Abstract:A three-dimensional primitive-equation ocean front model is employed to simulate mesoscaleinstabilities, and then to investigate the validity (and the contingent differences) of three alternativemethods used for the diagnosis of mesoscale vertical motion from combined density and horizontalvelocity mappings: (1) the isopycnic advection equation, (2) the vorticity advection equation, and (3) thew-equation. The model is integrated for 60 days during which period meanders form along the initiallyunidirectional jet, first preferably at a wavelength of just under 100 km and later also at smaller horizontalscales; these growing instabilities are associated with vertical velocities of up to some tens of metres perday. The horizontal distribution pattern of vertical velocity can reasonably be estimated by use of (3) andalso (2), but (1) may yield a pattern having the wrong phase relationship.