Reynolds Number Induced Growth of Large-scale Rolls in Plane Couette Flow and Invariant Scaling Laws for Added Wall-transpiration Using Resolvent Analysis

In DNS of turbulent plane Couette flow (PCF) long streamwise rolls further grow as the Reynolds number increases [1]. To analyse this, we utilise resolvent analysis, focusing on high Reynolds numbers \((Re \rightarrow \infty )\) and small streamwise wavenumbers \((\alpha \rightarrow 0)\) with the limit \(Re_{\alpha }=Re \cdot \alpha = O(1)\) . We observe that \(Re_{\alpha }\) acts as a local invariant in the amplification mechanism of the PCF characterised through the first singular value \(\sigma _1\) of the resolvent operator within this limit. To maintain constant streamwise structures for increasing Reynolds numbers, the streamwise wavenumber has to decrease, agreeing with DNS studies about increasing length of the streamwise structures with the Reynolds number. We further investigate the plane Couette flow with constant wall-tranpiration (PCFT) with emphasis on the effect of the wall-transpiration Reynolds number \(Re_{V0}\) on the coherent structures which move closer to the upper wall and become narrower for growing \(Re_{V0}\) .Invariant scaling laws within the amplification mechanims can be found for various flow parameters.