A data-driven emulator for the baroclinic double gyre ocean simulation is presented in this study. Traditional numerical simulations using partial differential equations (PDEs) often require substantial computational resources, hindering real-time applications and inhibiting model scalability. This study presents a novel approach employing neural operators to address these challenges in an idealized double-gyre ocean simulation. We propose a deep learning approach capable of learning the underlying dynamics of the ocean system, complementing the classical methods, and effectively replacing the need for explicit PDE solvers at inference time. By leveraging neural operators, we efficiently integrate the governing equations, providing a data-driven and computationally efficient framework for simulating the double-gyre ocean circulation. Our approach demonstrates promising results in terms of accuracy and computational efficiency, showcasing the potential for advancing ocean modeling through the fusion of neural operators and traditional oceanographic methodologies. In comparison to a dynamical numerical model, we obtain 600x speedups allowing us to create 2000-day ensembles in tens of seconds instead of hours.