Consider uniform flow past an oscillating body. Assume that the resulting farfield flow consists of both steady and time periodic components. The time periodic component can be decomposed into a Fourier expansion series of time harmonic terms. The form of the steady terms given by the steady oseenlets are wellknown. However, the timeharmonic terms given by the oscillatory oseenlets are not. In particular, the Green's functions associated with these terms are presented. In this thesis, the oscillatory oseenlet solution is presented for the velocity and pressure, and the forces generated by them are calculated. A physical interpretation is given so that the consequences for moving oscillating bodies can be determined. As the frequency of the oscillations tend to zero, it is shown that the steady oseenlet solution is recovered. Also, as the Reynolds number of the flow tends to zero, it is shown that the oscillatory stokeslet solution is recovered. In this latter case, the oscillatory oseenlets solution is an outer matching to the inner oscillatory stokeslet solution. An application of this new representation is discussed for future work.
