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How are active lava flows similar to fluvial geomorphology? You can search youtube for these dramatic videos of lava flows, and they all seem to look very similar to streams or rivers. I know that the major difference is laminar flow vs the sometimes turbulent flow of water. Is there any literature comparing stream models to lava flows?

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The similarities pretty much end at the fact that both water and lava flow downhill seeking the lowest possible level. As even the most fluid lavas flow somewhat slower than water because of their higher density and viscosity, their lower speed and in particular their viscosity makes them far less erosive of the terrain they flow over/through. In fact lava usually freezes to the surfaces it is in contact with so the channels that carry lava on the surface get narrower and shallower, their sides build up where the edges of the flow freeze and they slowly raise the ground they are flowing over rather than eroding it. Lava flows look more like river deltas than drainage basins but the mechanisms of deposition are very different. The closer model might be that of debris flows and the alluvial fans they create but instead of running out of slope and saturation and depositing it's load of material a lava flow runs out of heat.

There may be points of comparison between fluvial processes in the middle reaches of a river system and lava tubes but the study of lava tubes is pretty patchy, they're not the most accessible places on Earth.

I know of a lot of literature concerning interactions between lava flows and fluvial systems but not comparative studies, maybe someone else can help with that .

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In terms of rheology, there is a key difference between water and lava: water is a Newtonian fluid, lava isn't. In early volcanology days, there has been attempts to model lava as a Newtonian fluid (Nichols, 1939). This approach may be a good approximation in some cases (very fluid lavas, like pāhoehoe flows), but does not work for more viscous lavas ('a'ā and block flows, see Harris et al. (2017) for a review of these categories).

Hulme (1974) was the first to model lava as a Bingham plastic. In Bingham rheology, the shear rate still scales linearly with shear stress (like in Newtonian rheology), but you need to reach a minimum amount of stress (the "yield stress") before the flow starts. This rheology explains some key differences in terms of flow morphology, as stated by Hulme:

If lava were an ideal Newtonian liquid it would flow downhill and would continue to flow even after the supply at the vent had ceased until it ponded in a depression. Furthermore the flow would spread laterally until it was restricted by topography or until surface tension prevented spreading by which time it would be extremely thin. Observations show that lava does not behave like this. Commonly it comes to rest on a slope as soon as the supply of fresh lava ceases and many flow fronts are high and steep although unconfined by topographic features. It is clear that there is some process which limits the flow of lava, brings it to rest on slopes and prevents its lateral spreading.

In recent years, progress has been made to model lava as a multi-phase fluid: lava is indeed a suspension of bubble and/or crystals in a silicate melt, and these particles play a role on lava rheology. Finally, there is the case of silica-rich flows (dacite and rhyolite flows), which have very high viscosities ($10^8-10^{12}$ Pa s, compared to $10^3-10^6$ Pa s for basalts). These flows are so viscous that they advance very slowly (typically 1-100 meters per day). Hence their flow dynamics are very different from that of water. Unless you consider solid water: there are some similarities between these lava flows and the flow of glaciers, like the presence of ogives for instance (Thorarinsson, 1953).


References

Nichols (1939) Viscosity of Lava

Thorarinsson (1953) Ogives in Lava Streams

Hulme (1974) The Interpretation of Lava Flow Morphology

Harris et al. (2017) Pāhoehoe, ‘a‘ā, and block lava: an illustrated history of the nomenclature

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    $\begingroup$ If you want more details on some aspects of this answer, please feel free to ask. I have dozens of papers on this matter, so I feel like I barely scratched the surface of the topic. $\endgroup$ Sep 22 at 16:58

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