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A computational study of two possible modes of instability of developed Kelvin-Helmholtz (KH) billows is carried out. It is shown that depending on one of three factors, (i) symmetry of initial perturbation in the cross-flow direction, (ii) phase shift of initial perturbation in the streamwise direction, or (iii) excitation of either spanwise or oblique initial wave, the resulting instability can set in as a spanwise bending or bulging of a two-dimensional KH roller. To ensure that the observed secondary bifurcations result from the linear instability the study is carried out considering a two-dimensional flow combined of a distorted mean flow and developed frozen KH billow in under and/or over-saturated state as a base flow subject to three-dimensional instabilities.

Bulging and bending of Kelvin-Helmholtz billows controlled by symmetry and phase of initial perturbation