WRF plume modelling update NCAS, Leeds

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Presentation transcript:

WRF plume modelling update NCAS, Leeds Ralph Burton, Stephen Mobbs, Alan Gadian

WRF plume model: simple tests Weather Research and Forecasting model WRF configuration: 100m resolution (25km x 25km), 141 vertical levels, 30km top Resting atmosphere – U.S. Standard atmosphere; dry; no ambient wind Different thermal perturbations at “vent” “Circular” vent Results look like plumes, but - Do they follow various theoretical models of plume behaviour (cf. Mark Woodhouse & Co. work)?

Aspect ratio = 1:1 ~15km 25km

Section through umbrella cloud Very complex! – do simple tests on gross features.

Tests 1. Radial lengthscale, eruption / jet column. 4 3 Height (km) Turner, Buoyancy effects in Fluids 2 2 gradient ~1/8 b = (6/5)αz, b = radial lengthscale α = entrainment constant α = 0.10 (Turner again) gives b ~ z/8 1

Tests II. Radial spread of umbrella cloud H = 13.5km; ΔT = 86K H = 14.5km; ΔT = 111K H = 15.3km; ΔT = 136K WRF From Sparks et al. Volcanic Plumes p283

Tests III. Height of plume. Theory WRF Courtesy Mark Woodhouse gradient = 0.25 1/4 H = k (ΔT)

Summary. Results seem to agree with theoretical work This is a simple visual inspection – More rigorous tests to do But no evidence of fundamental differences Compare with Mark Woodhouse & Bristol team’s work.

Further Work. Similar approach adopted by e.g. Neri and Macedonio, “Numerical simulation of collapsing volcanic columns with particles of two sizes” J. Geophy Res. B4, 8153-8174

Further work: full multiphase WRF N + 1 phases: 1 air (gas + liquid and solid water) phase, N particulate phases (size bins) Fundamentally N + 1 momentum equations, one for each phase, with interaction forces (drag) between them Integrate N particulate momentum equations plus the combined (summed) momentum equation There is only one shared pressure field and so the combined momentum equation is simply the usual one in the model, taking account of the contribution of the particles to the density. All interaction forces between phases are equal and opposite (Newton's 3rd law) so cancel in the combined momentum equation Drag terms in each particulate momentum equation Modified equation of state taking account of the compressible fraction (air).

From Elghobashi (1994) “On predicting turbulent-laden flows”, Applied Scientific Research, 52