A study of eigenvalue sensitivity for hydrodynamic stability operators

The eigenvalue sensitivity for hydrodynamic stability operators is investigated. Classical matrix perturbation techniques as well as the concept of -pseudospectra are applied to show that parts of the spectrum are highly sensitive to small perturbations. Applications are drawn from incompressible plane Couette flow, trailing line vortex flow, and compressible Blasius boundary-layer flow. Parameter studies indicate a monotonically increasing effect of the Reynolds number on the sensitivity. The phenomenon of eigenvalue sensitivity is due to the nonnormality of the operators and their discrete matrix analogs and may be associated with large transient growth of the corresponding initial value problem.This work was started at NASA Langley Research Center, Hampton, VA (LaRC), at the Institute for Computer Applications in Science and Engineering (ICASE). The first author gratefully acknowledges financial support from both ICASE and LaRC during the course of this work. Partial support for the second author was provided by the Aeronautical Research Institute of Sweden (FFA). Support for the third and fourth authors was provided by NASA Langley Research Center under Contract NAS1-18240. Computer time was provided by LaRC.