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Stationary counter-rotating longitudinal vortex pairs emerge fromone-dimensional Prandtl slope flows under katabatic as well as anabaticconditions due to a linear instability when the imposed surface heat fluxmagnitude is sufficiently strong relative to the stable ambient stratification.For anabatic flows, these vortices have already been identified to exhibit anunique topology that bears a striking resemblance to speaker-wires since theystay coherent as a single unit without the presence of another vortex pair.Under katabatic conditions and at a constant Prandtl number, we find that thelongitudinal vortices emerging at a range of different slope angles possess thesimilar topology as their anabatic counterparts. We determine the existence ofboth fundamental and subharmonic secondary instabilities depending on the slopeangle for the most likely transverse base flow wavelength. Our results indicatethat the most dominant instability shifts from a fundamental to subharmonicmode with increasing slope angle. At shallow slopes, this dynamic contrast withthe speaker-wire vortices in anabatic slope flows at the same angle which forwhich the subharmonic instability is clearly dominant. These modes areresponsible for the bending and movement of single or multiple speaker-wirevortices, which may merge or reconnect to lead to dynamically more unstablestates, eventually leading to transition towards turbulence. We demonstratethat at sufficiently steep slopes, the dynamics of these vortex pairs aredominated by long-wave reconnections or two-dimensional mergers betweenadjacent pairs.

Instabilities of longitudinal vortex rolls in katabatic Prandtl slope flows