Nonlinear hydrodynamic and thermodynamic aspects of unsteady Gortler flows

Both steady and unsteady Gortler vortices may lead to an incompressible boundary layer flow to transition from laminar to turbulent flow. Gortler structures can modify hydrodynamic and thermal boundary layers nonlinearly, increasing the time and spanwise averaged velocity and temperature gradients near the surface compared with the laminar counterpart. The nonlinear aspects of unsteady Gortler vortices evolution on thermal boundary layer flows are investigated using a high-order numerical method. In the validation process, the adopted numerical method shows agreement with previously published experimental data in both linear and weakly-nonlinear regions. Nonlinear high-order analyses reveal competition between the temporal fundamental (1, +/- 1) and the steady super-harmonic (0, 2) modes. The higher the frequency of the excited mode, the lower its amplification rate. The results show that when a high-frequency three-dimensional wave (modes (1,+/- 1)) is introduced, the transition process is dominated by the super-harmonic (0,2) mode if it is unstable. The time and spanwise average skin friction coefficient and the Stanton number are investigated. The results show that the lower the disturbance frequency, the higher the gain in these two coefficients.

Automated summary

The translation mainly involves the influence of Gortler vortices on boundary layer flows and the competition relationship between nonlinear modes. The results show that the amplification rate of high-frequency excited modes is lower, and when high-frequency three-dimensional waves are introduced, the transition process is dominated by the super-harmonic mode.