### 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} = (l^{2} + m^{2})H^{2} = 2π[( 1 L_{x})^{2} + ( 1 L_{y})^{2}]H^{2}, where L_{x} and L_{y} are the wavelengths in the horizontal directions x and y, the aspect ratio /vbv/vb = /vb m l/vb = L_{x} L_{y}, 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)ζ^{2}(1 + ζ + ζ^{2})^{-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 = 10^{4}) than for a viscous layer (n = 1), at the same amplification.

Original language | English (US) |
---|---|

Pages (from-to) | 65-83 |

Number of pages | 19 |

Journal | Tectonophysics |

Volume | 247 |

Issue number | 1-4 |

DOIs | |

State | Published - Jul 30 1995 |

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### All Science Journal Classification (ASJC) codes

- Geophysics
- Earth-Surface Processes

### Cite this

*Tectonophysics*,

*247*(1-4), 65-83. https://doi.org/10.1016/0040-1951(95)00021-E

}

*Tectonophysics*, vol. 247, no. 1-4, pp. 65-83. https://doi.org/10.1016/0040-1951(95)00021-E

**Three-dimensional folding and necking of a power-law layer : are folds cylindrical, and, if so, do we understand why?** / Fletcher, Raymond C.

Research output: Contribution to journal › Article

TY - JOUR

T1 - Three-dimensional folding and necking of a power-law layer

T2 - are folds cylindrical, and, if so, do we understand why?

AU - Fletcher, Raymond C.

PY - 1995/7/30

Y1 - 1995/7/30

N2 - 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.

AB - 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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U2 - 10.1016/0040-1951(95)00021-E

DO - 10.1016/0040-1951(95)00021-E

M3 - Article

AN - SCOPUS:0029480753

VL - 247

SP - 65

EP - 83

JO - Tectonophysics

JF - Tectonophysics

SN - 0040-1951

IS - 1-4

ER -