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

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 L_x)² + ( 1 L_y)²]H², 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)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.