Quoted from: https://mitgcm.org/about-mitgcm/ 

MITgcm (MIT General Circulation Model) is a numerical model designed for study of the atmosphere, ocean, and climate. Its non-hydrostatic formulation enables it to simulate fluid phenomena over a wide range of scales; its adjoint capability enables it to be applied to parameter and state estimation problems. By employing fluid isomorphisms, one hydrodynamical kernel can be used to simulate flow in both the atmosphere and ocean.

You are welcome to download and use MITgcm.

Papers charting the development of MITgcm can be found here.

For visualizations of MITgcm output as applied to atmosphere, ocean and climate research, see MITgcm youtube channel.

Below are quoted from: https://mitgcm.readthedocs.io/en/latest/overview/overview.html#illustrations-of-the-model-in-action 

MITgcm has a number of novel aspects:

• it can be used to study both atmospheric and oceanic phenomena; one hydrodynamical kernel is used to drive forward both atmospheric and oceanic models - see Figure 1.1

Figure 1.1 MITgcm has a single dynamical kernel that can drive forward either oceanic or atmospheric simulations.

• it has a non-hydrostatic capability and so can be used to study both small-scale and large scale processes - see Figure 1.2

Figure 1.2 MITgcm has non-hydrostatic capabilities, allowing the model to address a wide range of phenomenon - from convection on the left, all the way through to global circulation patterns on the right.

• finite volume techniques are employed yielding an intuitive discretization and support for the treatment of irregular geometries using orthogonal curvilinear grids and shaved cells - see Figure 1.3

Figure 1.3 Finite volume techniques (bottom panel) are used, permitting a treatment of topography that rivals σσ (terrain following) coordinates.

• tangent linear and adjoint counterparts are automatically maintained along with the forward model, permitting sensitivity and optimization studies.

• the model is developed to perform efficiently on a wide variety of computational platforms.

Key publications reporting on and charting the development of the model are Hill and Marshall (1995), Marshall et al. (1997a), Marshall et al. (1997b), Adcroft and Marshall (1997), Marshall et al. (1998), Adcroft and Marshall (1999), Hill et al. (1999), Marotzke et al. (1999), Adcroft and Campin (2004), Adcroft et al. (2004b), Marshall et al. (2004) (an overview on the model formulation can also be found in Adcroft et al. (2004c)):