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Viscous flow past a finite flat plate moving in direction normal to itself isstudied numerically.The plate moves with velocity $at^p$, where $p=0,0.5,1,2$.We present the evolution of vorticity profiles, streaklines and streamlines,and study the dependence on the acceleration parameter $p$. Four stages in thevortex evolution, as proposed by Luchini & Tognaccini (2002), are clearlyidentified. The initial stage, in which the vorticity consists solely of aRayleigh boundary layer, is shown to last for a time-interval whose lengthshrinks to zero like $p^3$, as $p \to 0$. In the second stage, a center ofrotation develops near the tip of the plate, well before a vorticity maximumwithin the vortex core develops. Once the vorticity maximum develops, itsposition oscillates and differs from the center of rotation. The differencebetween the two increases with increasing $p$, and decreases in time. In thethird stage, the center of rotation and the shed circulation closely satisfyself-similar scaling laws for inviscid flow. Finally, in the fourth stage, thefinite plate length becomes relevant and the flow begins to depart from theself-similar behaviour. While the core trajectory and circulation closelysatisfy inviscid scaling laws, the vorticity maximum and the boundary layerthickness follow viscous scaling laws. The results are compared withexperimental results of Pullin & Perry (1980), and Taneda & Honji (1971), whereavailable.

Start-up vortex flow past an accelerated flat plate