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Nonlinear mode analysis of periodic roll waves and wave splitting

ABSTRACT This paper describes the characteristics of the formation of periodic roll waves and the splitting of waves based on nonlinear mode analysis. A novel system is developed to investigate the formation of roll waves through linear and nonlinear modal analyses. The nonlinear analysis shows the feasibility of the periodic roll waves and their splitting when the wavenumber is extremely small. It is observed that there are phase shifts in each term of the momentum equation for the periodic roll waves. The phase of the nonlinear convection term in the fundamental mode is shifted forward relative to the phase of the linear convective term, and it acts as the viscosity term. In contrast, the phase of the nonlinear convection term in the higher mode is delayed, and it acts as the friction term. At a smaller wavenumber, the phase shift in the nonlinear interaction between the fundamental and second modes leads to the suppression of the fundamental mode development, resulting in the wave splitting.