Research on the Threshold of Flow State of Viscous Fluids Based on Chaotic Dynamics

In order to choose the threshold of different fluid state and reveal the physical mechanism of the flow, the thermal convection of channel flow of viscous fluid is investigated by the chaos dynamics in this paper, in which the temperature at lower plate is slightly higher than the upper plate. Based on the Navies-Stokes equations of viscous fluids, the heat conduction equations of the troposphere, the changes of temperature and velocity fields and a truncated Fourier representation, the low-dimensional nonlinear dynamic equations of viscous fluids can be obtained; Then, the low-dimensional nonlinear dynamic equations reduce to the Lorenz equations, the variations of bifurcation curve of the flow state with Prandtl and Rayleigh parameters were analyzed by the chaos dynamics. It can be seen that the Lyapunov exponent curve of the output characteristics of the system vary with Re parameters, and reveals the relationship between the threshold of Prandtl and Rayleigh parameters, as well as the flow state. The research of this article have important reference values on the physical mechanism and flow characteristics of viscous fluids.