

Artikel
Localized disturbances in parallel shear flows.
Författare: 
Henningson, D.S.H., Gustavsson, L.H., Breuer, K.S. 
Dokumenttyp: 
Artikel 
Tillstånd: 
Publicerad 
Tidskrift: 
Appl. Sci. Res. 
Volym: 
53
5197 
År: 
1994 
AbstractThe development of localized disturbances in parallel shear flows is reviewed. The inviscid case is considered, first for a general velocity profile and then in the special case of plane Couette flow so as to bring out the key asymptotic results in an explicit form. In this context, the distinctive differences between the wavepacket associated with the asymptotic behavior of eigenmodes and the nondispersive (inviscid) continuous spectrum is highlighted. The largest growth is found for threedimensional disturbances and occurs in the normal vorticity component. It is due to an algebraic instability associated with the liftup effect. Comparison is also made between the analytical results and some numerical calculations. Next the viscous case is treated, where the complete solution to the initial value problem is presented for bounded flows using eigenfunction expansions. The asymptotic, wavepacket type behaviour is analyzed using the method of steepest descent and kinematic wave theory. For short times, on the other hand, transient growth can be large, particularly for threedimensional disturbances. This growth is associated with cancellation of nonorthogonal modes and is the viscous equivalent of the algebraic instability. The maximum transient growth possible to obtain from this mechanism is also presented, the so called optimal growth. Lastly the application of the dynamics of three dimensional disturbances in modeling of coherent structures in turbulent flows is discussed.

