The Stokesian flow field of an oscillatory submerged viscous jet impinging on a planar wall

This model of experiments on auditory sensory hair cells extends previous work via distributions on a cylindrical pipe of tangentially and normally directed oscillatory point forces, which are modified to achieve no-slip at the wall in two stages. Starting with the pressure and vorticity jumps associated with the oscillatory pressure-driven flow upstream in the pipe, the adjustment of the interior pipe flow from its upstream complex-valued profile to its exit profile is fully included. This is essentially achieved by modifying the steps of the steady case analysis. The flow field oscillates with phase dependent on position, and the level curves of the streamfunction indicate instantaneous particle motion but not streamlines. Thus, an eddy is not indicated by the closed curve that occurs midway through the two half cycles and is due to competing forces between the inflow and outflow, particularly in the second half cycle as the fluid enters the pipe. The wall pressure and wall shear stress also oscillate with the non-uniformities concentrated near the origin, but are relatively damped midway through the two half cycles. Independent of the orifice location, there is a small effect of frequency on the wall pressure and the wall shear stress.