A study of acoustic propagation in low Mach number flow with implications for the interpretation and measurement of aircraft noise.

In the pages that follow I have attempted to give a systematic description of some findings made during my investigation into the acoustic equations in flows at low Mach number. The practical justification for this study is the need to understand how noise produced by aircraft at take-off or landing propagates from sources, such as the engines, to people living around airports. We first construct a method for deriving a single acoustic equation which is correct to any desired order in the Mach number of the flow around the aircraft. Then we discuss the difficulties which exist when we try to express the acoustic pressure, for example, as a power series in the Mach number at high frequencies. We illustrate the problems involved by a detailed analysis of scattering by a region of fluid in solid body rotation. We go on to show how these difficulties can be circumvented in the case of potential flow by the application of a novel transformation. The considerable simplification achieved by the transformation enables a straightforward connection to be made between the acoustic field with flow to that without flow. This result leads me to question the generally accepted use oi emission time coordinates for describing aircraft noise measurements. I argue strongly that such coordinates far from clarifying the effect of flow on aircraft noise will in fact make it harder to interpret the changes brought about by the aircraft's flow field. My final conclusion is that emission time coordinates should be replaced by coordinates fixed in the aircraft body for the presentation of noise data