The onset of Taylor–Görtler vortices during impulsive spin-down to rest

The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using the propagation theory. The primary transient swirl flow is laminar but for an initially high rotating speed secondary motion sets in at a certain time. It is found here that the critical Reynolds number Rec=320Rec=320, below which the flow is unconditionally stable. For Re>RecRe>Rec the dimensionless critical time τcτc to mark the onset of a fastest growing instability is presented as a function of the Reynolds number Re  . Available experimental data and also predictions show that deviation of the velocity profiles from their primary ones occurs starting from a certain time τ≈4τcτ≈4τc. This means that secondary motion is detected experimentally at this characteristic time. It seems that during τc⩽τ⩽4τcτc⩽τ⩽4τc secondary motion is relatively very weak.