In turbulent channel flows with imposed pressure-gradient oscillations the extension of the Stokes second problem solution has been used as a laminar benchmark. The present study shows that the Stokes solution is an appropriate approximation to the laminar channel flow solution only in the limit of an infinitely wide channel or very high frequencies of imposed oscillations. In a finite-width channel with finite-frequency oscillations, the exact channel flow solution should be used. The paper provides the thorough examination of the spatio-frequency variations of such solution. Different frequency regimes are described. It is shown that the borders between these regimes vary depending on the distance from a channel wall and a flow characteristic considered. Difference in high-frequency regimes in profiles of the phase and the amplitude is pointed out. Changes in the behavior of the laminar oscillating flow characteristics in the presence of the turbulent mean flow are considered. Oscillating channel and pipe flows are qualitatively compared.
Planar channel flow of a discontinuous shear-thickening model fluid: Theory and simulation
