Degree-one mantle convection: Dependence on internal heating and temperature-dependent rheology

[ 1] Geophysical and geological observations suggest that a degree- one mantle flow pattern, consisting of one upwelling and one downwelling, may have existed at some time in the mantles of Mars, the Moon, and perhaps even for the Earth during times of supercontinent formation. Simple fluid experiments utilizing isoviscous rheologies predict shorter wavelength flow patterns, and it is therefore important to determine fluid dynamical parameter sets which lead to larger wavelength flow patterns consistent with observations. We perform a series of numerical fluid dynamics calculations in a spherical 3- D geometry in which we vary Rayleigh number, rheological activation parameter, and the degree of internal heating in order to define which parameter choices can lead to degree- one mantle convection. We find that increasing the degree of internal heating increases the interior temperature of the mantle which leads to a larger viscosity contrast across the top thermal boundary layer, and that degree- one mantle flow occurs only in cases which exhibit internal heating, utilize activation coefficients which lead to 10(3) or higher viscosity contrasts across the mantle, and have viscosity contrasts across the top thermal boundary layer within the range of 200 - 3000.