The present study explores three-dimensional vortex-dynamics past a wall-attached bluff body kept in a variable velocity field with numerical simulations. A trapezoidal pulse of mean velocity, consisting of acceleration phase from rest followed by constant velocity phase and deceleration phase to rest, is imposed at the inlet of the computational domain similar to the experimental study of Das et al. [“Unsteady separation and vortex shedding from a laminar separation bubble over a bluff body,” J. Fluids Struct. 40, 233–245 (2013)]. For a wide range of Reynolds numbers ([Formula: see text]), acceleration Reynolds numbers ([Formula: see text]), and deceleration Reynolds numbers ([Formula: see text]), different stages of flow evolution are systematically analyzed. The flow evolution starts with the formation of a primary vortex followed by a two-dimensional circular array of spanwise vortex tubes by inflectional shear-layer instability. At a sufficiently high Reynolds number, the shear layer vortices originated from two-dimensional fluctuations deformed by three-dimensional instabilities, giving fragmented streamwise vorticity. In addition, long-wavelength “tongue-like structures” and short-wavelength “rib-like structures” are evident near the top wall and the bluff body, respectively. The streamwise vorticity generation equation indicates that the spanwise vortex tubes initially tilt, resulting in streamwise vorticity, further amplified by the vortex stretching process. The distinct flow features, including mode shape, frequency, and growth rate associated with the shear-layer instability, are identified using the dynamic mode decomposition (DMD) algorithm. Using the maximum growth rate criteria, the DMD technique successfully separates the coherent shear layer modes associated with two-dimensional shear layer instability from the flow field.
This work investigates the stability and transition to turbulence in a diverging channel subjected to a time-varying trapezoidal-shaped inflow boundary condition. Numerical simulations are performed for different deceleration rates and Reynolds numbers while maintaining a constant acceleration rate. The flow transition begins with two-dimensional primary instability with the formation of inflectional velocity profiles, followed by local separation and the emergence of an array of shear layer vortices. We divide simulation cases systematically into three categories based on the onset of secondary instability and the generation of streamwise vorticity. At low and medium Reynolds numbers (type I), the spanwise vortex rolls formed by inflectional instability remain two-dimensional and diffuse at the channel centre without exhibiting further instabilities. At high Reynolds numbers and deceleration rates (type II), the rolled shear layer exhibits secondary instability during the zero mean inflow phase, followed by local incipient turbulent structure formation. The streamwise vorticity that develops over the shear layer structures causes oscillations with a spanwise wavelength similar to those associated with the elliptic instability in a counter-rotating vortex pair. Using the Lamb–Oseen approximation of vortices in conjunction with the dynamic mode decomposition algorithm of the three-dimensional flow field, we captured successfully the characteristics of the secondary instability. The third category (type III) is characterized by periodic unsteady separation, secondary instability, and merging of shear layer vortices, which occurs when Reynolds numbers are high and deceleration rates are low.
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