  We consider a smooth forward facing step defined by the Gauss error function
of height 4-30\% and four times the width of the local boundary layer thickness
$\delta_{99}$. The boundary layer flow over a smooth forward-facing stepped
plate is studied with particular emphasis on stabilisation and destabilisation
of the Tollmien-Schlichting (TS) waves and subsequently on transition. The
interaction between TS waves at a range of frequencies and a base flow over a
single/two forward facing smooth steps is conducted by linear analysis. The
results indicate that for a high frequency TS wave, the amplitude of the TS
wave is attenuated in the unstable regime of the neutral stability curve
corresponding to a flat plate boundary layer. Furthermore, it is observed that
two smooth forward facing steps lead to a more acute reduction of the amplitude
of the TS wave. When the height of a step is increased to more than 20\% of the
local boundary layer thickness for a fixed width parameter, the TS wave is
amplified and thereby a destabilisation effect is introduced. Therefore,
stabilisation or destabilisation effect of a smooth step is typically dependent
on its shape parameters. To validate the results of the linear stability
analysis, where a high-frequency TS wave is damped by the forward facing smooth
steps direct numerical simulation (DNS) is performed. The results of the DNS
correlate favorably with the linear analysis and show that for the investigated
high frequency TS wave, the K-type transition process is altered whereas the
onset of the H-type transition is postponed. The results of the DNS suggest
that for a high-frequency perturbation $\mathcal{F}=150$ and in the absence of
other external perturbations, two forward facing steps of height 5\% and 12\%
of the boundary layer thickness delayed H-type transition scenario and
completely suppresses it for the K-type transition.
