Global and local absolute instabilities of 2D wakes are known to be stabilized by spanwise periodic modulations of the wake profile. The present study shows that this stabilizing effect is of general nature and can be mimicked by enforcing spanwise periodic modulations of the wave advection velocity in the generalized complex Ginzburg-Landau equation. The first order sensitivity of the absolute and global growth rate to the enforced modulation is zero, exactly as in the Navier-Stokes case. We show that a second order sensitivity analysis is effective to quantify and interpret the observed stabilizing effect. The global growth rates predicted by the second order expansion closely match those issued from a direct computation of the eigenvalues. It is shown that, at leading order, the modulation of the wave advection velocity alters the effective wave diffusion coefficient in the dispersion relation and that this variation induces a reduction of the absolute growth rate and the stabilization of the global instability.
Analytical model for balling defects in laser melting using rivulet theory and solidification
Stanford University（斯坦福大学）；SLAC National Accelerator Laboratory（SLAC国家加速器实验室）；European Synchrotron Radiation Facility（欧洲同步辐射装置）；University College London（伦敦大学学院）；Research Complex at Harwell, Rutherford Appleton Laboratory（拉瑟福·阿普尔顿实验室哈韦尔研究中心）；Lawrence Livermore National Laboratory（劳伦斯利弗莫尔国家实验室）
