Darcy E. Ogden

Numerical simulations of volcanic jets: Importance of vent overpressure

JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 113, B02204, doi:10.1029/2007JB005133, 2008 Numerical simulations of volcanic jets: Importance of vent overpressure Darcy E. Ogden, 1 Kenneth H. Wohletz, 2 Gary A. Glatzmaier, 1 and Emily E. Brodsky 1 Received 24 April 2007; revised 5 October 2007; accepted 5 November 2007; published 29 February 2008. [ 1 ] Explosive volcanic eruption columns are generally subdivided into a gas-thrust region and a convection-dominated plume. Where vents have greater than atmospheric pressure, the gas-thrust region is overpressured and develops a jet-like structure of standing shock waves. Using a pseudogas approximation for a mixture of tephra and gas, we numerically simulate the effects of shock waves on the gas-thrust region. These simulations are of free-jet decompression of a steady state high-pressure vent in the absence of gravity or a crater. Our results show that the strength and position of standing shock waves are strongly dependent on the vent pressure and vent radius. These factors control the gas-thrust region’s dimensions and the character of vertical heat flux into the convective plume. With increased overpressure, the gas-thrust region becomes wider and develops an outer sheath in which the erupted mixture moves at higher speeds than it does near the column center. The radius of this sheath is linearly dependent on the vent radius and the square root of the overpressure. The sheath structure results in an annular vertical heat flux profile at the base of the convective plume, which is in stark contrast to the generally applied Gaussian or top-hat profile. We show that the magnitude of expansion is larger than that predicted from previous 1D analyses, resulting in much slower average vertical velocities after expansion. These new relationships between vent pressure and plume expansion may be used with observations of plume diameter to constrain the pressure at the vent. Citation: Ogden, D. E., K. H. Wohletz, G. A. Glatzmaier, and E. E. Brodsky (2008), Numerical simulations of volcanic jets: Importance of vent overpressure, J. Geophys. Res., 113, B02204, doi:10.1029/2007JB005133. 1. Introduction [ 2 ] In large, explosive volcanic eruptions, the eruptive fluid issues from the vent as a high speed, compressible gas with entrained solid particulates. It is important to quantify the behavior of this gas-thrust region because it provides a connection between the fluid dynamics in the conduit and that of the buoyant column. If the eruptive fluid velocity is at or greater than sonic and vent pressure is higher than atmospheric pressure, the dynamics will be complicated by the presence of standing shock waves that can drastically alter the distribution of the vertical heat flux necessary for eruption column stability. The fluid dynamics and structure of a compressible jet issuing from a sonic nozzle into an ambient atmosphere of lower pressure are well known from experimental, analytical and computational studies [e.g., Crist et al., 1966; Young, 1975; Norman et al., 1982; Figure 1]. Although application of compressible jet dynamics to explosive volcanic eruptions was first sug- gested over 25 years ago by Kieffer [1981], the concept has Earth & Planetary Sciences Department, University of California at Santa Cruz, Santa Cruz, California, USA. Los Alamos National Laboratory, Los Alamos, New Mexico, USA. Copyright 2008 by the American Geophysical Union. 0148-0227/08/2007JB005133

The effects of different parameter regimes in geodynamo simulations

09.00 yet to be widely applied in modeling and analysis of explosive eruption columns. [ 3 ] In this paper, we present computational results that quantify the important effects of vent pressure on the fluid dynamics of volcanic jets and show that overpressured jets produce vertical heat flux profiles that are drastically different than those of pressure-balanced jets. (Note: to avoid confusion, here we use the physics convention and consider ‘‘heat flux’’ the thermal energy transfer per area per unit time (J m 2 s 1 ) and ‘‘heat flow’’ the thermal energy transfer integrated over an entire area per time (J s 1 ). In volcanology literature, the term ‘‘heat flux’’ is often used to mean either of these things [e.g., Woods, 1988; Mastin, 2007]). The simulations shown here are time-dependent, though they assume a steady vent condition. Through these simulations, we quantify the effects of vent pressure and radius on plume radius and heat flux distribution after expansion of the jet. This may allow the prediction of major features of the eruptive structure. We do not consider the effects of variations in conduit dynamics, buoyancy, or the presence of a crater in order to focus only on the effects of vent pressure and radius alone. This study is not a complete picture of the complicated flow dynamics of a volcanic eruption. Rather, the results presented here could be consid- ered the ‘‘simplest case’’ to which one could compare the dynamics resulting from more complicated simulations and observations of high-pressure volcanic jets. B02204 1 of 18

Modeling the Earth's Dynamo

Over the past 10 years, geodynamo simulations have grown rapidly in sophistication. However, it is still necessary to make certain approximations in order to maintain numerical stability. In addition, models are forced to make assumptions about poorly known parameters for the Earths core. Different magnetic Prandtl numbers have been used and different assumptions about the presence of radiogenic heating have been made. This study examines some of the consequences of different approximations and assumptions using the Glatzmaier–Roberts geodynamo model. Here, we show that the choice of magnetic Prandtl number has a greater influence on the character of the magnetic field produced than the addition of a plausible amount of radiogenic heating. In particular, we find that prescribing a magnetic Prandtl number of unity with Ekman number limited by current computing resources, results in magnetic fields with significantly smaller intensities and variabilities compared with the much more Earth-like results obtained from simulations with large magnetic Prandtl numbers. A magnetic Prandtl number of unity, with both the viscous and magnetic diffusivities set to the Earths magnetic diffusivity, requires a rotation rate much smaller than that of the Earth for currently reachable Ekman numbers. This results in a reduced dominance of the Coriolis forces relative to the buoyancy forces, and therefore, a reduction in the magnetic field intensity and the variability compared to the large Prandtl number cases.

Effects of vent overpressure on buoyant eruption columns: Implications for plume stability

For the past decade, three-dimensional time-dependent computer models have been used to predict and explain how the geomagnetic field is maintained by convection in the Earths fluid core. Geodynamo models have simulated magnetic fields that have surface structure and time dependence similar to the Earths field, including dipole reversals. However, no dynamo model has yet been run at the spatial resolution required to simulate a broad spectrum of turbulence, which surely exists in the Earths fluid core. Two-dimensional simulations of magnetoconvection show how the structure and time dependence of even the large-scale features change dramatically when the solution becomes strongly turbulent. Although these two-dimensional turbulent simulations lack the important effects of three-dimensional spherical geometry, based on their results one must question how geophysically realistic the large-scale dynamo mechanism is in current three-dimensional laminar simulations. Whatever the answer, we look forward to new discoveries from the next generation of turbulent dynamo models.