Three-dimensional folding and necking of a power-law layer: are folds cylindrical, and, if so, do we understand why?

Raymond C. Fletcher

Research output: Contribution to journalArticle

42 Citations (Scopus)

Abstract

The rate of amplification of a general component, A cos(lx) cos(my), in the folding or necking of a single layer of power-law fluid embedded in a viscous medium depends on the dimensionless separation constant (λH)2 = (l2 + m2)H2 = 2π[( 1 Lx)2 + ( 1 Ly)2]H2, where Lx and Ly are the wavelengths in the horizontal directions x and y, the aspect ratio /vbv/vb = /vb m l/vb = Lx Ly, the ratio of the in-plane principal rates of deformation of the basic-state flow, ζ = D ̄yy D ̄xx, the stress exponent, n, and a ratio, R, between the strengths, or effective viscosities of the medium and layer. The present treatment excludes basic-state layer-parallel shear: D ̄xz = D ̄yz = 0. For a cylindrical perturbation with axis parallel to y (m = 0), the non-kinematic contribution to the growth rate is the same as that for the plane-flow case (ζ = 0), but with the intrinsic stress-exponent replaced by an apparent value n* = 4n[4 + 3(n - 1)ζ2(1 + ζ + ζ2)-1]. A value of 'n' estimated from the conventional interpretation of data from a set of single-layer folds is better interpreted as an estimate of the apparent value, n*. The simultaneous development of folds and pinch-and-swell structures at right angles to each other is difficult, discounting possible effects of strain-softening. In a basic state of plane flow (ζ = 0), simulated three-dimensional fold arrays show markedly greater fold aspect ratios for a plastic layer (n = 104) than for a viscous layer (n = 1), at the same amplification.

Original languageEnglish (US)
Pages (from-to)65-83
Number of pages19
JournalTectonophysics
Volume247
Issue number1-4
DOIs
StatePublished - Jul 30 1995

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folding
power law
fold
aspect ratio
amplification
exponents
swell
softening
plastic deformation
plastics
viscosity
plastic
perturbation
shear
wavelength
fluid
fluids
estimates
wavelengths
rate

All Science Journal Classification (ASJC) codes

  • Earth-Surface Processes
  • Geophysics

Cite this

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title = "Three-dimensional folding and necking of a power-law layer: are folds cylindrical, and, if so, do we understand why?",
abstract = "The rate of amplification of a general component, A cos(lx) cos(my), in the folding or necking of a single layer of power-law fluid embedded in a viscous medium depends on the dimensionless separation constant (λH)2 = (l2 + m2)H2 = 2π[( 1 Lx)2 + ( 1 Ly)2]H2, where Lx and Ly are the wavelengths in the horizontal directions x and y, the aspect ratio /vbv/vb = /vb m l/vb = Lx Ly, the ratio of the in-plane principal rates of deformation of the basic-state flow, ζ = D ̄yy D ̄xx, the stress exponent, n, and a ratio, R, between the strengths, or effective viscosities of the medium and layer. The present treatment excludes basic-state layer-parallel shear: D ̄xz = D ̄yz = 0. For a cylindrical perturbation with axis parallel to y (m = 0), the non-kinematic contribution to the growth rate is the same as that for the plane-flow case (ζ = 0), but with the intrinsic stress-exponent replaced by an apparent value n* = 4n[4 + 3(n - 1)ζ2(1 + ζ + ζ2)-1]. A value of 'n' estimated from the conventional interpretation of data from a set of single-layer folds is better interpreted as an estimate of the apparent value, n*. The simultaneous development of folds and pinch-and-swell structures at right angles to each other is difficult, discounting possible effects of strain-softening. In a basic state of plane flow (ζ = 0), simulated three-dimensional fold arrays show markedly greater fold aspect ratios for a plastic layer (n = 104) than for a viscous layer (n = 1), at the same amplification.",
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Three-dimensional folding and necking of a power-law layer : are folds cylindrical, and, if so, do we understand why? / Fletcher, Raymond C.

In: Tectonophysics, Vol. 247, No. 1-4, 30.07.1995, p. 65-83.

Research output: Contribution to journalArticle

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