THE 3-DIMENSIONAL GEOMETRY OF SIMULATED PORPHYROBLAST INCLUSION TRAILS - INERT-MARKER, VISCOUS-FLOW MODELS

A fluid dynamic model for a rigid spherical porphyroblast growing in a viscous fluid matrix undergoing simple shear deformation predicts an arrangement of captured inert inclusions that is remarkably similar to the spiral pattern observed in synkinematic 'rolled' garnets. The model assumes only creeping (Stokes) flow of the matrix and a kinetic model for the growth of the porphyroblast of the form r(m) = k(m)OMEGA, where r is the crystal radius, OMEGA is the amount of shear-induced rotation, and m and k are kinetic parameters. For rotation less than 180-degrees, J. B. Thompson and J. L. Rosenfeld's simple ring-model provides a surprisingly accurate description of the three-dimensional geometry of the central inclusion surface in the simulated porphyroblasts. Although marker planes, originally parallel to the shear plane, are deflected around the porphyroblast, their intersections with its surface remain approximately circular for much larger amounts of rotation than anticipated by Rosenfeld. The polar coordinate equation, T(r, theta), of the double spiral formed by the trace of the central inclusion surface in a section through the centre of simulated porphyroblasts, is also surprisingly simple, as follows: r(m) almost-equal-to (6/5k)(m)theta. This relationship was observed over the complete range of rotation angles investigated, 0-720-degrees, and could form a reasonable basis for estimating the growth-rotation history of rolled garnets from the shape of their spiral inclusion trails. Two-dimensional sections through the simulated porphyroblasts, parallel to the rotation axis, yield 'clamshell' (Rosenfeld's term) inclusion geometries similar to the controversial 'millipede' patterns observed in many natural porphyroblasts.