# Instability of diverging and converging flows in an annulus

@article{Ilin2012InstabilityOD, title={Instability of diverging and converging flows in an annulus}, author={Konstantin Ilin and Andrey Morgulis}, journal={arXiv: Fluid Dynamics}, year={2012} }

The stability of two-dimensional diverging and converging flows in an annulus between two permeable cylinders is examined. The basic flow is irrotational and has both the radial and azimuthal components. It is shown that for a wide range of the parameters of the problem, the basic flow is unstable to small two-dimensional perturbations. The instability is inviscid and oscillatory and persists if the viscosity of the fluid is taken into consideration.

## References

SHOWING 1-10 OF 19 REFERENCES

### Hydromagnetic stability of dissipative flow between rotating permeable cylinders

- Engineering, PhysicsJournal of Fluid Mechanics
- 1967

The theory of stability of the flow of a viscous, electrically conducting fluid between rotating cylinders in the presence of an axial magnetic field is extended to the case where the cylinders are…

### Stability of Viscous Flow between Two Concentric Rotating Porous Cylinders

- Engineering, Physics
- 2014

The stability of a viscous flow between two concentric rotating porous cylinders has been examined when the difference in radii of the cylinders is small in comparison with their mean radius.…

### On the hydrodynamic and hydromagnetic stability of swirling flows

- PhysicsJournal of Fluid Mechanics
- 1962

Some general stability criteria for non-dissipative swirling flows are derived, and extended to the case of an electrically conducting fluid in the presence of axial magnetic field and current. In…

### Azimuthal instability of divergent flows

- PhysicsJournal of Fluid Mechanics
- 1993

We investigate a new mechanism for instability (named divergent instability), characterized by the formation of azimuthal cells, and find it to be a generic feature of three-dimensional steady…

### Convective instability boundary of Couette flow between rotating porous cylinders with axial and radial flows

- Engineering, Mathematics
- 1997

The convective instability boundary of a circular Couette flow in the annular region bounded by two co- or counter-rotating coaxial cylinders with angular velocities ω1 and ω2, respectively, is…

### Hydrodynamic stability of viscous flow between rotating porous cylinders with radial flow

- Physics, Engineering
- 1994

A linear stability analysis has been carried out for flow between porous concentric cylinders when radial flow is present. Several radius ratios with corotating and counter‐rotating cylinders were…

### Remarks on the Prandtl Equation for a Permeable Wall

- Mathematics
- 2000

The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to…

### The role of boundary conditions in a simple model of incipient vortex breakdown

- Physics
- 2004

We consider incipient vortex breakdown and describe how infinitesimal perturbations may destabilize a columnar swirling jet. The framework is axisymmetric and inviscid following Wang and Rusak’s [J.…