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 pl...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 t<sub>0</sub>. We have defined a new model hypermarameter Δ<sub>k</sub>t = t – t<sub>0</sub>, 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.展开更多
文摘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 t<sub>0</sub>. We have defined a new model hypermarameter Δ<sub>k</sub>t = t – t<sub>0</sub>, 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.
