FRACTAL FEATURES IN MIXING OF NON-NEWTONIAN AND NEWTONIAN MANTLE CONVECTION

Mixing processes in mantle convection depend on the theology. We have investigated the dynamical differences for both non-Newtonian and Newt onian rheologies on convective mixing for similar values of the effect ive Rayleigh number. A high-resolution grid, consisting of up to 1500 X 3000 bi-cubic splines, was employed for integrating the advection pa rtial differential equation, which governs the passive scalar field ca rried by the convecting velocity. We show that, for similar magnitudes of the averaged velocities and surface heat flux, the local patterns of mixing are quite different for the two theologies. There is a great er richness in the scales of the spatial heterogeneities of the passiv e scalar field exhibited by the non-Newtonian flow. We have employed t he box-counting technique for determining the temporal evolution of th e fractal dimension, D, passive scalar field of the two theologies. We have explained theoretically the development of different regimes in the plot of N, the number of boxes, covered by a range of colors in th e passive scalar field, and S, the grid size used in the box-counting. Mixing takes place in several stages. There is a transition from a fr actal type of mixing, characterized by islands and clusters to the com plete homogenization stage. The manifestation of this transition depen ds on the scales of the observation, and the initial heterogeneity and on the theology. Newtonian mixing is homogenized earlier for long-wav elength observational scales, while a very long time would transpire b efore this transition would take place for non-Newtonian rheology. The se results show that mixing dynamics in the mantle have properties ger mane to fluid turbulence and self-similar scaling.