## Appendix B. The change of the number of crossing modes with the change of meridional width of computational domain

In section 5.2, it is discussed that the existence of computational domain outside the inertially unstable region causes crossing modes. In this section, with a series of results in which computational domains are enlarged gradually from the case only with the inertially unstable region, it is shown that the number of crossing modes increases with enlarging the meridional extent of the computational domain.

Table B-1 is a summary of the number of crossing modes for various meridional width of the computational domain. Figure shown in each case is dispersion curves for log E=7.50. Under this value of E, there exist only the dispersion curves of crossing modes outside of dispersion curves of continuous modes. Adding a grid point outside the inertially unstable region 0 ≤ y ≤ 1 causes an eastward crossing mode, an westward crossing mode, and a continuous mode.

Table B-1: Summary of the number of crossing modes for various meridional width of the computational domain. Left column shows a series of results in which computational domains are enlarged northward from the case with 0 ≤ y ≤ 1. Right column shows a series of results in which computational domains are enlarged southward from the case with 0 ≤ y ≤ 1. Figure shown in each case is dispersion curves for log E=7.50. Click the figure to show a larger figure. Click [Animation] to show dispersion curves for various values of E .

 Domain sizeNumber of gridAnimation figure (link) Number of crossing modes Dispersion curves(log E=7.50) +0.00 < y < +1.00(number of grid: 13)[Animation] eastward: 0 westward: 0 +0.00 < y < +1.20(number of grid: 16)[Animation] eastward: 2 westward: 2 +0.00 < y < +1.40(number of grid: 19)[Animation] eastward: 5 westward: 5 +0.00 < y < +1.60(number of grid: 22)[Animation] eastward: 8 westward: 8 +0.00 < y < +1.80(number of grid: 25)[Animation] eastward: 11 westward: 11 +0.00 < y < +2.00(number of grid: 28)[Animation] eastward: 14 westward: 14 +0.00 < y < +2.20(number of grid: 31)[Animation] eastward: 16 westward: 16 +0.00 < y < +2.40(number of grid: 34)[Animation] eastward: 19 westward: 19 +0.00 < y < +2.60(number of grid: 37)[Animation] eastward: 22 westward: 22 +0.00 < y < +2.80(number of grid: 40)[Animation] eastward: 25 westward: 25 +0.00 < y < +3.00(number of grid: 43)[Animation] eastward: 28 westward: 28
 Domain sizeNumber of gridAnimation figure (link) Number of crossing modes Dispersion curves(log E=7.50) +0.00 < y < +1.00(number of grid: 13)[Animation] eastward: 0 westward: 0 -0.20 < y < +1.00(number of grid: 16)[Animation] eastward: 2 westward: 2 -0.40 < y < +1.00(number of grid: 19)[Animation] eastward: 5 westward: 5 -0.60 < y < +1.00(number of grid: 22)[Animation] eastward: 8 westward: 8 -0.80 < y < +1.00(number of grid: 25)[Animation] eastward: 11 westward: 11 -1.00 < y < +1.00(number of grid: 28)[Animation] eastward: 13 westward: 13 -1.20 < y < +1.00(number of grid: 31)[Animation] eastward: 16 westward: 16 -1.40 < y < +1.00(number of grid: 34)[Animation] eastward: 19 westward: 19 -1.60 < y < +1.00(number of grid: 37)[Animation] eastward: 22 westward: 22 -1.80 < y < +1.00(number of grid: 40)[Animation] eastward: 25 westward: 25 -2.00 < y < +1.00(number of grid: 43)[Animation] eastward: 28 westward: 28