Non-linear dynamics, chaos, complexity and enclaves in granitoid magmas

Abstract

ABSTRACT:Most natural systems display non-linear dynamic behaviour. This should be true for magma mingling and mixing processes, which may be chaotic. The equations that most nearly represent how a chaotic natural system behaves are insoluble, so modelling involves linearisation. The difference between the solution of the linearised and ‘true’ equation is assumed to be small because the discarded terms are assumed to be unimportant. This may be very misleading because the importance of such terms is both unknown and unknowable. Linearised equations are generally poor descriptors of nature and are incapable of either predicting or retrodicting the evolution of most natural systems. Viewed in two dimensions, the mixing of two or more visually contrasting fluids produces patterns by folding and stretching. This increases the interfacial area and reduces striation thickness. This provides visual analogues of the deterministic chaos within a dynamic magma system, in which an enclave magma is mingling and mixing with a host magma. Here, two initially adjacent enclave blobs may be driven arbitrarily and exponentially far apart, while undergoing independent (and possibly dissimilar) changes in their composition. Examples are given of the wildly different morphologies, chemical characteristics and Nd isotope systematics of microgranitoid enclaves within individual felsic magmas, and it is concluded that these contrasts represent different stages in the temporal evolution of a complex magma system driven by nonlinear dynamics. If this is true, there are major implications for the interpretation of the parts played by enclaves in the genesis and evolution of granitoid magmas.

The space and time complexity of chaotic mixing of silicate melts: Implications for igneous petrology

“…An effective conceptual framework, one which is capable of addressing the complexity inherent to this highly non-linear process, is the investigation of mixing processes via Chaos Theory (e.g. Bergantz, 2000;De Campos et al, 2011;Flinders and Clemens, 1996;Perugini et al, 2003cPerugini et al, , 2008. This approach reduces the study of magma mixing to the consideration of stretching and folding dynamics as the basic forces dispersing magmas (e.g.…”

The mixing of magmas in plutonic and volcanic environments: Analogies and differences

“…Flinders and Clemens, 1996). Unfortunately, such a jargon is not consistently used in the literature and this produced some misunderstanding.…”

“…Flinders and Clemens, 1996, Perugini et al, 2003a. From a kinematic point of view, the mixing of magmas is governed by the same stretching and folding processes which are responsible for (a) the development of chaotic dynamics in fluid mixing systems and (b) the production of scale invariant (fractal) patterns, down to the micron-length scale.…”

A virtual voyage through 3D structures generated by chaotic mixing of magmas and numerical simulations: a new approach for understanding spatial and temporal complexity of magma dynamics

“…In particular, the fingerprint of chaotic dynamics and the production of fractal patterns has been widely documented in both volcanic and plutonic rocks (e.g. Flinders and Clemens 1996;De Rosa et al 2002;Poli and Perugini 2002;Perugini et al 2003aPerugini et al , 2004. These studies focused on the analysis of magmatic enclaves (e.g.…”