Assessing Lagrangian schemes for simulating diffusion on non-flat isopycnal surfaces

In large-scale ocean flows diffusion mostly occurs along the density surfaces and its representation resorts to the Redi isopycnal diffusivity tensor containing off-diagonal terms. This study focuses on the Lagrangian/particle framework for simulating such diffusive processes. A two-dimensional idealised test case for purely isopycnal diffusion on non-flat isopycnal surfaces is considered. Implementation of the higher order strong Euler, Milstein and order 1.5 Taylor schemes on our idealised test case shows that the higher order strong schemes produce the better pathwise approximations. The effective spurious diapycnal diffusivity is measured for each Lagrangian scheme under consideration. The propensity of the particles to move away from the isopycnal surface on which they were released is also measured. This shows that for non-flat isopycnals the order of convergence of the Euler scheme is not sufficient to achieve the desired accuracy. However, the Milstein scheme seems to be a good choice to achieve in an efficient way a fairly accurate result.

► We considered the particle tracking model for simulating diffusion on non-flat isopycnal surface.
► This model provides us to assess the reliability of the Lagrangian schemes on non-flat surfaces.
► Higher order strong Lagrangian schemes are implemented to achieve the accurate and efficient results.
► Milstein scheme provides the reliable and efficient results on non-flat isopycnal surface with less computational effort.