Energy amplification of poiseuilleflow in a pipe lined with riblets

Using as a passive method for drag reduction, riblets are structures that run parallel to one another and are aligned longitudinally to fluid flows. While the benefits of riblets have been well known, the mechanism of drag reduction is not fully understood. This paper analyses the effects of riblet structures on energy amplification in streamwise constant Poiseuille flow in a circular pipe. The linearised governing equations of the flow are written into the two-dimensional/three-component form. Through a change of coordinates, the rough domain is transformed into a smooth one. The equations are discretised using spectral methods and the finite-dimensional approximation of the system is represented by a state space model. The transient growth in the flow without external forcing and H₂ norm of the system subject to stochastic noise are calculated. Our computation shows that the presence of riblets can reduce the transient growth and H₂ norm in pipe flow.