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 = (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.