Solitary waves in magma dynamics

Barcilon, Victor; Lovera, Oscar M.

doi:10.1017/s0022112089001680

Cited by 76 publications

(90 citation statements)

References 14 publications

(16 reference statements)

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“…To test the code, a constant viscosity matrix was set up with a 2D solitary wave initial condition and periodic boundary conditions, and allowed to evolve. As expected, the wave moved without changing form, with a velocity that agreed with that found theoreticany by Barcilon and Lovera [1989] (Fig. la).…”

Section: Gravity Controlled Flowsupporting

confidence: 87%

Melt flow in a variable viscosity matrix

Richardson

1998

Geophysical Research Letters

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Abstract. It is often assumed that the molten regions of planetary interiors can be modeled as a compacting viscous matrix permeated by a less viscous melt phase. In order to assess the true behaviour, it is important to test as many different aspects of these models as possible. In the calculations presented here, the matrix viscosity is made to decrease as the proportion of melt increases. New results in two dimensions show that if only gravity drives the flow, pockets of melt travel u•)wards as solitary waves, and the behaviour is similar to the well known constant viscosity case. However, when an external shear strain is applied, an instability occurs and melt flows into elongated pockets, or veins, perpendicular to the least compressive stress. Whilst veins much greater than a compaction length in width are suppressed, their minimum width is not clearly constrained. The growth rate of veins is directly proportional to the applied strain rate, so that their degree of development is proportional to the total strain. It is suggested that under mid-ocean ridges, the total strain may be enough for such veins to be important.

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Section: Gravity Controlled Flowsupporting

confidence: 87%

Melt flow in a variable viscosity matrix

Richardson

1998

Geophysical Research Letters

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“…Early work on solitary wave solutions in viscous media emphasized distinctions between one-dimensional and multidimensional solutions that are important for the small amplitude waves that initiate in the viscous scenario [Barcilon and Richter, 1986;Barcilon and Lovera, 1989]. The simulations here demonstrate that extraordinary amplitudes may be achieved by waves in a decompaction weakening matrix.…”

Section: Speed and Amplitudementioning

confidence: 64%

Decompaction weakening and channeling instability in ductile porous media: Implications for asthenospheric melt segregation

Connolly¹,

2007

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[1] We propose that a mechanical flow channeling instability, which arises because of rock weakening at high fluid pressure, facilitates segregation and transport of asthenospheric melts. To characterize the weakening effect, the ratio of the matrix viscosity during decompaction to that for compaction is treated as a free parameter R in the range 1 to 10 À6 . Two-dimensional numerical simulations with this rheology reveal that solitary, vertically elongated, porosity waves with spacing on the compaction length scale d initiate from miniscule porosity perturbations. By analogy with viscous compaction models we infer that in the absence of far-field stress, the three-dimensional expression of the waves is as pipe-like structures of radius d ffiffiffi R p , a geometry that increases fluid fluxes by a factor of $1/R. The waves grow by draining fluid from the background porosity but leave a wake of elevated porosity that localizes subsequent flow. Wave amplitudes grow linearly with time, increasing by a factor of R À3/8 in the time required to drain the porosity a distance of $d. Dissipation of gravitational potential energy by the waves has the capacity to enhance growth rates through melting. Maximum wave speeds are $40 times the speed of fluid flow through the unperturbed matrix. Such waves may provoke the elastic response necessary to nucleate, and localize the melt necessary to sustain, more effective transport mechanisms. The formulation introduces no melting effects and is applicable to fluid flow and localization problems in ductile porous media in general.

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“…Note the introduction of the solid matrix velocity v s , as well as the matrix shear and bulk viscosities η , ζ , which arise due to matrix compressibility and depend on the porosity as described below. For nondimensionalization, we follow the scalings described in Spiegelman (1993a) (a similar reduction was performed in Scott & Stevenson (1984; Barcilon & Richter (1986); Barcilon & Lovera (1989)). This requires the introduction of the natural length scale of matrix compaction δ and the natural velocity scale of melt percolation w 0 proposed by McKenzie (1984), which for a background porosity φ 0 are defined as…”

Section: Magma Geophysicsmentioning

confidence: 99%

Dispersive shock waves in viscously deformable media

2013

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The viscously dominated, low Reynolds' number dynamics of multi-phase, compacting media can lead to nonlinear, dissipationless/dispersive behavior when viewed appropriately. In these systems, nonlinear self-steepening competes with wave dispersion, giving rise to dispersive shock waves (DSWs). Example systems considered here include magma migration through the mantle as well as the buoyant ascent of a low density fluid through a viscously deformable conduit. These flows are modeled by a third-order, degenerate, dispersive, nonlinear wave equation for the porosity (magma volume fraction) or crosssectional area, respectively. Whitham averaging theory for step initial conditions is used to compute analytical, closed form predictions for the DSW speeds and the leading edge amplitude in terms of the constitutive parameters and initial jump height. Novel physical behaviors are identified including backflow and DSW implosion for initial jumps sufficient to cause gradient catastrophe in the Whitham modulation equations. Theoretical predictions are shown to be in excellent agreement with long-time numerical simulations for the case of small to moderate amplitude DSWs. Verifiable criteria identifying the breakdown of this modulation theory in the large jump regime, applicable to a wide class of DSW problems, are presented.

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Solitary waves in magma dynamics

Cited by 76 publications

References 14 publications

Melt flow in a variable viscosity matrix

Melt flow in a variable viscosity matrix

Decompaction weakening and channeling instability in ductile porous media: Implications for asthenospheric melt segregation

Dispersive shock waves in viscously deformable media

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