Figure 31
Top figures: ratio of yield stress for Arrhenius viscosity to that for exponential viscosity R τ and \(R_{\tau ^{\prime }}\) as a function of Arrhenius viscosity contrast normalized to exponential viscosity contrast Δ η Arr/ exp(θ). Δ η Arr/ exp(θ)≥1, and it can go up to many orders of magnitude. Bottom figures: ratio of yield stress multiplied by θ. For cases with the same θ but various Ra and a, these ratios do not differ much, meaning that θ is the controlling factor for the difference in yield stress predicted by Arrhenius viscosity and exponential viscosity. Asymptotically towards high Δ η Arr/ exp(θ), R τ and R τ′ are approximately proportional to θ.