Dipole Patterns Of The Vertical Velocity In Isolated Oceanic Mesoscale Eddies Induced By The β Effect

The global oceans are filled with mesoscale eddies in the range of tens to hundreds of kilometers in diameter,which are one of the most prominent motions of water column in the ocean.These eddies propagate nearly westward at approximately the phase speed of nondispersive baroclinic Rossby waves,and they can achieve longdistance material transportation by carrying water along with them during propagation.Oceanic eddies accompanied by a significant vertical velocity are of great importance for the vertical transport of biological or biogeochemical tracers such as heat,salt,dissolved oxygen,chlorophyll,and nutrients in the ocean.The conventional theory suggests that the vertical velocity of mesoscale eddies is a monopole pattern,i.e.,the warm eddy core downward isopycnals by convergence and the cold eddy core raises isopycnals by divergence,which is known as the "Eddy Pumping" mechanism.This mechanism is widely adopted by the oceanographic community.At the same time,the vertical velocity of the ocean is difficult to measure directly due to the limitation of observation.Therefor,a dynamical diagnostic ωequation is usually used to calculate vertical velocity indirectly.However,almost all related studies are based on the assumption of f plane,and the role of the β effect of the variation of f with latitude is neglected in the ω equation.While it is known that the vertical velocity of the whole water with large scale motion will be zero without the βeffect.Meanwhile,considering the β effect as the driving mechanism of Rossby westward propagation,the scaling analysis shows that the β effect is important for the mesoscale eddies.Therefore,what the vital influence doe β effect has on eddy vertical velocity is worth further discussion.In order to verify the effect of β effect on the vertical velocity of the mesoscale eddies,we firstly perform a new theoretical derivation of the ω equation on the β plane and obtain the expression form with a clearer physical significance.Then,numerical simulations of the idealized isolated eddies on the β plane and the f plane based on ROMS model are perfomed,respectively.The experimental results show that the vertical velocity of the idealized isolated eddy on the β plane shows a significant eastwest dipole pattern,while the eddy on the f plane does not have such a dipole pattern.Combining the results of the contrasting numerical solutions of the new form ωequation considering the β term and omitting the β term,we clearly prove that the vertical velocity of the isolated mesoscale eddies is a dipole pattern and that the dipole pattern is caused by the β effect.To further verify the dipole pattern of the vertical velocity within eddies,we use the high-resolution OFES model outputs and select two typical isolated eddies with similar analyses of idealized eddies.One of them is a cold eddy near the Kuroshio Extension and the other is a warm eddy originating from Cape Agulhas.It turns out that the vertical velocities in both eddies show significant dipole patterns,i.e.,along the direction of motion,there is a downwelling/upwelling in front of the warm/cold eddy and an upwelling/downwelling in the eastern part of eddy along the propagation direction.Similarly,the diagnosis of the ω equation with/without the β term redemonstrates that the vertical velocity in isolated eddies show strong east-west dipole patterns dominanted by the β effect.In the traditional "Eddy pumping" theory,the vertical motion of the eddy core is a monopole upwelling(cold eddy)or downwelling(warm eddy),i.e.,the water in the cold eddy core divergence and leads to upwelling,and the water in the center of the warm eddy convergence and leads to downwelling.The w-dipole patterns induced by the β effect proposed in our study is a modification for classical theory.Combining the above results,we propose an "eddy β spiral" mechanism,which extends the classical "β spiral" theory for gyre circulation to isolated and nearly symmetric oceanic mesoscale eddies.The "eddy β spiral" mechanism demonstrates that because an isolated mesoscale eddy always has an east-west dipole pattern in its meridional velocity,its vertical motion will also be dominated by an east-west dipole pattern caued by the β effect with its strength proportional to eddy meridional velocity.The numerical simulations of the idealized isolated eddies based on ROMS and the isolated eddied from the outputs of high-resolution OFES model,as well as the diagnostic results of the ω equation confirm the accuracy of the mechanism.It is notable that strength of w-dipole increases dramatically with depth.It appears to be very weak in the upper layer but strong in the deep ocean,with its maximum occurring at ocean depths of several kilometers.The w-dipoles may have considerable impacts on vertical motions in deep ocean along the eddy tracks,which in turn causes vertical transport and mixing within the eddies.Therefore,the vertical transport related to mesoscale eddies remains to be further investigate.Our studies provide a new insight into vertical motion of eddies and their effects on mixing and vertical transport in the deep ocean.