Lava Delta Formation: Mathematical Modeling and Laboratory Experiments

IF 3.5 2区 地球科学 Q1 GEOSCIENCES, MULTIDISCIPLINARY
J. J. Taylor-West, N. J. Balmforth, A. J. Hogg
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Abstract

We analyze the dynamics of evolving lava-fed deltas through the use of shallow-layer mathematical models and analog laboratory experiments. Numerical and asymptotic solutions are calculated for the cases of planar and three-dimensional flows fed by a point source upstream of the shoreline. We consider several modes of delta formation: a reduction in the driving buoyancy force; an enhanced viscosity of the submerged material; and the production of a granular subaqueous platform, over which a subaerial current can propagate. These modes of delta formation result in different behaviors. Under a steady supply of fluid upstream, the buoyancy-driven case develops a solution with a steady subaerial delta and a subaqueous current which propagates at a constant speed, while the granular platform model extends the delta indefinitely. We determine a late-time power-law relation for the shoreline extent with time in this case. When the viscosity contrast is large, the model with an enhanced subaqueous viscosity is shown to mimic the initial dynamics of the granular platform model, but ultimately reaches a steady shoreline extent at sufficiently late times, as for the buoyancy-driven model. The distinct behaviors of these models are further illustrated through laboratory experiments, utilizing the gelling reaction of sodium alginate solution in the presence of calcium ions as a novel analog for the abrupt rheological changes that occur when lava makes contact with water. These experiments provide quantitative verification of the buoyancy-driven model in the absence of the reaction, and demonstrate the effects of a subaqueous platform qualitatively in its presence.

Abstract Image

熔岩三角洲的形成:数学建模与实验室实验
我们利用浅层数学模型和模拟实验室实验分析了熔岩馈入三角洲的演变动力学。我们计算了由海岸线上游点源注入的平面流和三维流的数值解和渐近解。我们考虑了三角洲形成的几种模式:驱动浮力减小;水下物质的粘度增强;产生一个颗粒状的水下平台,水下流可以在该平台上传播。这些三角洲形成模式导致了不同的行为。在上游流体稳定供应的情况下,浮力驱动的情况下会形成稳定的亚水下三角洲和以恒定速度传播的亚水流,而粒状平台模型则会无限延伸三角洲。在这种情况下,我们确定了海岸线范围与时间的晚期幂律关系。当粘度对比较大时,具有增强水下粘度的模型会模仿颗粒平台模型的初始动力学,但最终会在足够晚的时间达到稳定的海岸线范围,这与浮力驱动模型的情况相同。通过实验室实验,利用海藻酸钠溶液在钙离子存在下发生的胶凝反应,进一步说明了这些模型的不同行为。这些实验在没有反应的情况下对浮力驱动模型进行了定量验证,并在有反应的情况下定性地展示了水下平台的影响。
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来源期刊
Journal of Geophysical Research: Earth Surface
Journal of Geophysical Research: Earth Surface Earth and Planetary Sciences-Earth-Surface Processes
CiteScore
6.30
自引率
10.30%
发文量
162
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