To obtain this, set ; apply the Fourier transform to the normalwash at midchord: .
To use this, we must first develop an expression for cl for a case of simple harmonic gust velocity variation, then substitute the indicial gust expression n the frequency domain. As before, we seek a generalized expression where the complicated parts of the integral are computed as a general function.
Simple harmonic transverse gust:
In flow-fixed coordinates, , a simple harmonic spatial function. In terms of , non-dimensional body-fixed coordinates, ; periodic in space and time.
Substitute in our expression for Cp in the frequency domain. Now
and . Substituting for Cp, we get (skipping some math here), , and .
Define . Thus . Transform cl(k,t) into the frequency domain: and
and . Substituting for , with (semi-chords traveled in time t),
is the Kussner Function.