Effects of hydrophobic surface on stability and transition

Abstract

The effects of a hydrophobic surface on stability and transition in wall-bounded shear flows are investigated. The hydrophobic surface is represented by a slip-boundary condition on the surface. The linear stability analysis with slip-boundary conditions shows that the critical Reynolds number increases with streamwise slip. The effects of slip-boundary conditions on the transient growth of initial disturbances are investigated through the singular value decomposition (SVD) analysis of the linearized Navier–Stokes equations. The maximum transient growth (i.e., the amplification factor for the optimal disturbance) is reduced with streamwise slip, indicating that non-normality of the linearized Navier–Stokes equations is reduced with streamwise slip. Finally, it is shown that the transition to turbulence is delayed significantly with streamwise slip, whereas spanwise slip induces an earlier transition. The present results suggest that it is desirable to develop a hydrophobic surface with specified directional sensitivity in order to meet a particular need for specific applications.