Towards improved numerical schemes of turbulent lateral dispersion

• Explores alternative approach of lateral dispersion based on linear spreading.
• Calibrates and tests approach against hydrodynamic model simulations.
• Proposes new approach as replacement for ill-defined Fickian diffusion models.

This paper focuses on an alternative approach of lateral turbulent dispersion, proposed by Benoit Cushman-Roisin in 2008, that is based on a linear increase of the width of dispersing patches in a field of isotropic horizontal turbulence. In the open ocean, this Richardson-like dispersion regime is a well-observed feature on sub-mesoscale length scales from 10 to 100 km. In this work, we successfully validate and calibrate the new diffusion scheme using Lagrangian particles and Eulerian tracer in turbulent velocity fields simulated with the shallow-water equations. In discretized form, the new diffusion scheme exclusively relies on specification of a turbulent velocity scale that, unlike the turbulent diffusivity of Fickian approaches, is well defined through statistical properties of the turbulent flow.

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