The structure of three-dimensional periodic boundary layers in a continuously stratified fluid

Small three-dimensional motions of a slightly viscous stratified fluid, generated by vertical and torsional oscillations of part of the surface of an infinite vertical cylinder of arbitrary cross-section, are investigated. The asymptotic method of boundary functions is used to analyse the structure of periodic motions. It is shown that two types of boundary layers are formed, one of which possesses the properties of the Stokes boundary layer in homogeneous fluid, while the other one, namely, the internal wave boundary layer, is a specific feature of heterogeneous media, whose thickness depends on both the wave frequency and the buoyancy frequency. On changing to the case of a homogeneous fluid, the viscous and internal boundary layers merge.