Abstract
The stability of the Stokes boundary layer generated by an acoustic disturbance in a two-dimensional waveguide is examined. Special attention is given to waveguides which have slowly varying cross sections. It is shown that the stability of the Stokes layer to three-dimensional vortical disturbances is governed by the value of three small parameters: ε, 1/R, and 1/S, where ε is the wall slope of the duct, 1/R is the ratio of the oscillatory boundary layer thickness to the typical duct height, and 1/S is the ratio of the oscillatory particle displacement to the duct height. A stability analysis is presented for the amplitude range ε2R/S2=O(R1/2). It is shown that instability occurs when ‖h″‖ε2R1/2/S2 is greater than 4.23. Attention is also given to the weakly nonlinear evolution of 3-D vortical disturbances. It is found that the Reynolds stress causes the solution for the disturbance field to bifurcate supercritically from that obtained by linear stability theory. The disturbance amplitude is shown to be governed by the solution of the nonlinear Schrödinger equation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
