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  1. Oceanic eddies accompanied by a significant vertical velocity ( w ) are known to be of great importance for the vertical transport of various climatically, biologically or biogeochemically relevant properties. Using quasi-geostrophic w -thinking to extend the classic “ β -spiral” w -theory for gyre circulations to isolated and nearly symmetric oceanic mesoscale eddies, we propose that their w motion will be dominated by a strong east-west dipole pattern with deep ocean penetrations. Contrasting numerical simulations of idealized isolated eddies together with w -equation diagnostics confirm that the w -dipole is indeed dominated by the “eddy β -spiral” mechanism in the β -plane simulation, whereas this w -dipole expectedly disappears in the f -plane simulation. Analyses of relatively isolated warm and cold eddy examples show good agreement with the proposed mechanism. Our studies further clarify eddy vertical motions, have implications for ocean mixing and vertical transport, and inspire further studies. 
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