Results 2, Entropy Increase Rate

Now we examine whether or not the maximization hypothesis of entropy increase rate is consistent with the regime transition between the 2-D and 3-D regimes. In contrast to Fig. 1, which has nondimensional ordinate and abscissa, an entropy increase rate is a dimensional variable, and hence we examine it in dimensional parameter space. Thus, the entropy increase rates for 93 experiments, which have constant heat flux of 800 W m^-2, are shown in Fig. 3 in a common-logarithm space of the Coriolis parameter and eddy diffusion coefficient.

Figure 3 shows that the entropy increase rate takes its minimal value around the separation curve between the 2-D and 3-D regimes in the perpendicular direction to the curve, for the most of the parameter range where is larger than three (< 10^-3). For the region where is smaller than three, although the entropy increase rate does not take its minimum at the separation curve, the gradient of the entropy increase rate is still different across the 2-D and 3-D regimes in a consistent manner with the hypothesis as seen in the right panel in Fig. 1. Consequently, the changes of entropy increase rates associated with the 2-D and 3-D transition support the hypothesis, suggesting that the mechanism determining the 2-D and 3-D transition can be understood from considerations of macroscopic thermodynamics.

Figure 3. Common logarithm of entropy increase rates, , in units of W/K (black contour) and the separation curve between the 2-D and 3-D regimes with the 2-D regime on the left hand side of the curve in a log-space of the Coriolis parameter and diffusivity. The crosses indicate the parameters where experiments are conducted, with the surface heat flux being fixed at 800 W m^-2. The contour interval is 0.1, and all contour values are negative (i.e., 0<<1).