Lorenz Model Animations

Animations of High-Dimensional Lorenz Models in Python

Janessa Tran

Department of Mathematics and Statistics

San Diego State University

(Created: 07/05/2016 by Janessa)

(Last Updated: 07/06/2016)

In the following, we apply the Python programming language to produce animations for the classical Lorenz Model (LM; e.g. Lorenz, 1963) and high-dimensional LMs, including the 5-dimensional (5D) and 7D LMs (e.g., Shen 2014, 2015, 2016). In addition to the animations, still images are also provided for a comparison of results produced by Python and other computer languages (e.g., Fortran and/or R). With the exception for the heating parameter (r), the following parameters are kept constant: σ = 10, b = 8 / 3, d_o = 19 / 3, d₁ = 17. The dimensionless time interval (▵τ) is 0.01 and the total number of time steps (N) is 5,000, yielding a total dimensionless time (τ) of 50. The still image displays results from the control run with an initial condition of Y = 1.0, the other parameters being 0. Source codes are available upon request.

3D Lorenz Model

This is an animation of a 3D Lorenz Model with r = 28.0.

5D Lorenz Model

This is an animation of a 5D Lorenz Model with r = 45.0.

7D Lorenz Model

This is an animation of a 7D Lorenz Model with r = 120.0.

2D Plots

References:

Lorenz, E., 1963: Deterministic nonperiodic flow. J. Atmos., Sci., 20, 130-141.

Shen, B.-W., 2014: Nonlinear Feedback in a Five-dimensional Lorenz Model. J. of Atmos. Sci. 71, 1701–1723. doi: http://dx.doi.org/10.1175/JAS-D- 13-0223.1

Shen, B.-W., 2015: Nonlinear Feedback in a Six-dimensional Lorenz Model. Impact of an Additional Heating Term. Nonlin. Processes Geophys., 22, 749-764, doi:10.5194/npg-22- 749-2015, 2015.

Shen, B.-W., 2016: Hierarchical scale dependence associated with the extension of the nonlinear feedback loop in a seven-dimensional Lorenz model. Nonlin. Processes Geophys. Discuss., doi:10.5194/npg-2016- 10. (accepted by Nonlin. Processes Geophys, June 23, 2016).

Links to animations:

1). 3DLM - https://youtu.be/Hx-Z5rTziXI

2). 5DLM - https://youtu.be/tkqTmyTqgOc

3). 7DLM - https://youtu.be/lDzYki9R94Q