Improving Numerical Accuracy in a Regularized Barotropic Vorticity Model of Geophysical Flow

We study the BV-α-Deconvolution model. It is a family of regularizations of the Barotropic Vorticity (BV) model that generalize the BV-α model and improve its accuracy. A both unconditionally stable and optimally convergent scheme for the BV-α-Deconvolution model is proposed and we show that it is O(α), where N is the deconvolution order, whereas the BV-α model is at most second order accurate. We perform numerical simulations to confirm the predicted convergence rates and test the model in the traditional double gyre wind experiment. For the latter test, we show that the BV-α-Deconvolution model can retrieve the expected high resolution pattern being more accurate for larger values of deconvolution order.