Tephra fallout hazard assessment for a Plinian eruption scenario at Volcán de Colima (Mexico)

Volcanic ash fallout associated with renewal of explosive activity at Colima, represents a serious threat to the surrounding urbanized area. Here we assess the tephra fallout hazard associated with a Plinian eruption scenario. The eruptive history of Volcán de Colima shows that Plinian eruptions occur approximately every 100 years and the last eruption, the 1913, represents the largest historic eruption of this volcano. We used the last eruption as a reference to discuss volcanic hazard and risk scenarios connected with ash fallout. Tephra fallout deposits are modeled using HAZMAP, a model based on a semi-analytical solution of the advection– diffusion–sedimentation equation for volcanic particles. Based on a statistical study of wind profiles at Colima region, we first reconstructed ash loading maps and then computed ground load probability maps for different seasons. The obtained results show that a Plinian eruptive scenario at Volcán de Colima, could seriously damage more than 10 small towns and ranches, and potentially affect big cities located at tens of kilometers from the eruptive center. The probability maps obtained are aimed to give support to the risk mitigation strategies

Ultra-distal tephra deposits from super-eruptions: examples from Toba, Indonesia and Taupo Volcanic Zone, New Zealand

Voluminous rhyolitic eruptions from Toba, Indonesia, and Taupo Volcanic Zone (TVZ), New Zealand, have dispersed volcanic ash over vast areas in the late Quaternary. The ~74 ka Youngest Toba Tuff (YTT) eruption deposited ash over the Bay of Bengal and the Indian subcontinent to the west. The ~340 ka Whakamaru eruption (TVZ) deposited the widespread Rangitawa Tephra, dominantly to the southeast (in addition to occurrences northwest of vent), extending across the landmass of New Zealand, and the South Pacific Ocean and Tasman Sea, with distal terrestrial exposures on the Chatham Islands. These super-eruptions involved ~2500 km^3 and ~1500 km3 of magma (dense-rock equivalent; DRE), respectively. Ultra-distal terrestrial exposures of YTT at two localities in India, Middle Son Valley, Madhya Pradesh, and Jurreru River Valley, Andhra Pradesh, at distances of >2000 km from the source caldera, show a basal ‘primary’ ashfall unit ~4 cm thick, although deposits containing reworked ash are up to ~3 m in total thickness. Exposures of Rangitawa Tephra on the Chatham Islands, >900 km from the source caldera, are ~15-30 cm thick. At more proximal localities (~200 km from source), Rangitawa Tephra is ~55-70 cm thick and characterized by a crystal-rich basal layer and normal grading. Both distal tephra deposits are characterized by very-fine ash (with high PM10 fractions) and are crystal-poor. Glass chemistry, stratigraphy and grain-size data for these distal tephra deposits are presented with comparisons of their correlation, dispersal and preservation. Using field observations, ash transport and deposition were modeled for both eruptions using a semi-analytical model (HAZMAP), with assumptions concerning average wind direction and strength during eruption, column shape and vent size. Model outputs provide new insights into eruption dynamics and better estimates of eruption volumes associ- ated with tephra fallout. Modeling based on observed YTT distal tephra thicknesses indicate a relatively low (<40 km high), very turbulent eruption column, consistent with deposition from a co-ignimbrite cloud extending over a broad region. Similarly, the Whakamaru eruption was modeled as producing a predominantly Plinian column (~45 km high), with dispersal to the southeast by strong prevailing winds. Significant ash fallout of the main dispersal direction, to the northwest of source, cannot be replicated in this modeling. The widespread dispersal of large volumes of fine ash from both eruptions may have had global environmental consequences, acutely affecting areas up to thousands of kilometers from vent.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

The gravity wave momentum flux in hydrostatic flow with directional shear over elliptical mountains

Semi-analytical expressions for the momentum flux associated with orographic internal gravity waves, and closed analytical expressions for its divergence, are derived for inviscid, stationary, hydrostatic, directionally-sheared flow over mountains with an elliptical horizontal cross-section. These calculations, obtained using linear theory conjugated with a third-order WKB approximation, are valid for relatively slowly-varying, but otherwise generic wind profiles, and given in a form that is straightforward to implement in drag parametrization schemes. When normalized by the surface drag in the absence of shear, a quantity that is calculated routinely in existing drag parametrizations, the momentum flux becomes independent of the detailed shape of the orography. Unlike linear theory in the Ri → ∞ limit, the present calculations account for shear-induced amplification or reduction of the surface drag, and partial absorption of the wave momentum flux at critical levels. Profiles of the normalized momentum fluxes obtained using this model and a linear numerical model without the WKB approximation are evaluated and compared for two idealized wind profiles with directional shear, for different Richardson numbers (Ri). Agreement is found to be excellent for the first wind profile (where one of the wind components varies linearly) down to Ri = 0.5, while not so satisfactory, but still showing a large improvement relative to the Ri → ∞ limit, for the second wind profile (where the wind turns with height at a constant rate keeping a constant magnitude). These results are complementary, in the Ri > O(1) parameter range, to Broad’s generalization of the Eliassen–Palm theorem to 3D flow. They should contribute to improve drag parametrizations used in global weather and climate prediction models.

Impact of non-hydrostatic effects and trapped lee waves on mountain wave drag in directionally sheared flow

The orographic gravity wave drag produced in flow over an axisymmetric mountain when both vertical wind shear and non-hydrostatic effects are important was calculated using a semi-analytical two-layer linear model, including unidirectional or directional constant wind shear in a layer near the surface, above which the wind is constant. The drag behaviour is determined by partial wave reflection at the shear discontinuity, wave absorption at critical levels (both of which exist in hydrostatic flow), and total wave reflection at levels where the waves become evanescent (an intrinsically non-hydrostatic effect), which produces resonant trapped lee wave modes. As a result of constructive or destructive wave interference, the drag oscillates with the thickness of the constant-shear layer and the Richardson number within it (Ri), generally decreasing at low Ri and when the flow is strongly non-hydrostatic. Critical level absorption, which increases with the angle spanned by the wind velocity in the constant-shear layer, shields the surface from reflected waves, keeping the drag closer to its hydrostatic limit. While, for the parameter range considered here, the drag seldom exceeds this limit, a substantial drag fraction may be produced by trapped lee waves, particularly when the flow is strongly non-hydrostatic, the lower layer is thick and Ri is relatively high. In directionally sheared flows with Ri = O(1), the drag may be misaligned with the surface wind in a direction opposite to the shear, a behaviour which is totally due to non-trapped waves. The trapped lee wave drag, whose reaction force on the atmosphere is felt at low levels, may therefore have a distinctly different direction from the drag associated with vertically propagating waves, which acts on the atmosphere at higher levels.

What is the shape of an air bubble on a liquid surface?

We have calculated the equilibrium shape of the axially symmetric meniscus along which a spherical bubble contacts a flat liquid surface, by analytically integrating the Young-Laplace equation in the presence of gravity, in the limit of large Bond numbers. This method has the advantage that it provides semi-analytical expressions for key geometrical properties of the bubble in terms of the Bond number. Results are in good overall agreement with experimental data and are consistent with fully numerical (Surface Evolver) calculations. In particular, we are able to describe how the bubble shape changes from hemispherical, with a shallow flat bottom, to lenticular, with a deeper, curved bottom, as the Bond number is decreased.