Turbulent-Laminar Patterns

Dwight Barkley and Laurette Tuckerman

This research concerns turbulent-laminar patterns found near transition in large-aspect-ratio plane Couette flow [6,7]. Such patterns are also found in circular Couette-Taylor flow [6,7] and in flow between a rotating and stationary disk [5]. These patterns appear to be related to spiral turbulence originally observed by Coles and van Atta [2,3,4].

Our work shows the existence of 3 basic types of states: intermittent, periodic, and localized.

Read the PRL and JFM here: [1]

Turbulent-Laminar Patterns in Experiments These are all very large-aspect-ratio flows. The two directions seen are large compared with the remaining (wall-normal) direction.
Plane Couette flow, from Prigent et al. [6,7]. In light regions the flow is turbulent and in dark regions the flow is relatively laminar.
Circular Couette-Taylor flow, from Prigent et al. [6,7]. In light regions the flow is turbulent and in dark regions the flow is relatively laminar.	Flow between disks, from Cros and Le Gal [5]. In dark regions the flow is turbulent and in light regions the flow is relatively laminar.

Turbulent-Laminar Patterns in Experiments

These are all very large-aspect-ratio flows. The two directions seen are large compared with the remaining (wall-normal) direction.

Plane Couette flow, from Prigent et al. [6,7]. In light regions the flow is turbulent and in dark regions the flow is relatively laminar.

Circular Couette-Taylor flow, from Prigent et al. [6,7]. In light regions the flow is turbulent and in dark regions the flow is relatively laminar.

Flow between disks, from Cros and Le Gal [5]. In dark regions the flow is turbulent and in light regions the flow is relatively laminar.

Turbulent-Laminar Patterns in Simulations of Plane Couette Flow These are some visualizations of the spatially periodic pattern in our simulations at Re=350.
Streamwise velocity in midplane between moving plates. The streamwise velocity is shown in greyscale in streamwise-spanwise coordinates. The wall-normal coordinate is not seen. The area shown is 120x120. The computational domain is shown in white.	Vorticity isosurfaces. Shown are iso-surfaces at plus and minus 0.5. Only a small region of the pattern is shown.

Turbulent-Laminar Patterns in Simulations of Plane Couette Flow

These are some visualizations of the spatially periodic pattern in our simulations at Re=350.

Streamwise velocity in midplane between moving plates. The streamwise velocity is shown in greyscale in streamwise-spanwise coordinates. The wall-normal coordinate is not seen. The area shown is 120x120. The computational domain is shown in white.

Vorticity isosurfaces. Shown are iso-surfaces at plus and minus 0.5. Only a small region of the pattern is shown.

Movies Re=350 These are some visualizations of the spatially periodic pattern in our simulations at Re=350.
Kinetic Energy in midplane. The wall-normal coordinate is not seen. The area shown is 120x120. Each loop shows three hundred time units of simulation. The pattern is stationary even though the flow in the turbulent regions is quite complex.
Streamwise velocity between moving plates. Domain is spanwise by wall-normal slice of dimensions 60 by 2.
Streamwise vorticity between moving plates. Same slice as above.

Movies Re=300 These are some visualizations of the localized turbulent state at Re=300.
Streamwise velocity between moving plates. Domain is spanwise by wall-normal slice of dimensions 90 by 2.
Streamwise vorticity between moving plates. Same slice as above.

Movies Re=300

These are some visualizations of the localized turbulent state at Re=300.

Streamwise velocity between moving plates. Domain is spanwise by wall-normal slice of dimensions 90 by 2.

Streamwise vorticity between moving plates. Same slice as above.

Dwight Barkley 2005-04-18