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

Published online by Cambridge University Press:  03 November 2011

James Flinders  and
John D. Clemens
James Flinders
Affiliation:
James Flinders, Department of Earth Sciences, The University of Manchester, Oxford Road, Manchester M13 9PL, U.K.
John D. Clemens
Affiliation:
John D. Clemens, School of Geological Sciences, Kingston University, Penrhyn Road, Kingston-upon-Thames, Surrey KT1 2EE, U.K.
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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.

Keywords

linearisationnon-linear dynamicsinterfacesstriationdeterministic chaostemporal evolutionfractals

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