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Direct numerical simulations of the Taylor-Couette (TC) problem, the flow between two coaxial and independently rotating cylinders have been performed. Reynolds numbers of up to $3\cdot 10^5$, corresponding to frictional Reynolds numbers $Re_\tau \approx 4000$ were reached. The gap between the cylinders was kept small by fixing the radius ratio to $\eta=r_i/r_o=0.909$. Small gap TC was found to be dominated by large scale structures, which are permanent in time and known as Taylor rolls (TRs). TRs are attached to the boundary layer, and are active, i.e they transport angular velocity through Reynolds stresses. Evidence for the existence of logarithmic velocity fluctuations, and of an overlap layer where the velocity fluctuations collapse in outer units was also found. An externally imposed axial flow of comparable strength as the wind of the TRs was found to convect them without any weakening effect.
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