Exact Perturbed Unsteady Boundary Layers

The time diffusive boundary layer from rest for Taylor series uniform outer flow is constructed by integration of the complementary error function of the diffusive similarity variable . The same erfc solution is also easily “Stokes” transformed to solve harmonic outer flow from rest. If the outer flow vector varies weakly along the boundary, the perturbation pressure gradient accelerates the slowest fluid nearest the wall the most to disproportionately vary the shear stress. So centripetal acceleration causes secondary crossflow inside the boundary layer with strong wall shear towards the center of curvature. But longitudinal acceleration also implies an inflow towards the wall which thins the outer boundary layer with a weak further increase of the wall shear, but the strongest perturbation steady streaming. Simple new particular solutions for these two perturbations are easily constructed in terms of products of integrals and derivatives of any primary diffusive solution. For an outer flow as a series in the square root of time, all homogeneous time coefficients remain just iterated error functions. Each systolic pulse in the aortic arch was considered as a Taylor series flow from rest to calculate the wall shear vectors. When the outer flow oscillates forever more, its primary diffusive boundary layer asymptotes to the Stokes oscillatory exponential decay with distance from the wall. The particular perturbations are exactly evaluated and also confined near the wall but with mean slip. The mean slip homogenous perturbations diffuse outside the Stokes layer into steady streaming as complementary error functions with inverse time correction functions. Extended Taylor series computations provide more detail of the perturbation transients.