We present a shallow, isothermal, Newtonian model for the transient interaction of lava flows with topography. Numerical integrations and simple mathematical approximations are deployed to quantify how topography controls lava thicknesses and flow speeds. Considering idealized topographic features, we show that modest depressions thicken and accelerate the flow—even far downstream—whilst mounds have the opposite effect. However, deep ponds of lava form in depressions of sufficient amplitude, which introduces a long timescale for lava to fill the depression and hence the accelerated downstream flow may never be attained. Relatively large mounds completely divert the lava, providing protected lava-free regions for homes and infrastructure. There can, however, be hazardous, deep, fast flow around the edges of the mound, owing to diversion. Additionally, we show that our model accurately predicts the lava-free region that has been observed in the eruption 35 kyr ago at Marcath Volcano, Nevada.

中文翻译：

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在地形上预测熔岩流中的安全区域

我们提出了一个浅层等温牛顿模型，用于熔岩流与地形的瞬态相互作用。采用数值积分和简单的数学近似来量化地形如何控制熔岩厚度和流动速度。考虑到理想化的地形特征，我们发现适度的洼地会变厚并加速流动——即使是在下游很远的地方——而土丘具有相反的效果。然而，在足够幅度的凹陷中形成深熔岩池，这为熔岩填充凹陷引入了很长的时间尺度，因此可能永远无法获得加速的下游流动。相对较大的土丘完全转移了熔岩，为家庭和基础设施提供了受保护的无熔岩区域。然而，由于转移，在土丘边缘可能存在危险的、深的、快速的流动。