Protracted episodes of 0.5–7 Hz pre-eruptive volcanic tremor (PVT) are common at active stratovolcanoes. Reliable links to processes related to magma movement consequently enable a potential to use properties of PVT as diagnostic eruptive precursors. A challenging feature of PVT is that generic spectral and amplitude properties of the signal evolve similarly, independent of widely varying volcano structures and conduit geometries on which most physical models rely. The ‘magma wagging’ model introduced in Jellinek & Bercovici (2011) and extended by Bercovici et al. (2013), Liao et al. and Liao & Bercovici (2018) makes progress because it depends on magma dynamics that are only weakly sensitive to volcano architecture: The flow of gas through a permeable foamy annulus of gas bubbles excites, modulates and maintains a wagging oscillation of a central magma column rising in an erupting conduit. ‘Magma wagging’ and resulting PVT are driven through an energy transfer from a ‘Bernoulli mode’ related to azimuthal variations in annular gas flow speeds. Consistent with observations, spectral and amplitude properties of PVT are predicted to evolve before an eruption as the width of the annulus decreases with increased gas fluxes. To confirm this critical Bernoulli-to-wagging energy transfer we use extensive experiments and restricted numerical simulations on wagging oscillations excited on analogue viscoelastic columns by annular air flows. We also explore sensitivities of the spatial and temporal characters of wagging to asymmetric annular air flows that are intractable in the existing magma wagging model and expected to occur in nature with spatial variations in annulus permeability. From high-resolution time-series of linear and orbital displacements of analogue column tops and time-series of axial deflections and accelerations of the column centre line, we characterize the excitation, evolution, and steady-state oscillations in unprecedented detail over a broad range of conditions. We show that the Bernoulli mode corresponds to the timescale for the buildup of axial elastic bending stresses in response to pressure variations related to air flows over the heights of columns. We identify three distinct wagging modes: (i) rotational (cf. Liao et al. 2018); (ii) mixed-mode and (iii) chaotic. Rotational modes are favoured for symmetric, high intensity forcing and a maximal delivery of mechanical energy to the fundamental magma wagging mode. Mixed-mode oscillations regimes are favoured for a symmetric, intermediate intensity forcing. Chaotic modes, involving the least efficient delivery of energy to the fundamental mode, occur for asymmetric forcing and where the intensity of imposed airflow is low. Numerical simulations also show that where forcing frequencies are comparable to a natural mode of free oscillation, power delivered by peripheral air flows is concentrated at the lowest frequency fundamental mode generally and spread among higher frequency natural modes where air pressure and column elastic forces are comparable. Our combined experimental and numerical results make qualitative predictions for the evolution of the character of volcanic tremor and its expression in seismic or infrasound arrays during natural events that is testable in field-based studies of PVT and syn-eruptive volcanic tremor.
Oscillations of a soft viscoelastic drop
A soft viscoelastic drop has dynamics governed by the balance between surface tension, viscosity, and elasticity, with the material rheology often being frequency dependent, which are utilized in bioprinting technologies for tissue engineering and drop-deposition processes for splash suppression. We study the free and forced oscillations of a soft viscoelastic drop deriving (1) the dispersion relationship for free oscillations, and (2) the frequency response for forced oscillations, of a soft material with arbitrary rheology. We then restrict our analysis to the classical cases of a Kelvin–Voigt and Maxwell model, which are relevant to soft gels and polymer fluids, respectively. We compute the complex frequencies, which are characterized by an oscillation frequency and decay rate, as they depend upon the dimensionless elastocapillary and Deborah numbers and map the boundary between regions of underdamped and overdamped motions. We conclude by illustrating how our theoretical predictions for the frequency-response diagram could be used in conjunction with drop-oscillation experiments as a “drop vibration rheometer”, suggesting future experiments using either ultrasonic levitation or a microgravity environment.
more » « less- Award ID(s):
- 1750208
- NSF-PAR ID:
- 10308281
- Publisher / Repository:
- Nature Publishing Group
- Date Published:
- Journal Name:
- npj Microgravity
- Volume:
- 7
- Issue:
- 1
- ISSN:
- 2373-8065
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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