Analysis of convective hydrodynamic instabilities in a symmetric wavy channel
Résumé
The dynamic development of a laminar flow in a two-dimensional symmetric wavy channel is
studied numerically by numerical integration of the unsteady NavierStokes 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 dominant wavenumber which does not correspond to the
geometrical periodicity. Spatial amplification factors computed with the theoretical group velocities
determined from linear stability of the fully developed flow are in very good agreement with the
numerically measured values, both for the sinuous and varicous modes. © 2004 American Institute
of Physics.