10:45 AM - 12:15 PM
[SVC29-P02] Application of a one-dimensional volcanic plume model to submarine volcanoes
Keywords:entrainment coefficient, 1D steady plume model, submarine volcanoes
Introduction
Many studies have worked on conduit flow and atmospheric plume modeling in volcanology and quantified the effects of external water on eruption dynamics. However, there are few models of volcanic flow in seawater, assuming shallow-water explosive eruptions. Here, we apply the 1D steady plume model in the air (Mastin, 2007) to investigate the eruption dynamics through the water layer. Recently, Rowell et al. (2022) used a similar approach in their joint model of a volcanic flow through the conduit, the sea, and the atmosphere. However, their main target was the SO2 transportation to the stratosphere, and their discussion on the plume in the sea was limited. Besides, for the entrainment coefficient, which is the essential factor of the plume dynamics, they followed Carrazzo et al. (2008), who assume similar densities between the plume and ambient fluids. The applicability of the model is yet to be validated. In this study, we explored the dependence of the model solutions on the entrainment coefficient.
Method
Mastin (2007) calculated the plume shape and height by integrating the conservation equations of mass, momentum, and enthalpy with the atmospheric conditions at each altitude. We replaced the atmospheric air with seawater. The calculation was performed from the bottom to the surface of the sea.
The input parameters were the radius, velocity, temperature, density, specific heat, and gas mass fraction of the input flow at the bottom, which are the same as Mastin (2007), and the water depth and entrainment coefficient (EC) in the water layer. We changed EC and the vent radius (Rv) with the other parameters fixed. Note that the initial parameters represent the flow conditions after the free expansion of the chocked flow at the conduit exit.
Results
First, we fixed Rv at 15 m and changed EC. In the case of EC=0.09, as widely used in the 1D plume model, the plume radius increased rapidly right above the vent and soon decreased due to the vapor condensation. The plume became a mixture of pyroclasts and hot water, having a larger density than seawater, which kept rising due to the initial momentum. The water mass fraction reached 91%, and the temperature was 36℃ on the sea surface. With EC=0.001, the plume maintained its vapor and ascended as a low-density, high-velocity flow. Its shape was cylindrical, balancing the shrinkage by condensation and the expansion by decompression. The mass fraction of water was about half at the surface.
Next, we fixed EC at 0.03 and changed Rv. When Rv=75 m, the plume sustained the low density and initial velocity to the surface. The radius gradually increased due to the evaporation of the entrained seawater up to 50 m above the vent. Then, it shrank slightly due to the condensation, and finally, the gas expansion overcame the condensation effect. For Rv=25 m, the plume changed into a mixture of hot water and solid particles but expanded due to re-boiling near the surface. In the case of Rv=15 m, the plume entrained a significant amount of seawater and flowed up relatively slowly. The hot (70℃) water plume spouted out on the surface at 39 m/s.
Discussion and future works
The plume in the sea changed its radius drastically with rising. The reason is that it entrains the external fluid with high density and low enthalpy, which undergoes evaporation, condensation, and re-boiling. Also, the pressure gradient in the sea is much larger than that in the atmosphere.
We showed that the plume's shape depends on EC and Rv (or mass discharge rate). If its volume and shape change rapidly, the plume may generate oceanic waves, including tsunamis. In further work, we will develop a model for an adequate entrainment coefficient for the seawater and explore the dependence on each parameter (vent radius, entrainment coefficient, water depth, and mass flux). Also, the stability of the 1D steady flow should be examined.
Many studies have worked on conduit flow and atmospheric plume modeling in volcanology and quantified the effects of external water on eruption dynamics. However, there are few models of volcanic flow in seawater, assuming shallow-water explosive eruptions. Here, we apply the 1D steady plume model in the air (Mastin, 2007) to investigate the eruption dynamics through the water layer. Recently, Rowell et al. (2022) used a similar approach in their joint model of a volcanic flow through the conduit, the sea, and the atmosphere. However, their main target was the SO2 transportation to the stratosphere, and their discussion on the plume in the sea was limited. Besides, for the entrainment coefficient, which is the essential factor of the plume dynamics, they followed Carrazzo et al. (2008), who assume similar densities between the plume and ambient fluids. The applicability of the model is yet to be validated. In this study, we explored the dependence of the model solutions on the entrainment coefficient.
Method
Mastin (2007) calculated the plume shape and height by integrating the conservation equations of mass, momentum, and enthalpy with the atmospheric conditions at each altitude. We replaced the atmospheric air with seawater. The calculation was performed from the bottom to the surface of the sea.
The input parameters were the radius, velocity, temperature, density, specific heat, and gas mass fraction of the input flow at the bottom, which are the same as Mastin (2007), and the water depth and entrainment coefficient (EC) in the water layer. We changed EC and the vent radius (Rv) with the other parameters fixed. Note that the initial parameters represent the flow conditions after the free expansion of the chocked flow at the conduit exit.
Results
First, we fixed Rv at 15 m and changed EC. In the case of EC=0.09, as widely used in the 1D plume model, the plume radius increased rapidly right above the vent and soon decreased due to the vapor condensation. The plume became a mixture of pyroclasts and hot water, having a larger density than seawater, which kept rising due to the initial momentum. The water mass fraction reached 91%, and the temperature was 36℃ on the sea surface. With EC=0.001, the plume maintained its vapor and ascended as a low-density, high-velocity flow. Its shape was cylindrical, balancing the shrinkage by condensation and the expansion by decompression. The mass fraction of water was about half at the surface.
Next, we fixed EC at 0.03 and changed Rv. When Rv=75 m, the plume sustained the low density and initial velocity to the surface. The radius gradually increased due to the evaporation of the entrained seawater up to 50 m above the vent. Then, it shrank slightly due to the condensation, and finally, the gas expansion overcame the condensation effect. For Rv=25 m, the plume changed into a mixture of hot water and solid particles but expanded due to re-boiling near the surface. In the case of Rv=15 m, the plume entrained a significant amount of seawater and flowed up relatively slowly. The hot (70℃) water plume spouted out on the surface at 39 m/s.
Discussion and future works
The plume in the sea changed its radius drastically with rising. The reason is that it entrains the external fluid with high density and low enthalpy, which undergoes evaporation, condensation, and re-boiling. Also, the pressure gradient in the sea is much larger than that in the atmosphere.
We showed that the plume's shape depends on EC and Rv (or mass discharge rate). If its volume and shape change rapidly, the plume may generate oceanic waves, including tsunamis. In further work, we will develop a model for an adequate entrainment coefficient for the seawater and explore the dependence on each parameter (vent radius, entrainment coefficient, water depth, and mass flux). Also, the stability of the 1D steady flow should be examined.