Modal and nonmodal growths of inviscid planar perturbations in shear flows with a free surface

摘要: Shear flows with a free surface possess diverse branches of modal instabilities. By approximating the mean flow piecewise linear profile, an understanding and classification instabilities can be achieved by studying interaction edge waves that arise at density discontinuity vorticity are supported gradient discontinuities in interior. The various instability identified their physical origin is clarified. giving rise to also lead modest transient growth extends into regions neutrality flow. However, when continuous spectrum excited substantial optimal perturbations attain greater energy compared fastest growing perturbation. These utilize excite large amplitude neutral or amplifying modes system.