Abstract



We apply direct transient growth analysis in complex geometries to investigate its role in the primary and secondary bifurcation/transition process of the flow past a circular cylinder. The methodology is based on the singular value decomposition of the NavierStokes evolution operator linearized about a twodimensional steady or periodic state which leads to the optimal growth modes. Linearly stable and unstable steady flow at Re=45 and 50 is considered first, where the analysis demonstrates that strong twodimensional transient growth is observed with energy amplifications of order of 10(3) at Uinfinity tau/D approximate to 30. Transient growth at Re=50 promotes the linear instability which ultimately saturates into the well known vonKaacutermaacuten street. Subsequently we consider the transient growth upon the timeperiodic base state corresponding to the vonKaacutermaacuten street at Re=200 and 300. Depending upon the spanwise wavenumber the flow at these Reynolds numbers are linearly unstable due to the socalled mode A and B instabilities. Once again energy amplifications of order of 10(3) are observed over a time interval of tau/T=2, where T is the time period of the base flow shedding. In all cases the maximum energy of the optimal initial conditions are located within a diameter of the cylinder in contrast to the spatial distribution of the unstable eigenmodes which extend far into the downstream wake. It is therefore reasonable to consider the analysis as presenting an accelerator to the existing modal mechanism. The rapid amplification of the optimal growth modes highlights their importance in the transition process for flow past circular cylinder, particularly when comparing with experimental results where these types of convective instability mechanisms are likely to be activated. The spatial localization, close to the cylinder, of the optimal initial condition may be significant when considering strategies to promote or control shedding.  
International

Si 
JCR

Si 
Title

PHYSICS OF FLUIDS 
ISBN

10706631 
Impact factor JCR

1,738 
Impact info


Volume

21 


Journal number

4 
From page

0441031 
To page

0441031 
Month

ABRIL 
Ranking
