Streamwise streaks and secondary instability in a two-dimensional bent channel

Abstract

Streamwise streaks generated from a pair of oblique waves and secondary instability of the streaks are studied in a two-dimensional bent channel. Nonlinear parabolized stability equations (NPSE) are employed to investigate streamwise streaks and vortices. A pair of oblique waves from linear stability analysis is imposed as initial disturbances. Generation of streamwise streaks and vortices and subsequent development are described in detail. The case of plane channel is also studied to provide comparable data. Through comparison, the effect of bent region is clearly highlighted. Results of parametric studies to examine the effect of Reynolds number, radius of curvature, and bent angle are also given and discussed in detail. Secondary instability analysis for the modified mean flow due to the streamwise streaks is carried out by solving a two-dimensional eigenvalue problem. Several unstable modes which can be classified into fundamental and subharmonic mode of secondary instability are identified. Among several unstable modes, two modes are turned out to be dominant modes. Details on these two modes including generation mechanism, typical pattern, and dependency on wave number and streak amplitude are discussed. It is found that the presence of bent channel can lead to early oblique-mode breakdown via strong growth of the streamwise streaks due to the curved section. Such large amplitude of streaks and its secondary instability eventually could trigger transition even for small amplitude oblique waves at subcritical channel Reynolds numbers.