The pressure fluctuations generated by propellers in the wake of hulls are markedly different from those produced in uniform inflow. The flow in the propeller plane abaft a hull varies spatially as well as temporally. Here we deal only with the effects attending spatial variations peripherally and radially as provided by wake surveys which give the averaged-over-time velocity components as a function of r and γ for a fixed axial location. Temporal variations in the components are aperiodic and cannot be addressed until sufficient measurements have been made to determine their frequency spectra. Ultimately, numerical solutions of the Navier-Stokes equations may provide both spatial and temporal aspects of hull wakes.

Here the spatial variations in the axial and tangential components are reflected in the pressure jump Δp which is taken to vary harmonically with blade position angle γ0. Then we discover a coupling between the harmonics of Δp(γo) and the harmonics of the propagation function yielding a plethora of terms all at integer multiples of blade frequency. Graphical results are given for pressure and velocity fields showing the effect of spatial non-uniformity of the inflow.

We have seen in the previous chapter that the pressure field arising from a lifting-surface model of a propeller in a uniform flow is that due to pressure and velocity dipoles distributed over the blade. Both dipole strengths were constant in time since we considered uniform and stationary inflow.