The three-dimensional (3-D) modelling of water systems involving double-diffusive processes is challenging due to the large computation times required to solve the flow and transport of constituents. In 3-D systems that approach axisymmetry around a central location, computation times can be reduced by applying a 2-D axisymmetric model setup. This article applies the Reynolds-averaged Navier-Stokes equations described in cylindrical coordinates and integrates them to guarantee mass and momentum conservation. The discretized equations are presented in a way that a Cartesian finite-volume model can be easily extended to the developed framework, which is demonstrated by the implementation into a non-hydrostatic free-surface flow model. This model employs temperature-and salinity-dependent densities, molecular diffusivities, and kinematic viscosity. One quantitative case study, based on an analytical solution derived for the radial expansion of a dense water layer, and two qualitative case studies demonstrate a good behaviour of the model for seepage inflows with contrasting salinities and temperatures. Four case studies with respect to doublediffusive processes in a stratified water body demonstrate that turbulent flows are not yet correctly modelled near the interfaces and that an advanced turbulence model is required. Kunze (2003) stresses that numerical and analytical methods to model double diffusion are often only applicable on specific scales. For example in oceans, internal wave shear and strain enhance salt-finger growth, leading to higher salt and heat fluxes over stratified interfaces. Traxler et al. (2011) addresses the issue of scale by describing four modes of instability in salt-fingering systems, which play a role on different scales. Their 3-D simulations of large-scale instability in salt-fingering systems are the first known successful direct numerical simulations (DNSs). Carpenter et al. (2012) were among the first to model systems in the double-diffusive convection regime with 3-D DNS. Their detailed simulations showed that, in this regime, the salt and heat fluxes across the interface are largely governed by molecular diffusion and that these salt and heat diffusion rates control the thickness of the salt and heat interface, respectively. Kimura and Smyth (2007) used 3-D DNS to model salt sheets for a doublediffusively stratified flow interacting with inflectional shear.