The transport of momentum, heat and salt by mesoscale eddies is an important component of the large-scale ocean circulation. General circulation models often do not resolve eddies directly but have to rely on turbulence closure parameterizations. One particular weakness of common parameterizations is that they do not allow up-gradient fluxes, where eddy fluxes feed into the large-scale gradients rather than erode them. This study will explore a novel approach to circumvent this limitation by representing the non-resolved eddy effects in terms of random forces. First, solutions of a hierarchy of ocean models of increasing complexity and realism will be analyzed. Here, a new dynamical decomposition of the oceanic turbulence into the eddy- and large-scale components will be applied. The large-scale/eddy interactions, that is, components of the eddy fluxes and their divergences, will be systematically analyzed. Second, the performance of the random model of the eddy forces will be systematically evaluated and compared against several existing parameterization schemes. The broader impacts of the proposed work is that it will aid in the general circulation and climate system modeling, in the interpretation of observational data sets, and in the planning of future observational strategies aimed at estimating the key eddy fluxes. Also, the ideas pursued are likely to have an impact on other areas of turbulence, where modeling subgrid-scale processes is an important issue.