Laminar and Turbulent Lava Flow in Sheets, Channels, and Tubes: Estimating Terrestrial and Planetary Lava Flow Rates EP23F-2383 Susan E. H. Sakimoto 1,2 and Tracy K. P. Gregg 1 1 Department of Geology, University at Buffalo, Buffalo, NY 2 Space Science Institute, Boulder, CO susansakimoto@gmail.com or tgregg@buffalo.edu Planetary Approach: Compute or predict basic flow properties from lava flow length and width. Terrestrial Approach: Compute or predict lava flow length and width from basic flow properties. To date, actively flowing lava has only been observed on Earth and on Jupiter’s moon Io. This lack of observation means that for the vast majority of volcanic systems in the Solar System, solidified lava-flow morphologies are used to infer important information about eruption and emplacement parameters. These include: lava supply rate, lava composition, lava rheology, and determination of laminar or turbulent emplacement regimes. Commonly used models that relate simple lava flow morphologic properties (e.g., width, thickness, length) to emplacement characteristics are based on assumptions that are readily misinterpreted. For example, the simplifying assumption of fully turbulent lava flow allows for a thermally mixed flow interior, but ignores the lava properties that naturally work to suppress full turbulence (such as thermal boundary layers encasing active lava flows, and a temperature-dependent lava rheology). However, full turbulence in silicate lava flows erupted into environments that have temperatures lower than the lava solidification temperature requires a rare combination of characteristics. We model Bingham Plastic, Newtonian, and Herschel-Bulkley fluids in rectangular channels, tubes, and sheets with computational fluid dynamics (COMSOL) software to obtain flow solutions and general flow rate equations and compare them to field measurements of volcanic velocity and flow rates. We present these as more realistic alternatives to older simpler rate-from-morphology models. We find that several lava rheology properties work together to delay the onset of turbulence as compared to isothermal Newtonian materials, and that while turbulent lavas flows certainly exist, they are not as prevalent as the published literature might indicate. Results obtained from models that assume full turbulence in silicate flows on the terrestrial planets should therefore be interpreted cautiously. Abstract Image Credit: USGS, July 2, 2018 Fissure 8 Lava Channel, Kilauea Volcano, HI. Analytic Flow Rate Models Discussion and Conclusions • The Hulme and Jeffries approximation approaches for estimating planetary flow properties should be retired, since they are demonstrably unreliable, and we have vastly improved analytic AND computational approaches that yield more tightly constrained and consistent results. • We do not yet adequately understand the effects of temperature-dependent rheology, composition, and ambient conditions on terrestrial or planetary flows. So: —Inferring composition variations from flow morphology is fraught with pitfalls —Inferring laminar or turbulent emplacement from flow morphology and multiple simplifying assumptions has significant potential for incorrect results. • With current computational tools, we can construct semi-empirical relationships as well as self- contained model applications that are specific to flow conditions and planetary conditions —...increasing our understanding of planetary flow properties AND general lava flow processes under different ambient conditions.. Model Approaches GEOMETRY FLOW REGIME RHEOLOGY THERMAL COUPLING Exporting Models to Planetary Flows Shear Rate Newtonian Shear Thinning (i.e. Power Law) Hershel-Bulkeley Bingham Plastic Shear Thickening w/ Yield Stress Shear Thickening Rheology Definitions or dv/dy or rate of strain LESS COMPLEX MORE COMPLEX Tube Flow Sheet Flow Laminar Turbulent Newtonian Shear Rate Hershel-Bulkeley Shear Rate Flow Velocity Temperature X Independent Solutions Flow Velocity Temperature Partial Rheology temperature dependence Flow Velocity Temperature All rheology parameters temperature dependent Common Approach: For: Observed Flow Dimensions Model: Coupled Rheology and Flow Rate On Earth, rheology is often further constrained with geochemistry or geothermometry Hulme model: (Isothermal laminar Bingham Approximation) Jeffries Equation: (Isothermal laminar Newtonian Approximation) Isothermal laminar Bingham Flow Examples Blair, D. M. , L. Chappaz, R. Sood, C. Milbury, A. Bobet, H.J. Melosh, K. C. Howell, A. M. Freed, (2017), The structural stability of lunar lava tubes, Icarus, 282, 47-55, 10.1016/j.icarus.2016.10.008. Bird, R.B., R.C. Armstrong, and O. Hassager, (1987) Dynamics of Polymeric Liquids, 649 pp., John Wiley, NY. Bird, R.B., G.C. Dai, and B.J. Yarusso, (1983) The rheology and flow of viscoplastic materials, Reviews in Chemical Engineering, 1 (1), 1-70. Bird, R.B., W.E. Stewart, and E.N. Lightfoot, (1960) Transport Phenomena, 780 pp., John Wiley and Sons, NY. Bruno, B.C., S.M. Baloga, and J. Taylor, (1996) Modeling gravity-driven flows on an inclined plane, Journal of Geophysical Research, 101 (B5), 11565-11577. Burger, J., Haldenwang, R., & Alderman, N. (2015). Laminar and Turbulent Flow of Non-Newtonian Fluids in Open Channels for Different Cross-Sectional Shapes. J. of Hydraulic Engineering, 141(4), DOI:10.1061/(ASCE)HY.1943-7900.0000968 Carr, M.H., R. Greeley, K.R. Blasius, J.E. Guest, and J.B. Murray, (1977) Some Martian volcanic features as viewed from the Viking Orbiters, Journal of Geophysical Research, 82, 3985-4015. Cattermole, P., (1987) Sequence, rheological properties, and effusion rates of volcanic flows at Alba Patera, Mars, Journal of Geophysical Research, 92, E553-E560. COMSOL Multiphysics® v. 5.4a. (2018 release) www.comsol.com COMSOL AB, Stockholm, Sweden. Deane, A., S. Sakimoto, and E. Ronquist (1997), Spectral element simulations in Earth and Space Sciences., Int. Conf. on HPC, Dec 18-21, 1997, Bangalore, India Dragoni, M., M. Bonafede, and E. Boschi, (1986) Downslope flow models of a Bingham liquid: implications for lava flows, Journal of Volcanology and Geothermal Research, 30, 305-325. Dragoni, M., A. Piombo, and A. Tallarico, (1995), A model forthe formation of lava tubes by roofing overof a channel, J. Geophys. Res., 100(B5), 8435-8447, 10.1029/94JB03263. Dragoni, M., F. D’Onza, A. Tallarico, (2002), Temperature distribution inside and around a lava tube, J. Volc. Geotherm. Res., 115, 43-51, 10.1016/S0377-0273(01)00308-0. Greeley, R., (1971), Observations of actively forming lava tubes and associated structures, Hawaii, NASA Technical Memorandum X-62,014. Gregg, T. K. P. (2017) Patterns and Processes: Subaerial lava flow morphologies: A review, J. Volc. Geotherm. Res., 342, 3-12, 10.1016/j.jvolgeores.2017.04.022. Gupta, R.C., (1995) Developing Bingham fluid flow in a channel, Mathematical Computer Modeling, 21 (8), 21-28. Harris, A. J. L., (2013), Lava Flows, Chapter 5, in Modeling Volcanic Processes: The Physics and Mathematics of Volcanism, Cambridge University Press, 978-0-521-89543-9. Hulme, G., (1974) The interpretation of lava flow morphology, Geophys. J. R. Astr. Soc., 39, 361-383. Hulme, G., (1976) The determination of the rheological properties and effusion rate on an Olympus Mons Lava, Icarus, 27, 207-213. Hulme, G., and G. Fielder, Effusion rates and rheology of lunar lavas, Philosophical Transactions of the Royal Society of London A, 285, 227-234, 1977. Jeffries, H. (1925) The flow of water in an inclined channel of rectangular section. Phil. Magazine, 49, 793-807. Kauahikaua, J., K. V. Cashman, T. N. Mattox, C. C. Heliker, K. Hon, M. T. Mangan, C. R. Thornber (1998) Observations on basaltic lava streams in tubes from Kilauea Volcano, island of Hawaii, J. Geophys. Res. 103(B11), 27303-27323, 10.1029/97JB03576. Keszthelyi, L., (1995) A preliminary thermal budget for lava tubes on the Earth and planets, J. Geophys. Res., I00, 20411-20420, 10.1029/95JB01965. Lopes-Gautier, R. Extraterrestrial lava flows, in Active Lavas: Monitoring and Modelling, edited by C.J. Kilburn, and G. Luongo, pp. 107-144, UCL Press, London, 1993. Moore, H.J., D.W.G. Arthur, and G.G. Schaber, Yield Strengths of flows on the Earth, Mars, and Moon, Proceedings of the LPSC 9th, 3351-3378, 1978. Murty, V.D., (1993) On Nonisothermal flows of Bingham Plastics, Chemical Engineering Communications, 126, 127-140. Piau, J.M., (1996) Flow of a yield stress fluid in a long domain. Application to fluid on an inclined plane, Journal of Rheology, 40 (4), 711-723. Sakimoto, S. E. H., and T. K. P. Gregg (2001), Channeled flow: Analytic solutions, laboratory experiments, and applications to lava flows, J. Geophys. Res., 106(B5), 8629– 8644, 10.1029/2006JE002803. Sakimoto, S. E. H, J. Crisp, S.M. Baloga, Eruption constraints on tube-fed planetary lava flows, J. Geophys. Res., 102 (1997), pp. 6567-6613, 10.1029/97JE00069. Sakimoto, S. E. H., and M. T. Zuber, (1997), Flow and convective cooling in lava tubes, J. Geophys. Res., 103(B11), 27465-27487, 10.1029/97JB03108. Sehlke, A., A. Whittington, B. Robert, A. Harris, L.Gurioli, E. Medard, (2014), Pahoehoe to aa transition of Hawaiian lavas: an experimental study, Bull. Volcanol. 76:876 10.1007/s00445-014-0876-9. Shaw, H.R., (1969) Rheology of basalt in the melting range, Journal of Petrology, 10, 510-535. Skelland, A.H.P., (1967) Non-Newtonian Flow and Heat Transfer, 469 pp., Wiley, New York. Self, S. Th. Thordarson, L. Keszthelyi, G P. L. Walker, K. Hon, M. T. Murphy, P. Long, and S. Finnemore, (1996) A new model for the emplacment of Columbia Riverbasalts as large, inflated pahoehoe lava flow fields, Geophys. Res. Lett. 23(19), 2689-2692, 0094-8534/96/96GL-02450. Tallarico, A. and M. Dragoni, (1999) Viscous Newtonian laminar flow in a rectangular channel: application to Etna lava flows, Bulletin of Volcanology, 61, Issue 1/2, pp 40-47. White, F. M., (2006) Viscous Fluid Flow, 3 rd ed., McGraw-Hill, 629p. 0-07-240231-8. Zimbelman, J.R., (1985) Estimates of rheologic properties of flows on the Martian volcano Ascraeus Mons., Journal of Geophysical Research, 90 (LPSC 16), D157-D162. Zimbelman, J.R., (1998) Emplacement of long lava flows on planetary surfaces, Journal of Geophysical Research, 103 (B11), 27503-27516. u= flow velocity h = flow depth g = acceleration of gravity rho = density B = geometry parameter n = fluid viscosity This approximation (Jeffries, 1925) should be replaced with the appropriate exact solution. See, for example, White (2006). Y B = Bingham yield stress rho = flow density g = acceleration of gravity W L = Levee width theta = slope This approximation (e.g. Hulme, 1976) relies on problematic assumptions and should be replaced with an exact or empirical solution (e.g. Skelland 1967, Deane and Sakimoto, 1997; Burger et al. 2015; and others). Numerous exact and empirical solutions: Skelland, 1967, circular tube, parallel plates Burger et al (2015), and many others: rectangular channel Deane and Sakimoto (1997) Parabolic Channel ...etc... • Planetary volcanology approach inverts the terrestrial approach: - Planetary ... often predicting flow properties from flow dimensions and shape rather than flow dimensions from flow properties . • Planetary flows do not have geochemistry or geothermometry constraints that may be available for terrestrial flows. Ambient conditions must be considered. • Computational approaches modeling flows with changed ambient conditions for planetary flows are expected to yield improved results compared to exporting vintage terrestrial approximations. Computational approaches can yield empirical equations appropriate for specific model/planet conditions. • parabolic velocity profile • expected turbulence transition • more flow in the boundary layers • slower center velocity • delayed turbulence transition • less boundary layer flow • faster center velocity • delayed turbulence transition • substantial fast center plug • thin boundary layer • delayed turbulence transition ESSOAr | https://doi.org/10.1002/essoar.10500344.1 | CC_BY_NC_ND_4.0 | First posted online: Wed, 9 Jan 2019 09:48:40 | This content has not been peer reviewed.