Large aspect ratio cells in two-dimensional thermal convection |
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| Authors: | JM Hewitt DP McKenzie NO Weiss |
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| Institution: | Bullard Laboratories, Department of Earth Sciences, Madingley Rise, Madingley Road, Cambridge CB3 0EZ, U.K.;Department of Applied Mathematics and Theoretical Physics, Silver Street, Cambridge CB3 9EW, U.K. |
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| Abstract: | Numerical experiments have been carried out on two-dimensional thermal convection, in a Boussinesq fluid with infinite Prandtl number, at high Rayleigh numbers. With stress free boundary conditions and fixed heat flux on upper and lower boundaries, convection cells develop with aspect ratios (width/depth) λ? 5, if heat is supplied either entirely from within or entirely from below the fluid layer. The preferred aspect ratio is affected by the lateral boundary conditions. If the temperature, rather than the heat flux, is fixed on the upper boundary the cells haveλ ≈ 1. At Rayleigh numbers of 2.4 × 105 and greater, small sinking sheets are superimposed on the large aspect ratio cells, though they do not disrupt the circulation. Similar two-scale flows have been proposed for convection in the earth's mantle. The existence of two scales of flow in two-dimensional numerical experiments when the viscosity is constant will allow a variety of geophysically important effects to be investigated. |
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