TY - JOUR

T1 - Instability of an anisotropic power-law fluid in a basic state of plane flow

AU - Fletcher, Raymond C.

N1 - Funding Information:
This work was supported by NSF grant OPP-9815160. Many years ago, the author was inspired by a defective copy of John Ramsay's Folding and Faulting of Rock, in which a figure of a deformed trilobite was superposed on a Mohr's circle, to give up paleontology and study the physics of ductily deformed rocks. Reviews by Peter Cobbold and Martin Casey and comments by the editor Peter Hudleston (all three among the distinguished former students of John Ramsay) are greatly appreciated, and led to significant improvement of the paper.

PY - 2005/7

Y1 - 2005/7

N2 - Initiation of cylindrical structures by buckling or necking in an anisotropic power-law fluid is treated for general plane flow. The principal axis of anisotropy, x′, in the stiffest direction in shortening or extension may be viewed as the trace of a foliation or lamination. Plane-flow constitutive relations between components of rate of deformation, D′xx and D′xy, and of deviatoric stress, s′xx and s′xy, for the fluid are D′xx = B(Y′2[(n-1)/2]s′xx and D′xy = a2 B(Y′2 [(n-1)sol;2]s′xy, where Y′2 = (s′xx)2 + a2(s′xy)2 is an anisotropic invariant, a2 is the anisotropy parameter, and n is the stress exponent. We determine the rate of amplification of wavelength components in the deflection of the foliation, θ, from a mean orientation parallel to x. Linearly independent, or non-interacting normal modes have a periodic, band-like form θ(x,y) ≅ ∂ζ/∂x = -(λ A) sin[λ (x - vy)], where ζ is the height of a foliation trace above its mean plane, v=tanβ, where β is the angle between the normal to mean foliation and the axial surface, positive clockwise, and L=2π/λ is the foliation-parallel wavelength. Evolution of a component may be followed through a finite bulk deformation provided θ remains ≪1. The growth rate of slope, λA, is independent of L. Components with axial plane normal to the foliation (β=0) are strongly amplified in foliation-parallel shortening. If n > > 1, internal necking (boudinage) occurs in foliation-parallel extension for components with axial plane inclined at a large angle to the foliation normal. In combined shortening and shear, the most rapidly growing component has an axial plane that dips steeply in the direction of shear. For n>1, maximum instability occurs for combined foliation-parallel shear and shortening rather than pure shortening. Weak instability is present in foliation-parallel shear. This anisotropic nonlinear fluid approximates the behavior of an isotropic power-law medium containing preferentially oriented but anastomosing slip surfaces, or that of a rock in which a stiffer component of lenticular form is embedded in a softer matrix.

AB - Initiation of cylindrical structures by buckling or necking in an anisotropic power-law fluid is treated for general plane flow. The principal axis of anisotropy, x′, in the stiffest direction in shortening or extension may be viewed as the trace of a foliation or lamination. Plane-flow constitutive relations between components of rate of deformation, D′xx and D′xy, and of deviatoric stress, s′xx and s′xy, for the fluid are D′xx = B(Y′2[(n-1)/2]s′xx and D′xy = a2 B(Y′2 [(n-1)sol;2]s′xy, where Y′2 = (s′xx)2 + a2(s′xy)2 is an anisotropic invariant, a2 is the anisotropy parameter, and n is the stress exponent. We determine the rate of amplification of wavelength components in the deflection of the foliation, θ, from a mean orientation parallel to x. Linearly independent, or non-interacting normal modes have a periodic, band-like form θ(x,y) ≅ ∂ζ/∂x = -(λ A) sin[λ (x - vy)], where ζ is the height of a foliation trace above its mean plane, v=tanβ, where β is the angle between the normal to mean foliation and the axial surface, positive clockwise, and L=2π/λ is the foliation-parallel wavelength. Evolution of a component may be followed through a finite bulk deformation provided θ remains ≪1. The growth rate of slope, λA, is independent of L. Components with axial plane normal to the foliation (β=0) are strongly amplified in foliation-parallel shortening. If n > > 1, internal necking (boudinage) occurs in foliation-parallel extension for components with axial plane inclined at a large angle to the foliation normal. In combined shortening and shear, the most rapidly growing component has an axial plane that dips steeply in the direction of shear. For n>1, maximum instability occurs for combined foliation-parallel shear and shortening rather than pure shortening. Weak instability is present in foliation-parallel shear. This anisotropic nonlinear fluid approximates the behavior of an isotropic power-law medium containing preferentially oriented but anastomosing slip surfaces, or that of a rock in which a stiffer component of lenticular form is embedded in a softer matrix.

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U2 - 10.1016/j.jsg.2004.08.002

DO - 10.1016/j.jsg.2004.08.002

M3 - Article

AN - SCOPUS:23944439639

VL - 27

SP - 1155

EP - 1167

JO - Journal of Structural Geology

JF - Journal of Structural Geology

SN - 0191-8141

IS - 7

ER -