Analysis of convective hydrodynamic instabilities in a symmetric wavy channel

The dynamic development of a laminar flow in a two-dimensional symmetric wavy channel is studied numerically by numerical integration of the unsteady Navier–Stokes equations. It is shown that beyond a critical Reynolds number the flow is convectively unstable and exhibits an exponential spatial growth of the velocity fluctuations. The amplification factor for these “natural instabilities” increases with Reynolds number. It is characteristic of the geometry but independent of the number of the periods chosen for the simulation and other numerical parameters. The amplitude of velocity fluctuations saturates at a distance from the entry that decreases with increasing Reynolds number. The structure of the developing unsteady flow is compared with the most unstable modes of the fully developed laminar steady flow obtained by linear stability analysis. Although visual inspection would tend to favor the assumption of a single mode disturbance, it is found that the disturbances are wave packets centered around a ...