Figure 10

Time constant of exponential growth in wave amplitude. The e-folding time for the amplitude of linearly unstable antisymmetric solution to grow is plotted as a function of the peak flow speed at the center of the fluid layer. Calculation results are shown for three wavelengths of L^∗ = 3.2 km (solid line), 1.6 km (broken line), and 0.8 km (dotted line) and for four fluid viscosities of ζ^∗ = 10⁴ Pa ·s (black line), 10³ Pa ·s (red line), 10² Pa ·s (blue line), and 10 Pa ·s (orange line). In these examples, we set${\alpha }_0^{\ast }=1$ km/s,${\beta }_{\mathrm{s}}^{\ast }=2.5$ km/s,${\alpha }_{\mathrm{s}}^{\ast }=4.3$ km/s,${\rho }_{\mathrm{s}}^{\ast }={\rho }_0^{\ast }=2700$ kg/m ³, δ = 0.5, and the fluid layer thickness, 2a^∗, is (a) 0.2 m, (b) 0.5 m, and (c) 1 m.