Long waves over a bi-viscous seabed: transverse patterns

The coupled interaction of long standing hydrodynamic waves with a deformable non-Newtonian seabed is examined using a two-layer model for which the upper layer fluid is inviscid and the lower layer is bi-viscous. The two-dimensional response of the system to forcing by a predominantly longitudinal (cross-shore) standing wave perturbed by a small transverse (along-shore) component is determined. With a constant yield stress in the bi-viscous lower layer, there is little amplification of these transverse per-turbations and the model response typically remains quasi-one-dimensional. However, for a bi-viscous layer with a pressure-dependent yield stress (which represents the effect that the seabed deforms less readily under compression and hence renders the rheology history dependent), the initially small transverse motions are amplified in some parameter regimes and two-dimensional, permanent bedforms are formed in the lower layer. This simple dynamical model is, therefore, able to explain the formation of permanent bedforms with significant cross- and along-shore features by predominantly cross-shore standing wave forcing

Melt-band instabilities with two-phase damage

Deformation experiments on partially molten rocks in simple shear form melt bands at 20◦ to the shear plane instead of at the expected 45◦ principal compressive stress direction. Thesemelt bands may play an important role in melt focusing in mid-ocean ridges. Such shallow bands are known to form for two-phase media under shear if strongly non-Newtonian power-law creep is employed for the solid phase, or anisotropy imposed. However laboratory experiments show that shallow bands occur regardless of creep mechanism, even in diffusion creep, which is nominally Newtonian. Here we propose that a couple of forms of two-phase damage allow for shallow melt bands even in diffusion creep.Support was provided by the National Science Foundation (NSF, grant EAR-1015229), the Natural Environment Research Council (NERC, grant NE/I023929/1) and Trinity College.This is the final published version. This article has been accepted for publication in Geophysical Journal International ©: 2015 the Authors. Published by Oxford University Press on behalf of the Royal Astronomical Society. All rights reserved

A mechanism for mode selection in melt band instabilities

The deformation of partially molten mantle in tectonic environments can lead to exotic structures, which potentially affect both melt and plate-boundary focussing. Examples of such structures are found in laboratory deformation experiments on partially molten rocks. Simple-shear and torsion experiments demonstrate the formation of concentrated melt bands at angles of around 20° to the shear plane. The melt bands form in the experiments with widths between a few to tens of microns, and a band spacing roughly an order of magnitude larger. Existing compaction theories, however, cannot predict this band width structure, let alone any mode selection, since they infer the fastest growing instability to occur for wavelengths or bands of vanishing width. Here, we propose that surface tension in the mixture, especially on a diffuse interface in the limit of sharp melt-fraction gradients, can mitigate the instability at vanishing wavelength and thus permit mode selection for finite-width bands. Indeed, the expected weak capillary forces on the diffuse interface lead to predicted mode selection at the melt-band widths observed in the experiments.The authors sincerely thank Sam Butler and Ben Holtzman for thoughtful reviews. Support was provided by the National Science Foundation (NSF, grant EAR-1344538), the Natural Environment Research Council (NERC, grant NE/I023929/1) and Trinity College.This is the final version of the article. It first appeared from Elsevier via http://dx.doi.org/10.1016/j.epsl.2015.10.05

Long waves over a bi-viscous seabed: transverse patterns

International audienceThe coupled interaction of long standing hydrodynamic waves with a deformable non-Newtonian seabed is examined using a two-layer model for which the upper layer fluid is inviscid and the lower layer is bi-viscous. The two-dimensional response of the system to forcing by a predominantly longitudinal (cross-shore) standing wave perturbed by a small transverse (along-shore) component is determined. With a constant yield stress in the bi-viscous lower layer, there is little amplification of these transverse per-turbations and the model response typically remains quasi-one-dimensional. However, for a bi-viscous layer with a pressure-dependent yield stress (which represents the effect that the seabed deforms less readily under compression and hence renders the rheology history dependent), the initially small transverse motions are amplified in some parameter regimes and two-dimensional, permanent bedforms are formed in the lower layer. This simple dynamical model is, therefore, able to explain the formation of permanent bedforms with significant cross- and along-shore features by predominantly cross-shore standing wave forcing