A numerical study of turbulent mixing in eruption clouds using a three‐dimensional fluid dynamics model

Suzuki, Yujiro; Koyaguchi, Takehiro; Ogawa, Masaki; Hachisu, Izumi

doi:10.1029/2004jb003460

Cited by 106 publications

(117 citation statements)

References 54 publications

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“…[9] Turbulent mixing in and around eruption clouds is an essential part of the dynamics of eruption clouds [Suzuki et al, 2005]. In the 1-D plume model, the turbulent mixing with the environment is parameterized on the basis of the entrainment hypothesis of Morton et al [1956] that the mean inflow velocity across the edge of turbulent flow (jet and/or plume) is proportional to the mean vertical velocity.…”

Section: The 1-d Plume Model Of Eruption Columnmentioning

confidence: 99%

“…[17] Using a 3-D model by Suzuki et al [2005] (see Appendix A), we carried out simulations of explosive eruptions that generate large-scale umbrella clouds in the atmosphere. The model is designed to describe the injection of a mixture of solid pyroclasts and volcanic gas from a circular vent above a flat surface of the earth in a stationary atmosphere.…”

Section: General Features Of Eruption Cloudsmentioning

confidence: 99%

“…[5] Over the past 20 years, the development of multidimensional (2-D and/or 3-D), time-dependent fluid dynamics models enables us to calculate the dynamics of eruption clouds for given eruption conditions at the vent without empirical constants like those in the simplified models [e.g., Wohletz et al, 1984;Valentine and Wohletz, 1989;Dobran et al, 1993;Neri and Dobran, 1994;Neri and Macedonio, 1996;Neri et al, 1998Neri et al, , 2002Neri et al, , 2003aNeri et al, , 2003bNeri et al, , 2007Oberhuber et al, 1998;Clarke et al, 2002;Dartevelle et al, 2004;Ishimine, 2005;Suzuki et al, 2005;Textor et al, 2005Textor et al, , 2006. These multidimensional fluid dynamics models, however, also have difficulties to quantitatively reproduce the dynamics of eruption clouds.…”

Section: Introductionmentioning

confidence: 99%

“…These multidimensional fluid dynamics models, however, also have difficulties to quantitatively reproduce the dynamics of eruption clouds. Suzuki et al [2005] have shown that the fluid dynamics models should be calculated in 3-D coordinates with a high spatial resolution scheme and a fine grid size in order to reproduce the quantitative features of turbulent mixing between eruption clouds and the ambient air. Such calculations are computationally highly demanding.…”

Section: Introductionmentioning

confidence: 99%

“…[6] The aim of this study is to establish the relationship between the observable quantities of the eruption clouds and the eruption conditions at the vent using a 3-D timedependent fluid dynamics model for eruption cloud by Suzuki et al [2005]. The 3-D model has been designed to correctly reproduce the quantitative features of turbulent mixing of steady turbulent jet and/or plume in the laboratory experiments [e.g., Fischer et al, 1979;Papanicolaou and List, 1988] as well as the variation of the mixture density of the ejected material plus ambient air (see Appendix A for brief descriptions of the 3-D model).…”

Section: Introductionmentioning

confidence: 99%

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A three‐dimensional numerical simulation of spreading umbrella clouds

Suzuki¹,

Koyaguchi²

2009

J. Geophys. Res.

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[1] During explosive volcanic eruptions, an eruption column buoyantly rises as a turbulent plume, and an umbrella cloud spreads laterally as a gravity current at the neutral buoyancy level. The source conditions of explosive eruptions such as mass discharge rates of magma at vents have been estimated from the field observations (e.g., satellite images) on the height of the eruption columns and the spreading rate of umbrella clouds on the basis of the one-dimensional (1-D) plume model and the gravity current model. However, these simplified models contain empirical constants (entrainment coefficient of turbulent plume, k, and Froude number of gravity current, l) that should be justified. We developed a time-dependent three-dimensional (3-D) numerical model of eruption clouds to independently determine the values of these constants. The 3-D model is designed to calculate quantitative features of turbulent mixing between an eruption cloud and the ambient air without any a priori empirical constants by applying a sufficiently fine grid size with a third-order accuracy scheme. It has reproduced the fundamental features of eruption clouds including eruption columns, pyroclastic flows, coignimbrite ash clouds, and umbrella clouds. The altitudes of the spreading umbrella clouds in the 3-D simulations are consistent with those of the neutral buoyancy level of eruption columns estimated by the 1-D plume model with the entrainment coefficient k $ 0.1. The relationship between the volumetric flow rate and the spreading rate of the umbrella cloud in the 3-D simulations is explained by the axisymmetrical gravity current model with l $ 0.2 for eruption clouds in the tropical atmosphere and l $ 0.1 for those in the midlatitude atmosphere. On the other hand, the total column height in the 3-D simulations strongly oscillates even for a constant mass discharge rate, and its time average tends to be substantially greater than the column height estimated by the 1-D plume model with k $ 0.1, particularly for large-scale eruption clouds in the midlatitude atmosphere. We recommend a method to estimate the mass discharge rate from the observation of the column height or the spreading rate of umbrella cloud. The method and the accuracy of the 3-D simulations are tested on the basis of the field data (e.g., the total height of the eruption column, the altitude and the spreading rate of the umbrella cloud, and the mass discharge rate) of the Pinatubo 1991 eruption.

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Section: The 1-d Plume Model Of Eruption Columnmentioning

confidence: 99%

Section: General Features Of Eruption Cloudsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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A three‐dimensional numerical simulation of spreading umbrella clouds

Suzuki¹,

Koyaguchi²

2009

J. Geophys. Res.

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The flow structure of jets from transient sources and implications for modeling short‐duration explosive volcanic eruptions

Chojnicki

Clarke

Adrian

et al. 2014

Geochem Geophys Geosyst

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We used laboratory experiments to examine the rise process in neutrally buoyant jets that resulted from an unsteady supply of momentum, a condition that defines plumes from discrete Vulcanian and Strombolian-style eruptions. We simultaneously measured the analog-jet discharge rate (the supply rate of momentum) and the analog-jet internal velocity distribution (a consequence of momentum transport and dilution). Then, we examined the changes in the analog-jet velocity distribution over time to assess the impact of the supply-rate variations on the momentum-driven rise dynamics. We found that the analogjet velocity distribution changes significantly and quickly as the supply rate varied, such that the whole-field distribution at any instant differed considerably from the time average. We also found that entrainment varied in space and over time with instantaneous entrainment coefficient values ranging from 0 to 0.93 in an individual unsteady jet. Consequently, we conclude that supply-rate variations exert first-order control over jet dynamics, and therefore cannot be neglected in models without compromising their capability to predict large-scale eruption behavior. These findings emphasize the fundamental differences between unsteady and steady jet dynamics, and show clearly that: (i) variations in source momentum flux directly control the dynamics of the resulting flow; (ii) impulsive flows driven by sources of varying flux cannot reasonably be approximated by quasi-steady flow models. New modeling approaches capable of describing the time-dependent properties of transient volcanic eruption plumes are needed before their trajectory, dilution, and stability can be reliably computed for hazards management.

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Effects of wind on entrainment efficiency in volcanic plumes

Suzuki

Koyaguchi

2015

JGR Solid Earth

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The entrainment of air by turbulent mixing plays a central role in the dynamics of volcanic eruption clouds, as the amount of entrained air controls the height of the plume. In one‐dimensional models of volcanic plumes, the efficiency of entrainment under a wind field is parameterized using two empirical constants. The first is the coefficient associated with the entrainment caused by the shear between the volcanic plume and the ambient air (i.e., the radial entrainment coefficient), and the other is associated with the entrainment caused by wind (i.e., the wind entrainment coefficient). In this study, we used three‐dimensional numerical simulations of volcanic plumes to determine the effective values of these empirical constants from the relationship between eruption conditions and plume heights. These simulations suggest that the value of the radial entrainment coefficient is 0.05–0.06, which is slightly smaller than that of pure jets or plumes seen in laboratory experiments (0.07–0.15). The value of the wind entrainment coefficient was estimated to be 0.1–0.3, which is significantly smaller than those estimated from laboratory experiments (0.3–1.0). The entrainment coefficients derived from these simulations successfully explain the observations made during the 2011 Shinmoe‐dake eruptions in which the volcanic plumes were significantly distorted by the wind.

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A numerical study of turbulent mixing in eruption clouds using a three‐dimensional fluid dynamics model

Cited by 106 publications

References 54 publications

A three‐dimensional numerical simulation of spreading umbrella clouds

A three‐dimensional numerical simulation of spreading umbrella clouds

The flow structure of jets from transient sources and implications for modeling short‐duration explosive volcanic eruptions

Effects of wind on entrainment efficiency in volcanic plumes

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