Non-linear and linear evolution of perturbation in stochastic basic flows

• Linear and nonlinear evolution for stochastic QG model on a sphere are examined.
• TLM will fail when time is long and stocahstic fuctuation becomes large.
• The stochastic fluctuationwill enhance dissipation and accelerate energy decay.

In this paper, we examine the non-linear and linear evolutions of perturbation in stochastic basic flows with two-dimensional quasi-geostrophic equations on a sphere. As the analytic solutions for the considered quasi-geostrophic equations are not available, the Fourier finite volume element method is used to perform numerical simulation. It is found that, the non-linear and linear evolutions of perturbation in stochastic basic flow will be consistent for a short period of time and small stochastic fluctuations when they are consistent in the deterministic basic flow. However, the tangent linear model will fail to approximate the original non-linear model when the time period is considerably long and stochastic fluctuation becomes large. Moreover, the global energy decays faster for stochastic basic flow with stronger fluctuations.