A quasi-periodic gravity modulation to suppress chaos in a Lorenz system

Abstract

This work is devoted to study the influence of quasi-periodic gravitational modulation on suppress chaos in a two-dimensional rectangular Newtonian fluid heated from below. The model consists of the heat equation coupled with the Navier–Stokes equation under the Boussinesq approximation. The problem is reduced to an autonomous system of ordinary differential equations by using the approximation on some Fourier modes. We solved these system by using the fourth-order Runge–Kutta method. A transition from periodic oscillatory convection to chaotic convection is identified for certain value of Rayleigh number and shape parameter in 3D Lorenz model. The results also show that the chaos can be suppressed by applied to a medium a quasi-periodic gravitational modulation for high and low Prandtl number in both Lorenz models 3D and 5D.