UNSTEADINESS AND CONVECTIVE INSTABILITIES IN 2-DIMENSIONAL FLOW OVER A BACKWARD-FACING STEP

A systematic study of the stability of the two-dimensional flow over a backward-facing step with a nominal expansion ratio of 2 is presented up to Reynolds number Re = 2500 using direct numerical simulation as well as local and global stability analysis. Three different spectral element computer codes are used for the simulations. The stability ana lysis is performed both locally (at a number of streamwise locations) and globally (on the entire field) by computing the leading eigenvalue s of a base flow state. The distinction is made between convectively a nd absolutely unstable mean flow. In two dimensions, it is shown that all the asymptotic flow states up to Re = 2500 are time-independent in the absence of any external excitation, whereas the flow is convectiv ely unstable, in a large portion of the flow domain, for Reynolds numb ers in the range 700 less than or equal to Re less than or equal to 25 00. Consequently, upstream generated small disturbances propagate down stream at exponentially amplified amplitude with a space-dependent spe ed. For small excitation disturbances, the amplitude of the resulting waveform is proportional to the disturbance amplitude. However, select ive sustained external excitation (even at small amplitudes) can alter the behaviour of the system and lead to time-dependent flow. Two diff erent types of excitation are imposed at the inflow: (i) monochromatic waves with frequency chosen to be either close to or very far from th e shear layer frequency; and (ii) random noise. It is found that for s mall-amplitude monochromatic excitation the flow acquires a time-perio dic behaviour if perturbed close to the shear layer frequency, whereas the flow remains unaffected for high values of the excitation frequen cy. On the other hand, for the random noise as input, an unsteady beha viour is obtained with a fundamental frequency close to the shear laye r frequency.