In this article, we investigate the effects of rotation on the dynamics, by neglecting stratification, in a 2D model where we incorporate the effects of the planetary rotation by adopting the β-plane approximation, which is a simple device used to represent the latitudinal variation in the vertical component of the Coriolis force. We consider the well-known 2D β-plane Navier-Stokes equations (2DβNS) in the statistically forced case. Our problem addresses energy-related phenomena associated with the solution of the equations. To maintain the fluid in a turbulent state, we introduce energy into the system through a stochastic force. In the 2D case, a scaling analysis argument indicates a direct cascade of enstrophy and an inverse cascade of energy. We compare the behaviour of the direct enstrophy cascade with the 2D model lacking the Coriolis force, observing that at small scales, the enstrophy flux from larger to smaller scales remains unaffected by the planetary rotation, confirming experimental and numerical observations. In fact, this is the first mathematically rigorous study of the above equations. In particular, we provide sufficient conditions to prove that at small scales, in the presence of the Coriolis force, the so-called third-order structure function’s asymptotics follows the third-order universal law of 2D turbulence without the Coriolis force. We also prove well-posedness and certain regularity properties necessary to obtain the mentioned results.