Figure 3

Simplification of \({(\cos {{\theta }}_{0})}^{1/4}(4\,{\cot }^{2}{{\theta }}_{0}+1)\) and two-dimensional contour map of \({v}({\theta },{H})\) as a function of θ and H. (a) Numerical calculations of \({(\cos {\theta }_{0})}^{1/4}\), \((4\,{\cot }^{2}{\theta }_{0}+1)\), and \({(\cos {\theta }_{0})}^{1/4}(\,4\,{\cot }^{2}{\theta }_{0}+1)\) as a function of θ ₀. (b) Two-dimensional contour map of \(v(\theta ,H)\) plotted with respect to θ and H. The colour contrast represents the value of \(\mathrm{log}(v)\) with scale bar on the right lower end. The purple solid line is the numerical evaluation of Eq. (3). The black dashed lines guide the eyes to the equi-speed contours.