Figure 9.

Dynamical constraints expressed in terms of a dimensionless ‘coefficient of meridional diffusion’ in the spirit of Lorenz et al. (2001). The effect of the dynamical constraints introduced in the present paper is to introduce a threshold value of d which cannot be exceeded. (The level of the threshold depends on the planetary parameters ω and ξ. In this illustration the threshold is 20.) Planets above the critical line in figure 2 have thresholds greater than 1, allowing the LEB solution to be obtained. Planets below the critical line in figure 2 have thresholds less than 1, meaning that the LEB solution cannot be obtained (solid line, ; dashed line, f_a; dotted line, t_ep; dash-dotted line, dynamical constraint).