Secondary instabilities of speaker-wire vortices in stratified katabatic Prandtl slope flows

Stationary longitudinal rolls, also dubbed speaker-wire vortices, arise as nonlinear saturation of a linear instability in Prandtl's laminar katabatic flows for a large range of slope angles when the ratio between imposed surface buoyancy gradient and ambient stratification exceeds a critical threshold. In the present work, the instability modes of these slope-aligned vortices are investigated with the help of bi-global linear stability analysis as well as direct numerical simulations. We identify multiple possible dynamics that depend strongly on the slope angle. It turns out that at shallow slopes, the most dominant instabilities are long-wave modes, which might help explain the observation of very large structures in stably stratified flows. For very specific vortex configurations, the two-dimensional subharmonic instability that is characteristic for the merger of adjacent vortex pairs becomes most dominant. The dependence of secondary instability growth rates and oscillation frequencies on the longitudinal wave number and the stratification perturbation number as well as the slope angle will be presented. A remarkable feature of all the configurations studied herein is the absence of any fundamental modes which would move vortices within the same pair in opposite directions, implying that the original vortex pair maintains its pair structure without reconnection even after the onset of secondary instability dynamics.