Two rotor configurations with different non-uniform inflows were studied: a rotor ingesting the wake of an upstream cylinder and a rotor ingesting a thick axially symmetric boundary layer from an upstream centerbody. In both cases, the undisturbed inflow was measured without the rotor present in order to characterize the inflow, in particular to calculate the unsteady upwash velocity distribution at the location of the rotor. In addition, detailed acoustic measurements were completed using a 251-channel large-area microphone array. In all, over 400 conditions covering different advance ratios, angles of yaw, and inflow conditions were measured. Measurements of the sound show that the source has a complex directivity, different from that of a streamwise aligned dipole, due to the inhomogeneous unsteady upwash distribution. In addition, observers at different far field locations will perceive sources from different locations on the rotor disk. The directivity is a function of both the rotor geometry and turbulent inflow. A simplified model of the sound source was developed using these inputs and accurately predicts trends observed in the far field noise. For the cylinder wake ingestion case, on-blade measurements of the flow field show that the wake is drawn to the center of the rotor disk with increasing thrust. This is particularly noticeable if the wake does not strike the center of the rotor disk. The effects of this flow distortion on the far field directivity are well predicted by the model. The effects of yaw to rotate the produced sound field can be inferred from this model as well. A novel beamforming procedure was used to isolate sources across the face of the rotor for the cylinder wake ingestion case for an upstream observer position. This method may be used to isolate different sound sources on a rotor if multiple sources are present or if different regions of the rotor disk need to be isolated. The directivity of a rotor ingesting an axially symmetric boundary layer is far less complex than the ingestion of a two-dimensional cylinder wake, but measurements still show the perceived source location shift with observer location. Overall, the proposed noise modeling technique is an efficient method to predict the directivity of turbulence ingestion noise for inhomogeneous inflows. This can enable quick absolute noise predictions at all far field locations using only a single point measurement or far field noise prediction to establish absolute levels. / Doctor of Philosophy / In many engineering applications, rotors interact with turbulence. Aircraft and ships with rear mounted propellers can have upstream appendages or discontinuities that generate turbulence that travels downstream and is drawn into the propeller. Wind turbines interact with turbulence in the atmosphere and with turbulent wakes from other turbines. Interaction of a rotor with turbulence results in unsteady loading on the rotor blades that can radiate as sound, causing unwanted community noise or vehicle detection. As such, prediction and reduction of noise due to turbulence ingestion is highly desirable and remains an active area of research. Turbulence ingestion noise is well understood from first principles and can be successfully predicted provided an accurate description of the turbulent inflow and unsteady aerodynamic response of the rotor blades. Much work has focused on homogenous, isotropic turbulence ingestion noise, however, in practical applications, the rotor inflow is often non-uniform, anisotropic, and can change dramatically with the thrusting condition of the rotor. Research efforts to develop noise predictions considering these more complex, but practical inflows have focused on the inflow modeling and measurement and have relied on a small subset of sound measurements for validation. The present study seeks to provide new physical insight into inhomogeneous, anisotropic turbulence ingestion noise through wind tunnel experiments. In particular, two rotor configurations with different practical non-uniform inflows are studied: a rotor ingesting the wake of an upstream cylinder and a rotor ingesting a thick axially symmetric boundary layer from an upstream center body. In both cases, the undisturbed inflow was measured without the rotor present in order to characterize the inflow, and detailed acoustic measurements were completed using a 251-channel large-area microphone array. In all, over 400 rotor operating conditions were measured. The acoustic directivity in each case is examined in detail as a function of rotor operating condition. A simplified directivity model is developed and validated with measurements. Ultimately, the directivity model can provide a good engineering approximation of the full directivity with reduced computational time or can be used to extrapolate measured results to positions in the far field where placement of sensors is not possible. The results can also be used to guide the analysis and interpretation of single point or microphone array measurements in the acoustic far field of a rotor.