3-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 (lambda H)(2) = (l(2) + m(2))H-2 = 2 pi[(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 \upsilon\ = \m/l\ = L(x)/L(y), the ratio of the in-plane principal rates of deformation of the basic-state flow, xi = ($) over bar D-yy/($) over bar 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: ($) over bar D-xz = ($) over bar 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 (xi = 0), but with the intrinsic stress-exponent replaced by an apparent value n* = 4n[4 + 3(n - 1)xi(2)(1 + xi + xi(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 (xi = 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.