Fig. 2

Relationship between the plate size, aspect ratio, plate motion, and toroidal/poloidal ratio, based on several idealized cases. Top idealized plate boundary and its motion. All the plates have the same Euler pole at the North pole, and the induced eastward plate motions are represented by orange vectors. a a square plate (\(60^\circ \times 60^\circ \)), b a rectangular plate (\(30^\circ \times 90^\circ \)), c a small rectangular plate with the same aspect ratio as in (b) (\(10^\circ \times 30^\circ \)) and d a rectangular plate with a smaller aspect ratio than (b) and (c) (i.e., closer to square, \(30^\circ \times 60^\circ \)). Bottom toroidal/poloidal (T/P) ratios for the plate motions of (a–d). Compared to the square plate (a) that has almost equal toroidal–poloidal power, i.e., T/P ratio \({\sim }1\), the rectangular plate (b) shows increased T/P ratios at higher spherical harmonic degrees (i.e., finer scale of motion). For the rectangular plate (d), the T/P ratio is smaller compared with (b), which suggests that the aspect ratio affects the amplitude of toroidal–poloidal spectra (a larger aspect ratio increases the T/P ratio). In addition, the small rectangular plate (c) shows significantly increased T/P ratios at even higher spherical harmonic degrees compared with (b) and (d)