[1] Long-and short-term strain variations along the Australian-Pacific plate boundary through the South Island of New Zealand, including a 300% increase in orogen width, coexistence of oblique thrusting on orthogonal structures, and variability in the locus of orogenic gold deposits, coincide with rheologically relevant geological variation. Our model investigates the consequences of thin, strong lower crust in the north and thick, weak lower crust in the south. Solution of the full 3-D mechanical equations reproduces the larger wavelength strain patterns of the orogen. A 3-D perturbation-based analytical solution leads to the identification of the sensitivity of displacement type to minor stress changes. Transition from boundary-normal thrusting to boundary-parallel thrusting occurs at the transition from strong to weak lower crust and is related to an increase in either t yz (shear stress in the yz plane) or the ratio of the coordinate normal stresses, (s yy /s xx ), where x and y are in the horizontal and z is vertical. Both mechanisms are compatible with the geologically dependent rheological variation employed in our model.
Abstract. We present simple analytical expressions for evaluating three-dimensional stress fields in critical wedges (Coulomb failure throughout) that are deforming within an oblique convergent zone. We assume that the load and geometry variations in the lateral direction, and the topographic slope, are relatively small. The stress state of a two dimensional critical wedge is perturbed by admitting a small lateral shear, which is accommodated (to maintain criticality) by a reduction in the dominant normal compressive stress. Cohesionless cases are further simplified with Taylor series expansions in the topographic slope. The analytical expressions distinguish the behavior of strong base wedges associated with steep slopes from weak base wedges with more modest slopes, and are reliable for lateral shear values as large as half the lithostatic load. In the weak base case where the vertical shear is small, the orientations of the principal stresses are very sensitive to the perturbation. As the lateral shear increases through relatively small values, the roles of the lateral and vertical coordinate axes are interchanged, with a resultant transition from predominantly ttu'ust failure to strike slip failure. Transition to strike slip in the strong base case is more gradual. The particular value of horizontal shear for which transition occurs also depends on the difference of the minor normal stresses. We produce an analytical expression predicting displacement patterns compatible with those observed in natural and analog orogens. Displacement partitioning is predicted for weak base wedges due to minor changes in lateral boundary conditions associated with variable orogen geometry.
Measurements are reported of the fluctuating lift acting on a sphere and the moment acting about the centre of a sphere at supercritical Reynolds numbers (R > 4 × 105). The lift and moment fluctuations are random functions of time which scale with the free-stream dynamic pressure and sphere dimensions. The power spectra of the lift and moment also scale with the above parameters and with the Strouhal number, nd/U. The spectra contain a maximum spectral density at very low frequencies (nd/U < 0·0003) and do not reveal appreciable effects of vortex shedding at discrete frequencies.Hot wire anemometers were placed near the surface but outside the boundary layer along a great circle in the meridian plane in which the lift was measured. The fluctuating velocity component near the surface on the upstream hemisphere in this meridian plane is highly correlated with the fluctuating lift in the same meridian plane. The correlation betweeen the lift and tangential velocity near the surface suggests that the fluctuating lift is produced by the component of fluctuating bound vorticity about the sphere that is normal to the meridian plane in which the lift force is measured. The fluctuating moment measured about an axis passing through the centre of the sphere and perpendicular to the above meridian plane is almost perfectly correlated with the fluctuating lift (the measured correlation coefficients were 0·99 and 1·00). The fluctuating moment coefficient is very small ($\sqrt{C^2_m}\simeq 5\times 10^{-4}$) compared to the fluctuating lift coefficient ($\sqrt{C^2_L}\simeq 6\times 10^{-2}$). The exceptional correlation between the random lift and moment suggests that the unsteady moment about the sphere centre (which can be produced only by shear stress fluctuations) is caused by the fluctuations of bound vorticity (residing in the boundary layer and wake) that are responsible for the unsteady lift.
A theoretical viscoelastic model based on the four-element Burgers model is devel oped to predict changes in load with time of ISO-301 stitched seams under longitudinal loading subjected to extension/recovery cycling at a constant rate of extension. Param eters calculated from experimental stress relaxation curves are used to determine the theoretical relationship between load and time for tensile cycling. The model gives good agreement with experimental stress relaxation behavior of seams over the range 0-30 seconds. Theoretical predictions of load versus time give the best agreement with experimentally derived tensile cycling curves for seams cycled between the lowest extension limits. The exact solution of the theoretical model consists of a double ex ponential expression, suggesting that two processes are responsible for the change in load of seams with tensile cycling, a result consistent with the statistical model for seam ageing and with visual observations described in Part I of this series.
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