Laminarization mechanisms and extreme-amplitude states in rapidly rotating plane channel flow

Abstract

AbstractFully developed plane channel flow rotating in the spanwise direction has been studied analytically and numerically. Linear stability analysis reveals that all cross-flow modes are stable for supercritical rotation numbers, $Ro\gt R{o}_{c} $, where $R{o}_{c} $ will approach 3 from below for increasing Reynolds number. Plane Tollmien–Schlichting (TS) waves are independent of rotation and always linearly unstable for supercritical Reynolds numbers. Direct numerical simulation (DNS) of the laminarization process reveals that the turbulence is damped when $Ro$ approaches $R{o}_{c} $. Hence, the laminarization is dominated by linear mechanisms. The flow becomes periodic for supercritical Reynolds numbers and rotation rates, i.e. when $Ro\gt R{o}_{c} $ and $Re\gt R{e}_{c} $. At such rotation rates, all oblique (cross-flow) modes are damped and when the disturbance amplitude becomes small enough, the TS modes start to grow exponentially. Secondary instabilities are initially blocked by the rotation since all cross-flow modes are linearly stable and the breakdown to turbulence will be strongly delayed. Hence, the TS waves will reach extremely high amplitudes, much higher than for typical turbulent fluctuations. Eventually, the extreme-amplitude state with TS-like waves will break down to turbulence and the flow will laminarize due to the influence of the rapid rotation, thus completing the cycle that will then be repeated. This flow is strongly dominated by linear mechanisms, which is remarkable considering the extremely high amplitudes involved in the processes of laminarization of the turbulence at $Ro\geq R{o}_{c} $ and the growth of the unstable TS waves.