Critical layers in shear flows.

*(English)*Zbl 0634.76046
Annu. Rev. Fluid Mech. 18, 405-432 (1986).

[For the entire collection see Zbl 0591.00022.]

The emphasis in this review has been on nonlinear aspects of critical- layer theory a reflection of recent developments in the field, as well as an acknowledgment that many phenomena of practical importance such as boundary-layer transition are inherently nonlinear. Both steady, nonlinear waves and (at the opposite extreme) critical layers originating from linear, initial values analyses have been discussed. Different balances between time-dependence, nonlinearity, and diffusive effects were seen to lead to a variety of amplitude-evolution equations. The relationships between different amplitude equations and their associations with specific physical processes still need to be clarified in some cases.

The emphasis in this review has been on nonlinear aspects of critical- layer theory a reflection of recent developments in the field, as well as an acknowledgment that many phenomena of practical importance such as boundary-layer transition are inherently nonlinear. Both steady, nonlinear waves and (at the opposite extreme) critical layers originating from linear, initial values analyses have been discussed. Different balances between time-dependence, nonlinearity, and diffusive effects were seen to lead to a variety of amplitude-evolution equations. The relationships between different amplitude equations and their associations with specific physical processes still need to be clarified in some cases.

##### MSC:

76E05 | Parallel shear flows in hydrodynamic stability |

76-02 | Research exposition (monographs, survey articles) pertaining to fluid mechanics |