In this paper we give sufficient conditions for random splitting systems to
have a positive top Lyapunov exponent. We verify these conditions for random
splittings of two fluid models: the conservative Lorenz-96 equations and
Galerkin approximations of the 2D Euler equations on the torus. In doing so, we
highlight particular structures in these equations such as shearing. Since a
positive top Lyapunov exponent is an indicator of chaos which in turn is a
feature of turbulence, our results show these randomly split fluid models have
important characteristics of turbulent flow.