Analytical and numerical investigations of laminar and turbulent Poiseuille–Ekman flow at different rotation rates

Abstract

Laminar and turbulent Poiseuille–Ekman flows at different rotation rates have been investigated by means of analytical and numerical approaches. A series of direct numerical simulations (DNSs) with various rotation rates (Ro2=0–1.82) for Reynolds number Reτ0=180 based on the friction velocity in the nonrotating case has been conducted. Both (laminar and turbulent) flow states are highly sensitive to the rotation. Even a small rotation rate can reduce the mean streamwise velocity and induce a very strong flow in the spanwise direction, which, after attaining a maximum, decreases by further increasing the rotation rate. It has been further observed that turbulence is damped by increasing the rotation rate and at about Ro2=0.145 a transition from the fully turbulent to a quasilaminar state occurs. In this region Reynolds number is only large enough to sustain some perturbations and the mean velocity profiles have inflection points. The instability of the turbulent shear stress is probably the main reason for the formation of the elongated coherent structures (roll-like vortices) in this region. In the fully turbulent parameter domain all six components of Reynolds stress tensor are nonzero due to the existence of the spanwise mean velocity. The Poiseuille–Ekman flow in this region can be regarded as a turbulent two-dimensional channel flow with a mean flow direction inclining toward the spanwise direction. Finally, due to the further increase in the rotation rate, at about Ro2=0.546 turbulence is completely damped and the flow reaches a fully laminar steady state, for which an analytical solution of the Navier–Stokes equations exists. The DNS results reproduce this analytical solution for the laminar state.