## Introduction

Spiral inclusion trails have been previously used for the interpretation of shear sense (e.g. Bell & Johnson, 1992), fold mechanisms (e.g. Stallard & Hickey, 2001), crenulation development, and the history of microstructural deformation in metamorphic rocks (e.g. Stallard, 1998). Despite the large numbers of publications that have sought to resolve the problematic origin and significance of spirals (e.g. Passchier et al, 1992; Bell et al, 1992), relatively few data have been presented to describe the 3D formation of spirals, or the 3D geometry of spirals (see Johnson, 1993a and Gray & Busa, 1994 for existing 3D data). Reconstructing the 3D spiral geometry, both from real rocks and using numerical simulations, is therefore important for our understanding of the mode of spiral formation, our interpretation of spirals, and for our interpretation of the varied 2D inclusion trail geometries encountered in thin sections containing spiral porphyroblasts.

Early attempts to model the geometry of spiral inclusion trails were either based on simplified mechanical models (Rosenfeld, 1970; Schoneveld, 1977) or conceptual models (Powell & Treagus, 1967, 1970). Masuda & Mochizuki (1989) presented the first 2D numerical simulations of spiral formation, and this was followed by a similar study by Bjornerud & Zhang (1994) and a 3D analysis of the problem by Gray & Busa (1994). Johnson (1993a) used serial sections to reconstruct the 3D geometry of spiral inclusion trails from real rocks, and most recently, Williams & Jiang (1999) provided a conceptual interpretation of the 3D geometry of spiral inclusion trails developed according to the ‘non-rotation’ model of spiral development. The non-rotation model describes spiral formation by irrotational garnet growth over multiple overprinting near-orthogonal foliations or crenulation cleavages (e.g. Bell, 1985; Bell & Johnson, 1989). In contrast, the rotation model predicts progressive capture of a single matrix foliation within a growing porphyroblast that is rotating in response to foliation-parallel shear (e.g. Spry, 1963; Passchier et al., 1992).

This study seeks to extend the work of previous studies by using numerical simulations to document both the 3D development of spirals, and the 3D geometry of the completed simulations. The aim is to assess the varied spiral geometries produced under different simulation conditions, and provide a visual aid to help researchers visualise the 3D development of spirals. Simulations were carried out to represent both the rotation and non-rotation models of spiral development. We also conducted simulations to explore the effect on spiral geometry of varying such factors as: degree of coupling between sphere and matrix, growth rate of sphere, angle between initial foliation and shear plane, and ratio of simple shear to pure shear.