# On the existence of two-dimensional nonlinear steady states in plane Couette flow

@article{Rincon2007OnTE, title={On the existence of two-dimensional nonlinear steady states in plane Couette flow}, author={F. Rincon}, journal={Physics of Fluids}, year={2007}, volume={19}, pages={074105-074105} }

The problem of two-dimensional steady nonlinear dynamics in plane Couette flow is revisited using homotopy from either plane Poiseuille flow or from plane Couette flow perturbed by a small symmetry-preserving identity operator. Our results show that it is not possible to obtain the nonlinear plane Couette flow solutions reported by Cherhabili and Ehrenstein [Eur. J. Mech. B/Fluids 14, 667 (1995)] using their Poiseuille-Couette homotopy. We also demonstrate that the steady solutions obtained by… Expand

#### 12 Citations

Equilibrium and travelling-wave solutions of plane Couette flow

- Physics
- Journal of Fluid Mechanics
- 2009

Axisymmetric travelling waves in annular sliding Couette flow at finite and asymptotically large Reynolds number

- Physics
- Journal of Fluid Mechanics
- 2013

Emergence of acoustic waves from vorticity fluctuations: impact of non-normality.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2009

#### References

SHOWING 1-10 OF 21 REFERENCES

On steady solutions of symmetry-preserving perturbations of the two-dimensional Couette flow problem

- Physics
- 2005

Exact coherent structures in pipe flow: travelling wave solutions

- Physics
- Journal of Fluid Mechanics
- 2004