Direct Numerical Simulation of Evolution and Control of Linear and Nonlinear Disturbances in Three-Dimensional Attachment-Line Boundary Layers

摘要

Spatially evolving linear and nonlinear disturbances in a three-dimensional (3D) attachment-line boundary layer are computed by direct numerical simulation of the unsteady, incompressible Navier-Stokes equations. Previously, a weakly nonlinear theory and computation revealed a high wave-number region of subcritical disturbance growth, which is a region where linear theory predicts the decay of small-amplitude disturbances. More recent computations have failed to achieve this subcritical growth. The present computational results duplicate and explain both subcritically growing and decaying disturbances and resolve the previous theoretical and computational discrepancy. The present results demonstrate that steady suction can be used to stabilize disturbances that otherwise grow subcritically along the attachment line. However, true 3D disturbances are more likely in practice. Disturbances generated off (but near) the attachment line are shown to spread both away from and toward the attachment line as they evolve. Furthermore, these disturbances generated near the attachment line can supply energy to attachment-line instabilities, but the results show that suction can be used to stabilize these instabilities. Finally, symmetric and asymmetric disturbance growth predicted by a two-dimensional-eigenvalue approach is demonstrated to agree with the DNS results.