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[SVC30-P11] Estimation of the lava temperature, speed and flow behavior from the lava tree mold configuration
Keywords:lava tree mold, lava flow, Fujivolcano
[Introduction]
At the foot of Mt. Fuji, many lava tree molds (Photos 1~4) remain after lava flows. Here, we will use the depth of the lava tree molds and the height of protrusions called Fudo to determine the temperature of the lava flow, the flow velocity and the non-dimensionless parameters (Reynolds number, Bingham number, Hedstrom number) that are indicators of flow behavior. The study target is the Higashiusuzuka-south lava flow, which extends approximately 4 km south from near the bottom side of the Higashiusuzuka scoria hill. This is a lava flow containing 51% silicic acid by weight, which flowed out around AD870 from a fissure in this area [1]. A recent survey revealed that 72 lava tree molds were found over a total length of about 4 km from near the spout to the lava flow end. The position, depth, and height of protrusions called Fudo were measured [2,3]. Figure 1 shows the distribution of the measured lava tree molds [2,3]. Based on these data[2,3], we conducted the study.
[Method for estimating lava flow temperature, flow velocity, and flow behavior]
Figure 2 shows a model of a cross-section of a lava tree mold. As lava erupts from the crater, a lava flow with a thickness of H flowing down a slope with an inclination angle of α hits standing trees, and then the eruption stops and the lava flow stops at a thickness of hB. The height of the protrusion called Fudo is H-hB. Figure 3 shows the estimated process. If the lava flow is Bingham fluid, the yield strength is calculated from the lava flow stop thickness hB:fB=hB(ρgsinα) (here, ρ=2.5g/cm3, g=980cm/sec2) . The viscosity coefficient can be obtained from the obtained temperature-dependent equation for the lava viscosity coefficient. From this, the flow velocity u = (H-hB)2[(ρgsinα)/2ηB] of the lava flowing down the slope can be determined. Then, the Reynolds number :Re=ρuH/ηB, Bingham number: B=fBH/ηBu, Hedstrom number: He=Re.B=ρfBuH2/ηB2 can be also estimated.
[Temperature dependent formula of lava yield strength and viscosity coefficient]
Here, we will use Ishihara et al.'s [4] temperature-dependent yield strength formula for the 1951 lava flow of Mt. Mihara, Izu Oshima:logfB = 13.67-0.0089θ (unit of fB is dyne/cm2), and Minakami [5]'s viscosity coefficient temperature dependence formula: logηB = 24.255-0.0181θ (unit of ηB is poise) was used.
[Estimation result]
Estimation was performed for four cases of tree mold: HUM-1, HUM-22, HUM-50, and HUM-69, including the most upstream tree mold to the most downstream tree mold. The location and the estimation conditions of each case are shown in Figure 1, The results are shown in Table 1. From upstream to downstream, the Fudo height decreases(1.1m to 0m) and the tree mold depth increases(1.1m to 3.0m). Correspondingly, the temperature and flow velocity decrease(1015deg to 996deg, 3.1cm/sec to 0cm/sec), then the viscosity coefficient and yield strength increase(7.6x105poise to1.7x106poise,4.3x104dyne/cm2 to 6.4x105dyne/cm2). The Reynolds number, Bingham number, and Hedstrom number are also shown in Table 1.
References:
[1]Akira Takada,Takahiro Yamamoto,Yoshihiro Ishizuka,Shun Nakano(2016):Explanatory Text of Geological Map of Fuji Volcano(Second Edition),Geological Survey of Japan,AIST.
[2] Tsutomu Honda,Takayoshi Katsumata,Masaru Hatanaka,Kazuyuki Kawamura (2020): P11 Yield strength,Viscosity,and Temperature of Higashiusuzuka-minami lava flow of Mt.Fuji. 2020 Fall Meeting of the
Volcanological Society of Japan
[3]Tsutomu Honda,Masaru Hatanaka,Takayoshi Katsumata,Kazuyuki Kawamura(2020):Yield strengthand flow speed estimation by tree molds of Higashiusuzuka-minami lava flow of Mt.Fuji,The Caving Journal,The Speleological Society of Japan,2020.8 No.69.p42-45
[4] Kazuhiro Ishihara,Masato Iguchi,Kosuke Kamo(1988): Reproduction of the l986 Izu-Oshima Lava Flows by a Numerical Calculation,Kazan,vol.33,Special issue,S64-S76
[5]Takeshi Minakami(1951):On the temperature and Viscosity of the Fresh Lava Extruded in the1951 Oo-shima Eruption, Bulletin of the Earthquake Research Institute, University of Tokyo, 29,487
At the foot of Mt. Fuji, many lava tree molds (Photos 1~4) remain after lava flows. Here, we will use the depth of the lava tree molds and the height of protrusions called Fudo to determine the temperature of the lava flow, the flow velocity and the non-dimensionless parameters (Reynolds number, Bingham number, Hedstrom number) that are indicators of flow behavior. The study target is the Higashiusuzuka-south lava flow, which extends approximately 4 km south from near the bottom side of the Higashiusuzuka scoria hill. This is a lava flow containing 51% silicic acid by weight, which flowed out around AD870 from a fissure in this area [1]. A recent survey revealed that 72 lava tree molds were found over a total length of about 4 km from near the spout to the lava flow end. The position, depth, and height of protrusions called Fudo were measured [2,3]. Figure 1 shows the distribution of the measured lava tree molds [2,3]. Based on these data[2,3], we conducted the study.
[Method for estimating lava flow temperature, flow velocity, and flow behavior]
Figure 2 shows a model of a cross-section of a lava tree mold. As lava erupts from the crater, a lava flow with a thickness of H flowing down a slope with an inclination angle of α hits standing trees, and then the eruption stops and the lava flow stops at a thickness of hB. The height of the protrusion called Fudo is H-hB. Figure 3 shows the estimated process. If the lava flow is Bingham fluid, the yield strength is calculated from the lava flow stop thickness hB:fB=hB(ρgsinα) (here, ρ=2.5g/cm3, g=980cm/sec2) . The viscosity coefficient can be obtained from the obtained temperature-dependent equation for the lava viscosity coefficient. From this, the flow velocity u = (H-hB)2[(ρgsinα)/2ηB] of the lava flowing down the slope can be determined. Then, the Reynolds number :Re=ρuH/ηB, Bingham number: B=fBH/ηBu, Hedstrom number: He=Re.B=ρfBuH2/ηB2 can be also estimated.
[Temperature dependent formula of lava yield strength and viscosity coefficient]
Here, we will use Ishihara et al.'s [4] temperature-dependent yield strength formula for the 1951 lava flow of Mt. Mihara, Izu Oshima:logfB = 13.67-0.0089θ (unit of fB is dyne/cm2), and Minakami [5]'s viscosity coefficient temperature dependence formula: logηB = 24.255-0.0181θ (unit of ηB is poise) was used.
[Estimation result]
Estimation was performed for four cases of tree mold: HUM-1, HUM-22, HUM-50, and HUM-69, including the most upstream tree mold to the most downstream tree mold. The location and the estimation conditions of each case are shown in Figure 1, The results are shown in Table 1. From upstream to downstream, the Fudo height decreases(1.1m to 0m) and the tree mold depth increases(1.1m to 3.0m). Correspondingly, the temperature and flow velocity decrease(1015deg to 996deg, 3.1cm/sec to 0cm/sec), then the viscosity coefficient and yield strength increase(7.6x105poise to1.7x106poise,4.3x104dyne/cm2 to 6.4x105dyne/cm2). The Reynolds number, Bingham number, and Hedstrom number are also shown in Table 1.
References:
[1]Akira Takada,Takahiro Yamamoto,Yoshihiro Ishizuka,Shun Nakano(2016):Explanatory Text of Geological Map of Fuji Volcano(Second Edition),Geological Survey of Japan,AIST.
[2] Tsutomu Honda,Takayoshi Katsumata,Masaru Hatanaka,Kazuyuki Kawamura (2020): P11 Yield strength,Viscosity,and Temperature of Higashiusuzuka-minami lava flow of Mt.Fuji. 2020 Fall Meeting of the
Volcanological Society of Japan
[3]Tsutomu Honda,Masaru Hatanaka,Takayoshi Katsumata,Kazuyuki Kawamura(2020):Yield strengthand flow speed estimation by tree molds of Higashiusuzuka-minami lava flow of Mt.Fuji,The Caving Journal,The Speleological Society of Japan,2020.8 No.69.p42-45
[4] Kazuhiro Ishihara,Masato Iguchi,Kosuke Kamo(1988): Reproduction of the l986 Izu-Oshima Lava Flows by a Numerical Calculation,Kazan,vol.33,Special issue,S64-S76
[5]Takeshi Minakami(1951):On the temperature and Viscosity of the Fresh Lava Extruded in the1951 Oo-shima Eruption, Bulletin of the Earthquake Research Institute, University of Tokyo, 29,487