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To capture the effects of mesoscale turbulent eddies, coarse‐resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper‐accelerations. These parameterizations are referred to as the first, second and third order "Markov models" (Markov‐N), respectively. Most previous studies investigate these parameterizations in two‐dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov‐0) dispersion. Here, we present a three‐dimensional isoneutral formulation of the Markov‐1 model. We also implement an anisotropic, shear‐dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov‐1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov‐1 produce similar particle distributions over time when using our ocean model output, Markov‐1 yields Lagrangian trajectories that better resemble trajectories from eddy‐resolving simulations. Markov‐1 also yields a smaller spurious dianeutral flux. Plain Language Summary: Turbulent eddies stir and disperse material in the ocean. Depending on the resolution of ocean models, these eddies can have length scales that are too small to be resolved explicitly, so they need to be represented by parameterizations. This implies that when particle pathways are computed in Lagrangian simulations, the effect of eddy dispersion also needs to be parameterized. This is traditionally done by adding a random walk on top of successive particle positions. An improvement of this parameterization, referred to as the Markov‐1 model, adds random perturbations to particle velocities instead. Dispersion parameterizations have been studied primarily at the surface in two dimensions. In contrast, eddies in the ocean interior predominantly stir and disperse along tilted surfaces of neutral buoyancy. We present a novel three‐dimensional formulation of the Markov‐1 model and compare it to the random walk model in an idealized setup, as well as using more realistic coarse and coarsened (50 km) ocean model output. Particle distributions produced by both models are similar, but the trajectories produced by Markov‐1 better resemble trajectories from simulations that explicitly resolve eddies. Markov‐1 also is better able to restrict particle movement to the tilted neutral buoyancy surfaces. Key Points: We create a 3D isoneutral version of the Markov‐1 Lagrangian dispersion model, similar to Redi's isopycnal rotation of the diffusion tensorDispersion from Markov‐1 includes ballistic and diffusive regimes, making trajectories more realistic than those from random walk modelsMarkov‐1 produces a much smaller spurious dianeutral diffusivity than Markov‐0 (random walk) [ABSTRACT FROM AUTHOR]

Abstract To capture the effects of mesoscale turbulent eddies, coarse‐resolution Eulerian ocean models resort to tracer diffusion parameterizations. Likewise, the effect of eddy dispersion needs to be parameterized when computing Lagrangian pathways using coarse flow fields. Dispersion in Lagrangian simulations is traditionally parameterized by random walks, equivalent to diffusion in Eulerian models. Beyond random walks, there is a hierarchy of stochastic parameterizations, where stochastic perturbations are added to Lagrangian particle velocities, accelerations, or hyper‐accelerations. These parameterizations are referred to as the first, second and third order “Markov models” (Markov‐N), respectively. Most previous studies investigate these parameterizations in two‐dimensional setups, often restricted to the ocean surface. On the other hand, the few studies that investigated Lagrangian dispersion parameterizations in three dimensions, where dispersion is largely restricted to neutrally buoyant surfaces, have focused only on random walk (Markov‐0) dispersion. Here, we present a three‐dimensional isoneutral formulation of the Markov‐1 model. We also implement an anisotropic, shear‐dependent formulation of random walk dispersion, originally formulated as a Eulerian diffusion parameterization. Random walk dispersion and Markov‐1 are compared using an idealized setup as well as more realistic coarse and coarsened (50 km) ocean model output. While random walk dispersion and Markov‐1 produce similar particle distributions over time when using our ocean model output, Markov‐1 yields Lagrangian trajectories that better resemble trajectories from eddy‐resolving simulations. Markov‐1 also yields a smaller spurious dianeutral flux.

Abstract: A large eddy simulation (LES) is used to compute passive scalar dispersion in a turbulent flow. Instead of resolving the passive scalar transport equation, fluid particles are tracked in a Lagrangian way and a Langevin stochastic modelling is used for the small scale component of the velocity of fluid particles at a subgrid-scale level. The stochastic model is written in terms of subgrid-scale statistics. The specificity of this study resides in the coupling of a LES with a stochastic model using the filtered subgrid-scale statistics in inhomogeneous turbulence. The results are compared with the wind tunnel experiments of Fackrell and Robins [J. Fluid Mech. 117 (1982) 1–26]. To cite this article: I. Vinkovic et al., C. R. Mecanique 333 (2005). [Copyright &y& Elsevier]