The effect of streaks on the instability of jets

The presence of elongated streaks of high and low streamwise velocity in the shear layer of circular jets breaks the axisymmetry of their steady-state solution. If the streaks are considered to be part of the base flow, for the purpose of linear instability analysis, the instability eigenmodes are thus affected by their presence. The resulting changes of growth rate and spatial shapes of eigenmodes, related to the shear instability in jets, are investigated here for parallel base flows. Optimal streamwise vortices ('rolls') with prescribed azimuthal periodicity are computed, such that the transient temporal growth of the streaks that they produce is maximal. The presence of finite-amplitude streaks requires the formulation of eigenvalue problems in a two-dimensional cross-plane. Sinuous rolls and streaks are found to have a stabilising effect on the Kelvin-Helmholtz instability, whereas the varicose rolls and streaks have a destabilising effect. Absolute instability is not found to occur. This work shows that the effects of rolls and streaks need to be taken into account for more precise modelling of jet instability.

Automated summary

This study explores the effects of elongated streaks of high and low streamwise velocity in the shear layer of circular jets on their steady-state solutions, showing their influence on the linear instability analysis. The presence of finite-amplitude streaks is found to impact the growth rate and spatial shapes of eigenmodes related to shear instability in jets. Different types of rolls and streaks are shown to have varying effects on the Kelvin-Helmholtz instability, with sinuous rolls and streaks stabilizing and varicose rolls and streaks destabilizing the flow.