scholarly journals Finite amplitude perturbation and spots growth mechanism in plane Couette flow

1995 ◽  
Vol 7 (2) ◽  
pp. 335-343 ◽  
Author(s):  
O. Dauchot ◽  
F. Daviaud
Keyword(s):  
Couette Flow ◽  
Growth Mechanism ◽  
Finite Amplitude ◽  
Plane Couette Flow

Three-dimensional finite-amplitude solutions in plane Couette flow: bifurcation from infinity

1990 ◽  
Vol 217 ◽  
pp. 519-527 ◽  
Author(s):  
M. Nagata
Keyword(s):  
Couette Flow ◽  
Rotation Rate ◽  
Three Dimensional ◽  
Finite Amplitude ◽  
Narrow Gap ◽  
Plane Couette Flow ◽  
Bifurcation Problem ◽  
Bifurcation From Infinity ◽  
Flow Bifurcation ◽  
Average Rotation

Finite-amplitude solutions of plane Couette flow are discovered. They take a steady three-dimensional form. The solutions are obtained numerically by extending the bifurcation problem of a circular Couette system between co-rotating cylinders with a narrow gap to the case with zero average rotation rate.

Finite-Amplitude Perturbation in Plane Couette Flow

1994 ◽  
Vol 28 (4) ◽  
pp. 225-230 ◽  
Author(s):  
O Dauchot ◽  
F Daviaud
Keyword(s):  
Couette Flow ◽  
Finite Amplitude ◽  
Plane Couette Flow

A simple model of the mutual interaction of parallel flow and cellular motion in a shear layer applied to the finite amplitude instability of plane Couette flow

1979 ◽  
Vol 94 (3) ◽  
pp. 595-607 ◽  
Author(s):  
J. Steppeler
Keyword(s):  
Couette Flow ◽  
Equations Of Motion ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Parallel Flow ◽  
Nonlinear Dependence ◽  
Plane Couette Flow ◽  
Field Representation ◽  
Flow Equations ◽  
Cellular Motion

The disturbing motion of plane Couette and Poiseuille flow is described using three parameters: two amplitudes corresponding to the disturbance of the parallel flow and the cellular motion, respectively, and the angle ϕ0 which defines the orientation of the vortex blobs with respect to the parallel flow. Equations of motion for these parameters are obtained using a Ritz-Galerkin method. For Reynolds numbers above a critical value sufficiently big disturbances will grow until a steady finite amplitude state is achieved. The energy of the disturbance remains finite, in spite of the highly truncated field representation using only three parameters. This is possible because of the nonlinear dependence of the field functions on ϕ0. The critical values of Reynolds number, above which finite amplitude states exist, are computed for the plane Couette flow and the Poiseuille channel flow.

Finite amplitude instability of plane Couette flow

1977 ◽  
Vol 83 (3) ◽  
pp. 401-413 ◽  
Author(s):  
Terence Coffee
Keyword(s):  
Couette Flow ◽  
Chebyshev Polynomials ◽  
Rayleigh Quotient ◽  
Finite Amplitude ◽  
Plane Couette Flow ◽  
Formal Expansion ◽  
Sommerfeld Equation ◽  
Generalized Rayleigh Quotient ◽  
Rayleigh Quotient Iteration

The Orr–Sommerfeld equation is solved numerically using expansions in Chebyshev polynomials and the generalized Rayleigh quotient iteration. Accurate results for large values of the parameters are obtained, and these further verify the belief that plane Couette flow is stable to infinitesimal disturbances. For finite disturbances, a formal expansion based on the method of Stuart and Watson as modified by Reynolds & Potter is used. This method shows a transition to instability for a large enough amplitude.

Finite-amplitude equilibrium states in plane Couette flow

1997 ◽  
Vol 342 ◽  
pp. 159-177 ◽  
Author(s):  
A. CHERHABILI ◽  
U. EHRENSTEIN
Keyword(s):  
Couette Flow ◽  
Stokes Equations ◽  
Travelling Waves ◽  
Three Dimensional ◽  
Reynolds Numbers ◽  
Finite Amplitude ◽  
Equilibrium States ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Plane Couette Flow

A numerical bifurcation study in plane Couette flow is performed by computing successive finite-amplitude equilibrium states, solutions of the Navier–Stokes equations. Plane Couette flow being linearly stable for all Reynolds numbers, first two-dimensional equilibrium states are computed by extending nonlinear travelling waves in plane Poiseuille flow through the Poiseuille–Couette flow family to the plane Couette flow limit. The resulting nonlinear states are stationary with a spatially localized structure; they are subject to two-dimensional and three-dimensional secondary disturbances. Three-dimensional disturbances dominate the dynamics and three-dimensional stationary equilibrium states bifurcating at criticality on the two-dimensional equilibrium surface are computed. These nonlinear states, periodic in the spanwise direction and spatially localized in the streamwise direction, are computed for Reynolds numbers (based on half the velocity difference between the walls and channel half-width) close to 1000. While a possible relationship between the computed solutions and experimentally observed coherent structures in turbulent plane Couette flow has to be assessed, the present findings reinforce the idea that subcritical transition may be related to the existence of finite-amplitude states which are (unstable) fixed points in a dynamical systems formulation of the Navier–Stokes system.

On Itoh's finite amplitude stability theory for pipe flow

1978 ◽  
Vol 86 (4) ◽  
pp. 695-703 ◽  
Author(s):  
A. Davey
Keyword(s):  
Couette Flow ◽  
Pipe Flow ◽  
Stability Theory ◽  
Finite Amplitude ◽  
Circular Pipe ◽  
Plane Couette Flow ◽  
Subtle Difference ◽  
Opposite Result ◽  
Damping Rate

In two recent papers Itoh has developed a finite amplitude stability theory which indicates that nonlinearity increases the damping rate of a small but finite amplitude disturbance to flow in a circular pipe when the disturbance is concentrated near the axis of the pipe. For such a centre mode, which is the only mode considered by Itoh, Davey & Nguyen found, in an earlier paper, the opposite result that nonlinearity decreases the damping rate. We examine the reasons for this discrepancy and we explain the subtle difference between Itoh's method and the method of Reynolds & Potter, which was used by Davey & Nguyen.We suggest that for the centre mode of pipe flow neither Itoh's result nor Davey & Nguyen's result is a reliable guide to the true situation. However, for the wall mode of pipe flow, and especially for plane Couette flow, both methods give very similar results and we suggest that this similarity indicates that in these cases the damping rate is decreased by nonlinearity. For a particular problem we believe that it is only when the results of the two methods are very similar that either method is likely to be useful.

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