A scaling law for approximating porous hydrothermal convection by an equivalent thermal conductivity: Theory and application to the cooling oceanic lithosphere

Abstract

In geodynamic models of mid-ocean ridges hydrothermal cooling processes are important to control the temperature and thus the rheological behaviour of the crust. However, the characteristic time scale of hydrothermal convection is considerably shorter than that of viscous flow of mantle material or cooling of the oceanic lithosphere and can hardly be addressed in a conjoined model. To overcome this problem we present an approach to mimic hydrothermal cooling by an equivalent, increased thermal conductivity. First the temperature and pressure dependence of crack related porosity and permeability are derived based on composite theory. A characteristic pore closure depth as a function of pressure, temperature and pore aspect ratio is defined. 2-D porous convection models are used to derive scaling laws for parameterized convection including a Rayleigh-Nusselt number relation for a permeability exponentially decreasing with depth. These relations are used to derive an equivalent thermal conductivity to account for consistently evolving hydrothermal heat transport in thermally evolving systems. We test our approach using a 1-D model for cooling of the oceanic lithosphere. Within the context of our modelling parameters we found a pronounced effect for young lithosphere (younger than 10 Ma) down to about 20 km. Significant deviations of the heat flux versus age from the 1/√t law may occur due to hydrothermal convection. For the bathymetry versus age curves slopes steeper than 1/√t slopes already occur for very young lithosphere. Hydrothermal convection leads to an increase of the total heat flux and heat loss with respect to the classical purely conductive cooling model. Comparison of the total heat flow and its conductive contribution with observations confirm previous suggestions that for young lithosphere heat flow measurements represent only the conductive part, while at older ages the total heat flow is observed. Within their scatter and uncertainties heat flow and bathymetry data are in general agreement with our hydrothermally enforced cooling model suggesting that hydrothermal convection may be important even up to high ages. © The Authors 2014. Published by Oxford University Press on behalf of The Royal Astronomical Society.