A Low-order Model of Two-dimensional Fluid Dynamics on the Surface of a Sphere

Without any other approximations apart from the spectral method which is employed, the energy spectra corre-sponding to two kinds of "negative temperatures" are simulated with a symmetric trapezium truncation. The simu-lated results with either of the two negative temperatures are reasonably consistent with those from the statistical the-ory of turbulence. The more usual case for two positive temperatures evolves differently from the theoretical predic-tion.The viscosity influence on the ergodicity is discussed. It is shown that two-dimensional (2D) ideal flows on the sphere have a less pronounced tendency to be ergodic than those on planar geometry due to the curvature of the spherical surface that weakens the interaction between different parts of the flow, enabling these parts to behave in more relative isolation. The expressions for the standard deviations from a canonical ensemble for the two different options of coefficients are shown to be proportional to (N is the total number of independent modes in the sys?tem), independent of the initial conditions of the system