Movies: Convective
Instability ,Absolute InstabilityThe onset of waves is somewhat more complicated than that of steady structures. Due to the group velocity term any perturbations are advected along while they grow. If the advection is strong enough the perturbations do not grow at any fixed location even though they grow if one follows along with the advection. Thus, there are two stability limits:
the convective stability limit
the absolute stability limit
Movies: Convective
Instability ,Absolute Instability
This distinction is also relevant for secondary instabilities that are oscillatory. Thus, the Eckhaus instability of waves can be convective or absolute. For the complex Ginzburg-Landau equation one finds the stability regions shown in the figure below (Aranson et al. PRA 46 (1992) 2992.)
The
convective nature of the Eckhaus instability is illustrated in the
simulation of the CGLE
for
c1=0,c2=1,L=76.