An immersed boundary (IB) resolvent framework for wall-bounded flows with spatial disturbances*

Turbulent wall-bounded flows often prove challenging to model, due to the complex flow structures that arise along the surface. This is especially true for fluid problems involving non-smooth surfaces, such as riblets, or compliant materials which further complicate modeling as a result of fluid-structure interactions. Resolvent analysis is useful for modeling turbulent wall-bounded flows, due to its ability as an operator-based method to generate response-forcing mode pairs. However, in its typical form resolvent analysis is limited to simple wall boundary conditions. Therefore, we have developed an immersed boundary (IB)-based resolvent analysis framework, capable of handling various surface conditions. The proposed method is fully derived in a resolvent setting and retains the property of streamwise-spanwise-homogeneity obeyed by wall-bounded flows, keeping the overall size of the resolvent system small. At the same time, the IB treatment enables significant generality in the boundary conditions applied at the wall surface. We present this IB resolvent method, including its application on a meaningful set of turbulent wall-bounded flow problems.