Invariance of the Doppler bandwidth with flow displacement in the illuminating field

It is known that if single frequency continuously transmitted ultrasound or electromagnetic energy is reflected from "straight line flow," defined here as one or more scatters moving with constant velocity along an infinite straight line, the Doppler effect will shift the echo spectrum center frequency from the transmitted value, and broaden its bandwidth. It is proved that if such straight line flow is shifted laterally or in range anywhere in the field, i.e., without change of orientation, its Doppler bandwidth remains unchanged. (The "Doppler bandwidth" is here defined as the frequency difference between the extrema of the echo power spectrum.) The theorem holds true even though the time domain echo changes dramatically with motion of the flow path, and is believed to be valid for electromagnetic as well as ultrasound waves. Its implications with respect to flow measurement, as well as preliminary experimental and computational confirmation, will be discussed.