Vertical velocities in quasigeostrophic laboratory vortices

Abstract: In the present study, we test the predictions of the ω-Equation against laboratory experiments with direct measurements of the vertical velocity w. Our results are further completed through the use of theoretical models of oceanic vortices, with the aim of helping oceanographers in better quantifying regions of upwelling and downwelling in the ocean. Using a rotating table and density stratification, we investigate non-axisymmetric surface vortices. The predicted vertical velocities calculated from the ω-Equation are relatively small (|w| ~ 20 μm/s) and primarily appear at the vortex edges, where the vorticity sign changes, acting to restore flow stratification. However, our estimates of w, obtained from the divergence of the horizontal velocity field measured by PIV, are five times larger. This discrepancy is further confirmed by direct particle tracking measurements, which indicate a magnitude of approximately 100 μm/s for w. To address this inconsistency, we incorporate dissipative terms into the ω-Equation to assess the role of viscous diffusion in enhancing internal recirculation in the vortex and thus vertical velocity magnitude. This hypothesis is favorably tested on a Gaussian vortex model.