Lorenz Equations: Explaining Apparent Unpredictability

  • Thread starter Thread starter Nusc
  • Start date Start date
  • Tags Tags
    Lorenz
Nusc
Messages
752
Reaction score
2
It's not clear to me why the Lorenz model shows us that the apparent unpredictability of turbulent fluid dynamics is deterministic.

Can anyone explain?
 
Physics news on Phys.org

Thread 'Volterra equation of the second kind'

There is the following linear Volterra equation of the second kind $$ y(x)+\int_{0}^{x} K(x-s) y(s)\,{\rm d}s = 1 $$ with kernel $$ K(x-s) = 1 - 4 \sum_{n=1}^{\infty} \dfrac{1}{\lambda_n^2} e^{-\beta \lambda_n^2 (x-s)} $$ where $y(0)=1$, $\beta>0$ and $\lambda_n$ is the $n$-th positive root of the equation $J_0(x)=0$ (here $n$ is a natural number that numbers these positive roots in the order of increasing their values), $J_0(x)$ is the Bessel function of the first kind of zero order. I...
View full post »

Similar threads

I Understanding Lorenz Gauge Derivation
Replies
1
Views
2K
Derivation: Maxwell's equation only from the Lorenz gauge
Replies
3
Views
2K
I Can Nonlinear Equations be Linearized Using Free Parameters?
Replies
4
Views
2K
B Solving Special Relativity Problems: Interval vs Lorenz Equations
Replies
9
Views
2K
Can an Ellipsoidal Region Contain All Trajectories of the Lorenz Equations?
Replies
2
Views
3K
Lorenz Attractors and Trajectories
Replies
1
Views
2K
A Why do the Navier-Stokes equations give us non-existent results for 3D flow?
Replies
9
Views
3K
Chaos and the Lorenz Equations
Replies
1
Views
2K
Understanding Lorenz Equations & Stability: A Homework Guide
Replies
1
Views
3K
Turbulence and Lorenz Attractor
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top