We propose and investigate three approaches to a fluid-fluid interaction problem with a nonlinear rigid lid condition on the joint boundary when one or both flows are at a high Reynolds number. To do so, we tr y to combine the Approximate Deconvolution Model of turbulence with a partitioned method of , called the Geometric Averaging. The nonlinear interface condition poses an extra difficulty, as there are different approaches to modeling the Reynolds stresses on the joint bounda r y of the two flows. We investigate three such approaches; a l l three models are shown to be quantitatively similar when tested on a model with a manufactured solution. Two of them are proven to be unconditionally stable, and yet it is the third model that clearly outperforms the others in the most computationally appealing case when high Reynolds number flow s are modeled on a coarse mesh with large filtering width.