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arXiv · 2606.11055

Exponential mixing and enhanced dissipation on the unit sphere with Rossby-Haurwitz flows

Augusto Del Zotto·Marc Nualart
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Abstract

We exhibit a family of smooth incompressible velocity fields on the two-dimensional unit sphere such that the time evolution of any mean-free initial data passively advected by any of them is mixed exponentially fast. In the presence of molecular diffusivity, we show that the solution to the associated advection-diffusion equation experiences enhanced dissipation with optimal decay rates. Each member of this family is an alternating combination of two Rossby-Haurwitz flows with random amplitudes and constitutes a spherical analogue to the sine shear-alternating example of Pierrehumbert.

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Augusto Del Zotto, Marc Nualart. 2026-06-09. Exponential mixing and enhanced dissipation on the unit sphere with Rossby-Haurwitz flows. https://arxiv.org/abs/2606.11055

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