circ \)无界均匀坡度和无界水平边界上,前位置历史遵循\({(x_f + x_0)} ^ {4} = K_ {VM} {{B} ^ {2/3} V ^ {2/3} _0} {\ nu} ^ {-1/3}({t + t_ {VM}})\),其中\(K_ {VM} \)是实验常数,而\(t_ {VM} \)t -截距。在减速阶段的后期识别出两种在质量上不同的流动形态。对于\(12 ^ \ circ \)\(9 ^ \ circ \)\(6 ^ \ circ \)无界均匀斜率上的重力流,“活动”的头部与电流的主体分开。对于\(3 ^ \ circ \)上的重力流无限制的均匀坡度和无限制的水平边界上,重力流在整个运动过程中保持整体形状。结果表明在无界的均匀斜坡上有两种可能的途径到达重力流的最终阶段。

更新日期:2020-07-29
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