The effect of spanwise and streamwise elastic coating on boundary layer transition

Abstract

Compliant coatings that are capable of delaying laminar–turbulent transition have received much attention. Most examined compliant coatings exhibit dominantly wall-normal motion, and although they are able to delay laminar–turbulent transition, they also give rise to other instability mechanisms that advance transition. Previous research (e.g., Carpenter and Morris (1990)) showed that streamwise motion of the coating can be beneficial regarding transition delay. In the present study, a coating capable of purely in-plane motion is investigated using modal local linear instability theory of spatially growing disturbances. A simple damped mass–spring model demonstrates that spanwise motion of the coating does not affect the growth rate of the Tollmien–Schlichting (TS) instabilities. Motivated by this finding, a new type of real coating structure is proposed, and it is proven that it can delay laminar–turbulent transition, but does not give rise to new convective instabilities.