Temporal secondary stability simulation of Rayleigh-Benard-Poiseuille flow

摘要

The onset of primary and secondary instability has important implications for Rayleigh-Benard-Poiseuille flows. This paper demonstrates that the primary and secondary instability can be investigated with temporal simulations based on the full and linearized Navier-Stokes equations. Three cases with subcritical Reynolds number and supercritical Rayleigh number are discussed. It is shown that the secondary instability results from a triad interaction of the fundamental steady three-dimensional mode with a two-dimensional and two oblique modes. As the disturbances grow to non-linear amplitudes, the longitudinal rolls exhibit a sinusoidal wavy deformation. The wavelength of the most amplified secondary instability wave is in good agreement with experimental observations. The phase speed of the waves is close to the basic flow bulk velocity as suggested in the literature.