  The proposed method aims to approximate a solution of a fluid-fluid
interaction problem in case of low viscosities. The nonlinear interface
condition on the joint boundary allows for this problem to be viewed as a
simplified version of the atmosphere-ocean coupling. Thus, the proposed method
should be viewed as potentially applicable to air-sea coupled flows in
turbulent regime. The method consists of two key ingredients. The geometric
averaging approach is used for efficient and stable decoupling of the problem,
which would allow for the usage of preexisting codes for the air and sea domain
separately, as "black boxes". This is combined with the variational multiscale
stabilization technique for treating flows at high Reynolds numbers. We prove
the stability and accuracy of the method and provide several numerical tests to
assess both the quantitative and qualitative features of the computed solution.
