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The assumption that distributions of mass versus size interval for fragmented materials fit the log normal distribution is empirically based and has historical roots in the late 19th century. Other often used distributions (e.g., Rosin‐Rammler, Weibull) are also empirical and have the general form for mass per size interval: n(l) = klα exp (−lβ), where n(l) represents the number of particles of diameter l, l is the normalized particle diameter, and k, α, and β are constants. We describe and extend the sequential fragmentation distribution to include transport effects upon observed volcanic ash size distributions. The sequential fragmentation/transport (SFT) distribution is also of the above mathematical form, but it has a physical basis rather than empirical. The SFT model applies to a particle‐mass distribution formed by a sequence of fragmentation (comminution) and transport (size sorting) events acting upon an initial mass m′: n(x, m) = C ∫∫ n(x′, m′)p(ξ)dx′ dm′, where x′ denotes spatial location along a linear axis, C is a constant, and integration is performed over distance from an origin to the sample location and mass limits from 0 to m. We show that the probability function that models the production of particles of different size from an initial mass and sorts that distribution, p(ξ), is related to mg, where g (noted as γ for fragmentation processes) is a free parameter that determines the location, breadth, and skewness of the distribution; g(γ) must be greater than −1, and it increases from that value as the distribution matures with greater number of sequential steps in the fragmentation or transport process; γ is expected to be near −1 for “sudden” fragmentation mechanisms such as single‐event explosions and transport mechanisms that are functionally dependent upon particle mass. This free parameter will be more positive for evolved fragmentation mechanisms such as ball milling and complex transport processes such as saltation. The SFT provides better fits to many types of volcanic ash samples than does the log normal curve. Modeling of the SFT shows its similarity to the log normal curve on size frequency histograms; it differs by its variable skewness controlled by γ. Skewed distributions are typical of many volcanic ash samples, and characterization of them by the SFT allows interpretation of eruptive and transport mechanisms.

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Numerical simulations of physical processes governing the large‐scale dynamics of Plinian eruption columns reveal conditions contributing to column collapse and emplacement of pyroclastic flows. The simulations are based on numerical solution of the time‐dependent, two‐phase, compressible Navier‐Stokes equations for jets in a gravitational field. This modeling effort is directed toward studying the steady discharge phase of eruptions in contrast to our previous models of the initial, unsteady blast phase. Analysis of 51 eruption models covers a wide range of vent exit pressures, inertial and buoyancy driving forces, and coupling of energy and momentum between gas and pyroclasts. Consideration of three dimensionless groups (Richardson and Rouse numbers and thermogravitational parameter) facilitates this analysis and defines conditions leading to column collapse. For eruptions with similar particle size characteristics, exit pressure ratios are also very important in determining column behavior; column behavior is much more sensitive to exit pressure ratio than to the density ratio between the column and the atmosphere. Model eruption columns with exit pressures exceeding atmospheric pressure have diamond‐shaped patterns at their bases with internal dynamics that correspond closely to observations of overpressured jets in laboratory experiments. Collapsing fountains form pyroclastic flows that consist of low‐concentration fronts, relatively thick heads, vortex development along the top surfaces, and rising clouds of buoyant ash. The presence of coarse‐grained proximal deposits primarily reflects tephra size sorting within the eruption column before collapse, as opposed to that which occurs during lateral transport of the material in pyroclastic flows. The dynamics and particle behavior in the proximal zone around collapsing eruption columns is examined; the modeling indicates that flow within a few kilometers of a vent will be at its highest particle concentration relative to other parts of the flow field.

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[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.