Planform of small-scale convection under the island arc

We have proposed an existence of small-scale convection in the mantle wedge in order to explain the alignment of group of volcanoes in the NE Honshu subduction zone, Japan. The roll type thermal convection whose axis is normal to the plate boundaries and "flip-flopping" of rolls (warmer and colder parts exchange their positions, as time passes) are reported. However, the subsequent study shows an existence of non-flip-flopping rolls, also. Thus, in this study, I investigate the possible causes of these differences systematically. I found that along-arc wavelength of small-scale convection is controlled by two length scales which may be associated with the inclined nature of the bottom of the low viscosity mantle wedge where the small-scale convection emerges. When the convection is in early stage of evolvement or the speed of subducting slab is small, the long-wavelength rolls become prominent. As the convection evolves or the speed of subduction increases, short-wavelength rolls tend to take over the long-wavelength rolls. The transition from the long-wavelength to the short-wavelength rolls occurs in a several way. It may occur through the splitting of rolls, adjustment of roll patterns and flip-flopping. If the pattern becomes short-wavelength roll, it becomes stable. The range of existence of flip-flopping is limited and the existence of viscosity jump in the top thermal boundary layer may be required.