A simple three-dimensional volcanic plume model that incorporates the effects of moisture and ambient wind is presented and used iteratively to refine the source mass flux, obtained from an empirical ...relationship between the plume rise height and source mass flux, according to the prevailing atmospheric conditions. It is applied to the eruption of Eyjafjallajökull in May 2010 using realistic atmospheric profiles appropriate to the time of the eruption. It is shown that the ambient wind has the largest effect on the refined source mass flux with moisture playing a secondary though still important role. It is also shown that significant differences in the values of the revised source mass fluxes can arise when the realistic atmospheric profiles are approximated by idealised profiles. The revised source mass flux is used to initialise a long-range dispersion model of ash in the atmosphere.
•3-D volcanic plume model including effects of ambient wind and moisture•Applied to realistic atmospheric profiles of wind speed, temperature and humidity•Eyjafjallajökull used as example•Results applied to long-range dispersion model
Droplet growth in warm turbulent clouds Devenish, B. J.; Bartello, P.; Brenguier, J.-L. ...
Quarterly journal of the Royal Meteorological Society,
July 2012 Part B, Letnik:
138, Številka:
667
Journal Article
We present an extension of Thomson’s (J. Fluid Mech., vol. 210, 1990, pp. 113–153) two-particle Lagrangian stochastic model that is constructed to be consistent with the
$4/5$
law of turbulence. The ...rate of separation in the new model is reduced relative to the original model with zero skewness in the Eulerian longitudinal relative velocity distribution and is close to recent measurements from direct numerical simulations of homogeneous isotropic turbulence. The rate of separation in the equivalent backwards dispersion model is approximately a factor of 2.9 larger than the forwards dispersion model, a result that is consistent with previous work.
The statistical properties of velocity and acceleration fields along the trajectories of fluid particles transported by a fully developed turbulent flow are investigated by means of high resolution ...direct numerical simulations. We present results for Lagrangian velocity structure functions, the acceleration probability density function, and the acceleration variance conditioned on the instantaneous velocity. These are compared with predictions of the multifractal formalism, and its merits and limitations are discussed.
A search for mixing between active neutrinos and light sterile neutrinos has been performed by looking for muon neutrino disappearance in two detectors at baselines of 1.04 and 735 km, using a ...combined MINOS and MINOS+ exposure of 16.36×10^{20} protons on target. A simultaneous fit to the charged-current muon neutrino and neutral-current neutrino energy spectra in the two detectors yields no evidence for sterile neutrino mixing using a 3+1 model. The most stringent limit to date is set on the mixing parameter sin^{2}θ_{24} for most values of the sterile neutrino mass splitting Δm_{41}^{2}>10^{-4} eV^{2}.
The volcanic plume-rise model of Devenish (2013) is applied to the duration of the 39-day eruption of Eyjafjallajökull in 2010 to produce a time series of the estimated source mass flux. This in turn ...is integrated to give the total emitted mass, which is found to lie within the error bounds of an observational estimate made by Gudmundsson et al. (2012). The calculation uses realistic profiles of key atmospheric variables such as wind speed, temperature, and humidity taken from a numerical weather prediction model and appropriate to the time of the eruption. The sensitivity of the model results to changes in the values of the entrainment coefficients is discussed. It is shown that including the radius of the plume (when it is strongly affected by the wind) in the comparison of the modelled and observed rise heights not only improves the accuracy of the estimated total emitted mass (compared with neglecting the radius) but also reduces the sensitivity of this estimate to the value of the entrainment coefficient associated with velocity differences normal to the plume axis.
•Source mass flux determined for total duration of 2010 Eyjafjallajökull eruption•Good agreement with observations•Quantify sensitivity to changes in the entrainment coefficients•Show how sensitivity to crosswind entrainment coefficient can be reduced
It is shown that the shape statistics of four correlated particles, known as a tetrad, in a direct numerical simulation of three-dimensional homogeneous isotropic turbulence agree very well with a ...simple diffusion equation with a separation-dependent eddy diffusivity. The latter is essentially an extension of Richardson's model for particle-pair dispersion to tetrads. It is also shown that the degree of elongation of the tetrad in the inertial subrange of a turbulentlike flow is controlled by the exponent, m, in an eddy diffusivity of the form K(r)proportionalityr(m) where r is the interparticle separation, becoming more elongated as m increases in the range 0≤m<2.
We consider large-eddy simulation (LES) of buoyant plumes in uniform and stably stratified environments. We show that in the former case the results agree well with the simple plume model of Morton, ...Taylor & Turner (Proc. R. Soc. Lond. A, vol. 234, 1956, p. 1). In particular, we calculate an entrainment constant which is consistent with laboratory and field measurements and find no significant difference between the radial spreading rates of vertical velocity and buoyancy. In a stably stratified environment, the LES plume shows better agreement with Morton et al. (1956) below the level at which the buoyancy first vanishes than above this level. Above the level of neutral buoyancy, the LES plume is characterized by an ascending core of negative buoyancy surrounded by a descending annulus of positive buoyancy. We compare the LES data with the model of Bloomfield & Kerr (J. Fluid Mech., vol. 424, 2000, p. 197), which explicitly accounts for these coherent motions. The model exhibits many qualitative aspects of the LES plume and quantitative agreement can be improved by adjusting the downward volume flux relative to the upward volume flux in a manner consistent with the LES plume. This simple adjustment, along with revised values of the entrainment constants, represents the combined effects of an overturning region at the top of the plume (where a fluid element reverses direction), ‘plume-top’ entrainment (whereby the plume entrains ambient fluid above the plume) as well as lateral entrainment and detrainment processes (both external and internal) occurring above the top of the model plume.
Abstract
Approximate solutions of the supersaturation equation are derived for a warm cloud. These solutions take account of the growth of the droplet radius but are only valid for small times. ...However, the validity of the solutions extends far enough to obtain reasonable estimates of the maximum supersaturation smax. It is shown that when the initial droplet radius and supersaturation are sufficiently small the scaling relation smax ∝ w3/4N−1/2 is obtained, where w is the vertical velocity and N is the droplet number density, in agreement with previous results. The range of validity of this result is discussed and other analytical expressions are derived when this result is not valid. It is shown that these analytical expressions generally agree well with numerical solutions.
We present a hybrid Lagrangian stochastic model for buoyant plume rise from an isolated source that includes the effects of temperature fluctuations. The model is based on that of Webster and Thomson ...(Atmos Environ 36:5031–5042,
2002
) in that it is a coupling of a classical plume model in a crossflow with stochastic differential equations for the vertical velocity and temperature (which are themselves coupled). The novelty lies in the addition of the latter stochastic differential equation. Parametrizations of the plume turbulence are presented that are used as inputs to the model. The root-mean-square temperature is assumed to be proportional to the difference between the centreline temperature of the plume and the ambient temperature. The constant of proportionality is tuned by comparison with equivalent statistics from large-eddy simulations (LES) of buoyant plumes in a uniform crossflow and linear stratification. We compare plume trajectories for a wide range of crossflow velocities and find that the model generally compares well with the equivalent LES results particularly when added mass is included in the model. The exception occurs when the crossflow velocity component becomes very small. Comparison of the scalar concentration, both in terms of the height of the maximum concentration and its vertical spread, shows similar behaviour. The model is extended to allow for realistic profiles of ambient wind and temperature and the results are compared with LES of the plume that emanated from the explosion and fire at the Buncefield oil depot in 2005.
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