On the Dynamics of Two-Dimensional Capillary-Gravity Solitary Waves with a Linear Shear Current

Figure 5

(a) Unstable elevation solitary wave with 𝑦(0)=0.2047, 𝑐=1.4897, and 𝜔=0.2.5% amplitude-decreasing perturbation is applied, and it finally evolves into a depression wave with some radiations. The plots are shown for 𝑡=0,125,300 from top to bottom; (b) stable large amplitude elevation wave with 𝑦(0)=0.05, 𝑐=1.2093, and 𝜔=−0.2. 5% amplitude-decreasing perturbation is applied, 𝑡=0, 1000, 2000 from top to bottom. The frame is moved with the original propagating speed 𝑐.

(a)

(b)