First- and second-order shape derivative-based analysis of roughness effects on channel flow

 ICES, University of Texas, Austin

The influence of boundary roughness characteristics on the rate of dissipation in a viscous fluid using first- and second-order shape derivatives is studied. We show that the flat boundary is a stationary point for the dissipation functional, and thus its local behavior is governed by the shape Hessian, whose eigenvectors are shown to be the Fourier modes. Numerical examples for laminar flow are presented, and the extension to turbulent flows is discussed. This is joint work with Shan Yang, Robert Moser and Omar Ghattas.