Stability and bifurcation in a modulated Burgers system
Abstract
The stability of the null state for a nonlinear Burgers system is examined. The results include (i) an energy estimate for global stability for states involving arbitrary modulation in time, and (ii) an analysis of the bifurcation from the null state for slow modulations. For the slow modulations it is determined that the amplitude A(tau) of the bifurcated disturbance velocity satisfies a Landautype equation with timedependent growth rate. Particular attention is given to periodic and quasiperiodic modulations of the system, which lead to analogous behavior in the growth rate. For each of these oscillatorytype modulations, it is found that Asquared(tau) has the same longtime mean value as the unmodulated case, implying no alteration of the final mean kinetic energy. Applications to various fluiddynamical phenomena are discussed.
 Publication:

Quarterly of Applied Mathematics
 Pub Date:
 January 1982
 Bibcode:
 1982QApMa..39..467O
 Keywords:

 Branching (Mathematics);
 Flow Stability;
 Nonlinear Systems;
 Systems Stability;
 Asymptotic Series;
 Computational Fluid Dynamics;
 Pressure Oscillations;
 Fluid Mechanics and Heat Transfer