The flow field around a lifting rotor in hover or forward flight is represented by a matched expansion that includes an inner expansion (near the blade chord) and an outer expansion that encompasses the rotor disk. The inner expansion is expanded in Glauert variables and is completely unsteady. It is driven by blade motions and the global flow-field variable λ0 which is provided by the outer expansion. The outer expansion is in terms of rotor harmonics and radial Legendre functions (which are polynomials in r on the blade). It is driven by the time-rate of change of bound circulation as provided from the inner expansion. Together, these form a robust convergent expansion of the rotor flow field that is good over a broad range of frequencies.

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