The absolute instability of thin wakes in an incompressible compressible fluid

The absolute/convective instability of two-dimensional wakes forming behind a flat plate and near the trailing-edge of a thin wedge-shaped aerofoil in an incompressible/compressible fluid is investigated. The mean velocity pr ofiles are obtained by solving numerically the classical compressible bound ary-layer equations with a negative pressure gradient for the flat plate ca se, and the incompressible triple-deck equations for a thin wedge-shaped tr ailing-edge. In addition for a Joukowski aerofoil the incompressible mean b oundary-layer flow in the vicinity of the trailing-edge is also calculated by solving the interactive boundary-layer equations. A linear stability ana lysis of the boundary-layer profiles shows that a pocket of absolute instab ility occurs downstream of the trailing-edge with the extent of the instabi lity region increasing with more adverse pressure gradients. The region of absolute instability persists along the near-wake axis, while the majority of the wake is convectively unstable. For a thin wedge-shaped trailing-edge in an incompressible fluid, a similar stability analysis of the velocity p rofiles obtained via a composite expansion, also shows the occurrence of ab solute instability behind the trailing-edge for a wedge angle greater than a critical value. For increasing values of the wedge angle and for thicker aerofoils, separation takes place near the trailing-edge and the extent of absolute instability increases. Calculations also show that for insulated p lates compressibility has a stabilizing effect but cooling the wall destabi lizes the flow unlike wall heating.