Summary

The 157 numerical experiments for open-ocean deep convection revealed that the transition between the 2-D and 3-D regimes occurs across the separation curve in the nondimensional parameter plane of the natural Rossby number and the flux Rayleigh number. This is a refined result for the previously proposed separation line by KM based on 19 experiments.

The distribution of the entropy increase rates is consistent with the maximization hypothesis of entropy increase rate in terms of the 2-D and 3-D regime transition, suggesting that the regime transition can be understood via considerations of macroscopic thermodynamics for a dissipative system. However, for the full understanding of the 2-D and 3-D regime transition, one must prescribe the separation curve based on a theory or scale analysis. The hypothesis may help us to step forward to this final goal.

The visualization of the vorticity and velocity fields showed that some plume structures are not explained by the hetons. Two specific structures, which are the roll structure and the mushroom structure, have been described. The roll structure is characterized by the longer anticyclonic rolls and shorter cyclonic ovals. The anticyclonic rolls are accompanied by the circulation approximately rotating around the roll axis, with a slight tilt from a vertical plane. The cyclonic ovals generally have a stronger vertical component of the vorticity than the anticyclonic rolls. The other structure is the mushroom structure, which consists of the vortex pairs at the top and bottom of the fluid as the hetons. In contrast to the idealistic quasi-stable hetons, the mushroom structure is not temporally stable, but exhibits energetic temporal variability of the structure itself.

The occurrences of the roll and mushroom structures indicate that the plume structures even in the 2-D regime are not explained by idealized hetons, but contain significant variety. In the present study, we employ heuristic and qualitative assessments with the aid of three-dimensional visualization and animation. Such approaches are useful for the finding of new features as described above. However, in order to fully understand the nature of the plume structures, it is desirable to identify the representative structures quantitatively probably on the non-dimensional parameter space, such as shown in Fig. 2, in future studies. Such attempts should form a basis to understand the mechanism of the plume structures.