The effects of dispersion acting on gravity currents propagating through porous media are considered theoretically and experimentally. We exploit the large aspect ratio of these currents to formulate a depth-averaged model of the evolution of the mass and buoyancy. Dispersion, acting predominantly at the interface between the current and the ambient, is velocity dependent and acts to entrain fluid into the gravity current, in direct analogy to turbulent mixing. Here, we show that when the gravity current is fed by a constant buoyancy and mass flux the buoyancy of the current is self-similar and recovers the classical solution for gravity currents in porous media. In contrast, the profile and the depth-averaged concentration of the current evolve in a non-self-similar manner. The total volume of the current increases with time as $t^{1/3}$ due to this dispersive entrainment. We test our theoretical predictions using a suite of laboratory experiments in which the evolution of the concentration within the current was mapped using a dye-attenuation technique. These experimental results show good agreement with the early-time limits of our theoretical model, and in particular accurately predict the evolution of the depth-averaged concentration profile. These results suggest that mixing within porous media may be modelled using an effective dispersive entrainment, the magnitude of which may be set by the underlying structure of the porous medium.

中文翻译：

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多孔介质中重力流的分散夹带

从理论上和实验上考虑了色散对通过多孔介质传播的重力流的影响。我们利用这些电流的大纵横比来制定质量和浮力演变的深度平均模型。弥散主要作用在水流和环境之间的界面上，与速度有关，并起到将流体夹带到重力流中的作用，与湍流混合直接类比。在这里，我们表明当重力流由恒定的浮力和质量通量馈送时，流的浮力是自相似的，并且恢复了多孔介质中重力流的经典解。相比之下，电流的剖面和深度平均浓度以非自相似的方式演变。由于这种分散的夹带，电流的总体积随时间增加为 $t^{1/3}$。我们使用一组实验室实验来测试我们的理论预测，其中使用染料衰减技术绘制了电流中浓度的演变。这些实验结果与我们的理论模型的早期限制非常吻合，特别是准确预测了深度平均浓度剖面的演变。这些结果表明，可以使用有效的分散夹带来模拟多孔介质内的混合，其大小可以由多孔介质的底层结构设定。我们使用一组实验室实验来测试我们的理论预测，其中使用染料衰减技术绘制了电流中浓度的演变。这些实验结果与我们的理论模型的早期限制非常吻合，特别是准确预测了深度平均浓度剖面的演变。这些结果表明，可以使用有效的分散夹带来模拟多孔介质内的混合，其大小可以由多孔介质的底层结构设定。我们使用一组实验室实验来测试我们的理论预测，其中使用染料衰减技术绘制了电流中浓度的演变。这些实验结果与我们的理论模型的早期限制非常吻合，特别是准确预测了深度平均浓度剖面的演变。这些结果表明，可以使用有效的分散夹带来模拟多孔介质内的混合，其大小可以由多孔介质的底层结构设定。