Structures and turbulent statistics in a rotating plane Couette flow

Abstract

This paper presents direct numerical simulations of various turbulent states and structures in a rotating plane Couette flow. The formations of patterns or roll cells were investigated in a wide range of the rotation number Ω, using a large domain size of 204.8δ × 2δ × 102.4δ. The controlling parameters are Re = Uwδ/ν = 750 and Ω = 2ΩZδ2 /ν, where Uw is half the wall velocity difference and Ωz is the spanwise-rotation angular velocity. The simulations reproduced many key features in the experiment of Tsukahara et al. (JFM, 648: 5–33). For stabilizing rotation with Ω ≤ −20, a striped pattern of laminar-turbulent regions was observed. For destabilizing rotation with Ω = 30, turbulent eddies seem to be contained in the three-dimensional roll cells. The wavy motion of the roll cells in the turbulent background reveals a 30δ periodicity in the streamwise direction, and the spacing of the turbulent stripe is of the order of 200δ. A computational domain needs to be large enough compared with these structures induced by the system rotation to ensure reliable quantitative results.