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Viscous dissipation pattern in incompressible Newtonian simple shear zones: an analytical model

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Abstract

An analytical model of shear heating in an inclined simple shear zone with Newtonian rheology under a reverse shear sense and an upward resultant pressure gradient is presented. Neglecting a number of secondary factors, the shear heat is expressed as a function of the total slip rates at the boundaries, pressure gradient, dip and thickness of the shear zone, and density, viscosity, and thermal conductivity of the rock. A quartic temperature profile develops with a point of maximum temperature near the bottom part of the shear zone in general. The profile is parabolic if pressure gradient vanishes leading to a Couette flow. The profile attains a bell shape if there is no slip at the boundaries, i.e., a true Pouseille flow. The present model of shear heating is more applicable in subduction channels and some extruding salt diapirs where the rheology is Newtonian viscous and pressure gradient drives extrusion.

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Acknowledgments

SM was supported by the Department of Science and Technology (New Delhi), Grant Number: IR/S4/ESF-16/2009(G). Discussions with Djordje Grujic (Dalhousie University) were very fruitful. Chief Editorial handling: Christian Dullo. Managing Editorial works: his wife Monika Dullo. Paris Xypolias (University of Patras) is thanked for providing a positive review. Chris Talbot (retired from Uppsala University) helped improve the English as an informal reviewer in an earlier version.

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  1. Department of Earth Sciences, Indian Institute of Technology Bombay, Powai, Mumbai, 400 076, Maharashtra, India

    Soumyajit Mukherjee

  2. Department of Applied Mathematics, School of Mathematical Sciences, University College, Cork, Ireland

    Kieran F. Mulchrone

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  1. Soumyajit Mukherjee
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  2. Kieran F. Mulchrone
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Correspondence to Soumyajit Mukherjee.

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Mukherjee, S., Mulchrone, K.F. Viscous dissipation pattern in incompressible Newtonian simple shear zones: an analytical model. Int J Earth Sci (Geol Rundsch) 102, 1165–1170 (2013). https://doi.org/10.1007/s00531-013-0879-3

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  • DOI: https://doi.org/10.1007/s00531-013-0879-3

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