Numerical simulations used for weather and climate predictions solve approximations of the governing laws of fluid motions. The computational cost of these simulations limits the accuracy of the predictions. Uncertainties in the simulations and predictions ultimately originate from the poor or lacking representation of processes, such as turbulence, that are not resolved on the numerical grid of global climate models. I will show that using machine learning (ML) algorithms with imposed physical constraints are good candidates to improve the representation of processes that occur below the scales resolved by global models. In this talk, I will propose new representations of ocean turbulence based on two different ML approaches using data from high-resolution simulations. Specifically, I will discuss how to use relevance vector machines to discover equation for the sub grid forcing, and convolutional neural networks to derive a stochastic representation of sub grid forcing. The new models of turbulent processes are interpretable and/or encapsulate physics, and lead to improved simulations of the ocean. Our results simultaneously open the door to the discovery of new physics from data and the improvement of numerical simulations of oceanic and atmospheric flows.