The Intrinsic Sensitivity of the Wave-Merger Problem

A nonlinear deterministic dynamical system is built for the wave-merger problem, in which two separate vorticity centers interact with each other within a confluent background flow. The sensitive region of the wave-merger problem in parameter space was found analytically. When the initial conditions of the two vortices and background flow of the system is close to the sensitive region, a very small difference in initial state can make the system evolve along completely different paths. This sensitivity is identified with the initial distance of the two centers, the initial azimuth and the ratio of the strength of the confluent flow over the sum of the strength of the two vorticity centers. Numerical simulations and available observations support the theoretical findings very well.