A deterministic model is developed to evaluate and explain the rate of dissipation of momentum in eddying oceanic flows. Theory is based on a classical conceptualization of mesoscale variability – Stern's modon-sea solution – which represents a closely packed array of steady compact dipolar vortices on the barotropic beta-plane. In our model, the periodic modon-sea pattern is subjected to a large-scale perturbation, weakly modulating the amplitude of the individual modons. The asymptotic multiscale analysis makes it possible to explicitly describe the interaction between the modon-sea eddies and the perturbing flow. This interaction results in a systematic weakening of the large-scale perturbation. The eddy viscosity in the model is found to be only weakly dependent on the explicit dissipation but rapidly decreases with increased separation of the modons. The estimates based on the modon-sea model are comparable to, but less than, the values of viscosity typically used in coarse resolution numerical ocean models. The eddy diffusivity of passive tracers is also evaluated and discussed in terms of a combination of analytical and numerical methods. The asymptotic theories are successfully tested by direct numerical simulations.