Skip to main content Accessibility help

Roll-cell instabilities in rotating laminar and trubulent channel flows

  • Dietrich K. Lezius (a1) (a2) and James P. Johnston (a1)


The stability of laminar and turbulent channel flow is examined for cases where Coriolis forces are introduced by steady rotation about an axis perpendicular to the plane of mean flow. Linearized equations of motion are derived for small disturbances of the Taylor type. Conditions for marginal stability in laminar Couette and Poiseuille flow correspond, in part, to the analogous solutions of buoyancy-driven convection instabilities in heated fluid layers, and to those of Taylor instabilities in the flow between rotating cylinders. In plane Poiseuille flow with rotation, the critical disturbance mode occurs at a Reynolds number of Rec = 88.53 and rotation number Ro = 0.5. At higher Reynolds numbers, unstable conditions canexist over the range of rotation numbers given by 0 < Ro < 3, provided the undisturbed flow remains laminar. A two-layer model is devised to investigate the onset of longitudinal instabilities in turbulent flow. The linear disturbance equations are solved essentially in their laminar form, whereby the velocity gradient of laminar flow is replaced by a numerically computed profile for the gradient of the turbulent mean velocity. The turbulent stress levels in the stable and unstable flow regions are represented by integrated averages of the eddy viscosity. Onset of instability for Reynolds numbers between 6000 and 35 000 is predicted to occur at Ro = 0.022, a value in remarkable agreement with the experimentally observed appearance of roll instabilities in rotating turbulent channel flow.



Hide All
Bradshaw, P. 1969 The analogy between streamline curvature and buoyancy in turbulent shear flow. J. Fluid Mech. 36, 177.
Cess, R. D. 1958 A survey of the literature on heat transfer in turbulent tube flow. Thesis, University of Pittsburgh, Pennsylvania.
Chandrasekhar, S. 1961a Hydrodynamic and Hydromagnetic Stability. Oxford University Press.
Chandrasekhar, S. 1961b Adioint differential systems in the theory of hydrodynamic stability. J. Math. Mech. 10, 683.
Debler, W. R. 1966 On the analogy between thermal and rotational hydrodynamic stability. J. Plwid Mech. 24, 165.
Halleen, R. M. & Johnston, J. P. 1967 The influence of rotation on flow in a long rectangular channel: an experimental study. Department of Mechanical Engineering, Stanford University, Rep. MD-18.
Hart, J. E. 1971 Instability and secondary motion in a rotating channel flow. J. Flwid Mech. 45, 341.
Hung, W. L., Joseph, D. D. & Munson, B. R. 1972 Global stability of spiral flow. Part 2. J. Fluid Mech. 51, 593.
Johnston, J. P., Halleen, R. M. & Lezius, D. K. 1972 Effects of spanwise rotation on the structure of two-dimensional fully developed turbulent channel flow. J. Fluid Mech. 56, 533.
Joseph, D. D. 1966 Nonlinear stability of the Boussinesq equations by the method of energy. Arch. Rat. Mech. Anal. 22, 163.
Lezius, D. K. 1975 Finite difference solutions of Taylor instabilities in viscous plane flow. Computers & Fluids, 3, 103.
Lezius, D. K. & Joenston, J. P. 1971 The structure and stability of turbulent wall layers in rotating channel flow. Department of Mechanical Engineering, Stanford University, Rep. MD-29.
Pedley, T. J. 1969 On the instability of viscous flow in a rapidly rotating pipe. J. Fluid Mech. 35, 97.
Pellew, A. & Southwell, R. V. 1940 On maintaining a convective motion in a fluid heated from below. Proc. Roy. Soc. A176, 312.
MathJax is a JavaScript display engine for mathematics. For more information see

Roll-cell instabilities in rotating laminar and trubulent channel flows

  • Dietrich K. Lezius (a1) (a2) and James P. Johnston (a1)


Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed