TITLE:
Finding the Fibonacci Spiral Patterns in Atmospheric Equatorial Waves
AUTHORS:
Ranis Ibragimov, Eleanor Blake
KEYWORDS:
Atmospheric Waves, Fibonacci Sequence, Shallow Water Theory, Exact Solutions
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.10 No.12,
December
29,
2022
ABSTRACT: The purpose of this paper is to analyze and visualize the exact invariant solution of the nonlinear simplified version of the shallow water equations which are being used to simulate equatorial atmospheric waves of planetary scales. The method of obtaining the exact solution is based on the Lie group invariance principle. It is shown that the obtained invariant solution has a Fibonacci spiral-like form and has two parameters k and t0. We have defined a new model hypermarameter Δkt = t – t0, where t is time. The question of particular interest is: can we tune the hypermarameter in order to match the exact solution to the actual Fibonacci spiral? It was discovered that the physically relevant part of the solution matches exactly the Fibonacci spiral.