The parameterization of sub-grid scale processes is one of the key challenges towards improved numerical simulations of the atmospheric and oceanic circulation. Numerical weather prediction models as well as climate models would benefit from more sophisticated turbulence closures that allow for less spurious dissipation at the grid-scale and consequently higher and more realistic levels of eddy kinetic energy (EKE). Recent studies propose to use a hyperviscous closure in combination with an additional deterministic forcing term as a negative viscosity to represent backscatter of energy from unresolved scales. The sub-grid EKE is introduced as an additional prognostic variable that is fed by dissipation at the grid scale, and enables recycling of EKE via the backscatter term at larger scales. This parameterization was previously shown to work well in zonally re-entrant channel configurations. Here, a generalization in the form of a Rossby number-dependent scaling for the strength of the backscatter is introduced to represent the emergence of a forward energy-cascade in unbalanced flows near the boundaries. We apply the parameterization to a shallow water model of a double gyre basin and provide evidence for its general applicability. In terms of mean state and variability, a low resolution model is considerably improved towards a high resolution control run at low additional computational cost.