The onset of hydrodynamical instability induced by impulsive spin-down to rest in a cylinder containing a Newtonian fluid is analyzed by using propagation theory. It is well-known that the primary transient swirl flow is laminar, but with initial high velocities secondary motion sets in at a certain time. The dimensionless critical time τc to mark the onset of instability is presented here as a function of the Reynolds number Re. Available experimental data indicate that for large Re deviation of the velocity profiles from their momentum diffusion occurs starting from a certain time τ ≒ 4 τc. This means that secondary motion is detected at this characteristic time. It seems evident that during τc ≤ τ ≤ 4 τc, secondary motion is relatively very weak and the primary diffusive momentum transfer is dominant.
Chandrasekhar S, "Hydrodynamic and Hydromagnetic Stability," Oxford University Press, Oxford, 1961
Chen CF, Kirchner RP, J. Fluid Mech., 48, 365, 1971
Choi CK, Park JH, Park HK, Cho HJ, Chung TJ, Kim MC, "Temporal Evolution of Thermal Convection in an Initially, Stably Stratified Fluid," Proc. Int. Symp. Transient Convective Heat and Mass Transfer in Single and Two-Phase Flows (Extended Abstracts), Cesme, pp. 63-66, 2003