The wonderful page of spirals
Claire CHAUVIN - Hallvard KOSBERG (ENSIMAG 2ème année, juin
2000)
On this page we present some of the images we have computed with
Matlab.
On the choice of parameters
When to truncate the Fourier series
The range of r and Gibb's phenomenon
The linkes above leeds to graphs who helped us determine the parameters
for our computations. In this case, when to truncate the Fourier series,
and for which values of r and t our calculations are accurate.
Computed images and animations.
The starting point
Evolution of a double spiral
Evolution in contours
Here, t ranges from 30 to 200 and 0 to 175 ,respectively, with
the parameters and equations given in Lundgren's article (except the change
a -> r in the average velocity).
Comparison in G
Comparison in a
Comparison in h
Comparison in nu
For the four physical (yet dimensionless) parameters we have tried
to illustrate their effect on the system by varying them one by one.
The comparisons appear in the links above.
A different double spiral
Effects of viscosity
As our graphs and simulations seemed to differ from the ones depicted
in Lundgren's article, we decided to try some other defining functions.
We have stayed with functions resembling Lundgren's and in coherence with
the differential equation linking w0 and the average angular velocity.
Following the above link, you will see an example of another vortex sheet
roll-up with different characteristics.
If you have comments or suggestions, email us at cchauvin@ensibull.imag.fr
or hkosberg@ensibull.imag.fr