We investigate whether or not the default ocean-atmosphere turbulent flux algorithm in the Energy Exascale Earth System Model version 2 (E3SMv2) converges to unique surface fluxes. We demonstrate that under certain conditions (i) discontinuities in the underlying equations result in the lack of a solution for the algorithm to converge to, and (ii) more than one set of surface fluxes may satisfy the aforementioned equations, some of which may have non-physical interpretation. These issues underpinning the theoretical foundations of the parameterization have significant impacts on the accuracy and convergence of turbulent fluxes in E3SM.   We address issues of non-existence and non-uniqueness of surface fluxes in E3SM’s default algorithm by (a) regularizing discontinuous exchange coefficients to enforce continuity and allow the algorithm to converge to a solution of the underlying equations, and (b) utilizing an adaptive procedure for selecting limiting values of the Monin-Obukhov length to ensure the underlying equations have a unique solution. The proposed revisions result in significant changes to model latent and sensible heat fluxes which are most notable in boreal winter in the Northern Hemisphere.