Sentence:  Here, γ<sub>0</sub>(ξ, t) is the vortex bound to "S"<sub>b</sub> in the <WSD>wakeless</WSD> ”quasi-steady” flow past "S"<sub>b</sub> which can be determined by steady airfoil theory for the original prescribed U<sub>n</sub>(ξ, t), with time t frozen to serve merely as a parameter for the moment. 
Meaning of the word marked with <WSD> tags:  Without a wake.