## Viscous evolution of 2D dipolar vortices

J.H.G.M. van Geffen and G.J.F. van Heijst

*Fluid Dynamics Research* **22**, 191--213 (1998)

### abstract

Numerical simulations with a finite difference method have revealed that a
Lamb dipole when placed in a viscous fluid moves along a straight line with
decreasing velocity and increasing radius.
The relationship between vorticity and streamfunction, which initially is
linear, becomes more and more sinh-like as the dipole decays.
Some other initial dipolar vorticity distributions (like two oppositely
signed monopolar vortices) were found to evolve to a dipolar structure with
Lamb-like characteristics.

1. Introduction
2. The numerical model
2.1 Governing equations
2.2 A finite difference method
2.3 Viscous decay of a Rankine vortex
3. Theory of the Lamb dipole
4. Simulation of the Lamb dipole
4.1 The Lamb dipole at *t=0*
4.2 The Lamb dipole at *t=100*
4.3 The evolution of the Lamb dipole
4.4 The fate of the decaying Lamb dipole
4.5 The effect of the magnitude of the Reynolds number
5. Other symmetrical dipolar vortices
5.1 Circular dipole with uniform vorticity patches
5.2 Dipole consisting of two elliptic uniform monopoles
5.3 Dipole consisting of two elliptic Bessel-type monopoles
6. Concluding remarks
Acknowledgments
References

Full paper (1.4MB)

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