Publication |
2006
Abstract
Sufficient conditions for the monotone decay of disturbances of oscillatory and steady Hagen-Poiseuille flow are rigorously derived within the framework of linear stability theory. The conditions hold both for axisymmetric and nonaxisymmetric disturbances, whereas the result for nonaxisymmetric disturbances to the oscillatory flow is of particular importance because in this case even numerical results are not available in the literature.
Furthermore, the conditions provide explicit bounds on the range of parameters that must be examined in any prospective search for nstability by numerical means. The derivation of the sufficient conditions on monotone decay is based on a detailed analysis of the spectrum of the Stokes operator.