Capturing Taylor–Görtler vortices in a streamwise-rotating channel at very high rotation numbers

Abstract

In this paper, we study the scales and dynamics of Taylor–Görtler (TG) vortices in streamwise-rotating turbulent channel flows at moderate and high rotation numbers ($Ro_{\unicode[STIX]{x1D70F}}=7.5$, 15, 30, 75 and 150) with a fixed Reynolds number. In order to precisely capture TG vortices in the streamwise and spanwise directions, direct numerical simulations have been performed on 15 test cases of different domain sizes and rotation numbers. A two-layer pattern of TG vortices is identified, and the characteristic length scales of TG vortices are quantified using the premultiplied energy spectra. It is observed that as the rotation number increases, the spanwise scale of TG vortices remains stable but the streamwise scale increases rapidly. Three criteria have been used for judging a domain-size-independent solution in both physical and spectral spaces. The weakest criterion ensures accurate predictions of the first- and second-order statistical moments of the velocity, which requires a minimum streamwise domain size of $L_{1}=64\unicode[STIX]{x03C0}h$, where $h$ is one-half the channel height. However, the streamwise domain size needs to be stretched drastically to $L_{1}=512\unicode[STIX]{x03C0}h$ if the most stringent criterion is considered, which demands that all energetic eddies be fully captured based on a predefined threshold value (i.e. $12.5\,\%$ of the peak value) of the premultiplied two-dimensional energy spectrum. The effects of streamwise system rotation on the scales and dynamics of TG vortices are investigated by comparing the statistical results of rotating and non-rotating channel flows, and through the analysis of two-point correlations, premultiplied energy spectra, and budget balance of turbulent stresses.