The development of localized disturbances in parallel shear flows is r
eviewed. The inviscid case is considered, first for a general velocity
profile and then in the special case of plane Couette flow so as to b
ring out the key asymptotic results in an explicit form. In this conte
xt, the distinctive differences between the wave-packet associated wit
h the asymptotic behavior of eigenmodes and the non-dispersive (invisc
id) continuous spectrum is highlighted. The largest growth is found fo
r three-dimensional disturbances and occurs in the normal vorticity co
mponent. It is due to an algebraic instability associated with the lif
t-up effect. Comparison is also made between the analytical results an
d some numerical calculations. Next the viscous case is treated, where
the complete solution to the initial value problem is presented for b
ounded flows using eigenfunction expansions. The asymptotic, wave-pack
et 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 three-dimensional disturbances.
This growth is associated with cancelation of non-orthogonal modes and
is the viscous equivalent of the algebraic instability. The maximum t
ransient growth possible to obtain from this mechanism is also present
ed, the so called optimal growth. Lastly the application of the dynami
cs of three dimensional disturbances in modeling of coherent structure
s in turbulent flows is discussed.