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The recent analytical of multi-layer analyses proposed by Sajjadi et al. (J Eng Math 84:73, 2014) (SHD14 therein) is solved numerically for atmospheric turbulent shear flows blowing over growing (or unsteady) Stokes (bimodal) water waves, of low-to-moderate steepness. For unsteady surface waves, the amplitude $$a(t)\propto e^{kc_it}$$ a ( t ) ∝ e k c i t , where $$kc_i$$ k...