The nonlinear interaction of the mean flow and disturbance in the Stokes boundary layer inside a 2-D waveguide having a slowly varying height will be investigated. Time scales and other nondimensionalized variables associated with this modulated flow will be discussed. It is shown that the dynamic behavior of the enclosed fluid is governed by the values of four parameters, ε = 1/R, 1/S, and RS, where ε is the wall slope, 1/R is the square of the ratio of the oscillatory boundary thickness lv to the typical duct height, H0, 1/S is the ratio of the oscillatory particle displacement u0/ω to H0, and Re is the Reynolds number Ū0L/v. The results of this analysis will be compared to that given by Thompson [J. Acoust. Soc. Am. Suppl. 1 75, S77 (1984)] who investigated the stability of the Stokes layer without mean flow.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.