Two Modes of Vertical Velocity in Subsurface Mesoscale Eddies

Abstract

Two fundamental modes of vertical velocity (w) in mesoscale subsurface eddies are described using the quasigeostrophic (QG) approximation and nonhydrostatic numerical modeling. The first mode of w (the spheroidal mode) arises when a spheroidal upright subsurface eddy acquires horizontal eccentricity and becomes an ellipsoid, still upright, vertically symmetric vortex. In this case, the vertical displacement of isopycnals vanishes at the middepth z 5 0. Conservation of potential vorticity anomaly (PVA) on elliptical concave/convex isopycnals entails a three-dimensional octupolar pattern of w which also vanishes at z 5 0. The second mode of w (the tilted mode) arises when the eddy remains spheroidal but its vertical axis tilts relative to the vertical direction. In this case, the displacement of isopycnals is largest at the middepth z 5 0 and has a dipolar distribution. The associated w is largest at the middepth and develops also a dipolar pattern. In both spheroidal and tilted modes, the vertical velocity pattern may be inferred from the fast advection of PVA conserving fluid particles on slower translating concave/convex or tilted isopycnals. This implies that the vertical velocity of both modes is approximately QG and may be correctly inferred from the QG omega equation as long as the Rossby number remains small. Under more general circumstances, the vortex is both spheroidal and tilted. In this case, both spheroidal and tilted modes coexist but remain, to a large extent, uncoupled, rotating with different and, at least at a first order of approximation, constant phase speeds.Plain Language Summary The vertical velocity in ocean eddies depends on how the fluid particles depart from plane horizontal circular trajectories. We describe two basic ways by which this departure may take place. In the first way, the fluid particles at different depths rotate around the same vertical axis, but their trajectories are no longer circles but almost ellipses on concave or convex ellipsoidal surfaces of constant density. In the second way, the fluid particles at different depths describe almost circles on concave or convex spheroidal surfaces of constant density, but their axis of rotation is no longer vertical but tilted. These two different ways of vertical motion may coexist in the same vortex so that the vertical velocity of the fluid particles is the sum of these two ways of motion.

Global Mapping of Mesoscale Eddy Vertical Tilt

“…In contrast, the tilted eddy has a dipolar pattern of w (Figures 6b and 6d). For the vertical tilted eddy, the isopycnals are anomalously up in one side and down in another side, and the fluid motion along the isopycnals tends to ascend on one side while descend on another side, generating the dipolar pattern of w , consistent with Figure 4 in Viúdez (2018). The maximal w in tilted eddy ($${w}_{\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{t}}$$) is at least one order of magnitude larger than in non‐tilted eddy ($${w}_{\mathrm{n}\mathrm{o}\mathrm{n}\mathrm{t}\mathrm{i}\mathrm{l}\mathrm{t}}$$) (Figure 6e), indicating w is greatly affected by eddy vertical tilt.…”

“…Eddy vertical tilt can significantly influence vertical motion (Koszalka et al., 2009; Viúdez, 2018). To investigate this behavior, we compare w of the composite eddies with idealized tilted and non‐tilted structure diagnosed from the quasi‐geostrophic omega equation.…”

“…The vertical tilt of mesoscale eddies can strongly affect displacements of isopycnals (Viúdez, 2018), and potentially affect vertical transport of heat and tracers. It is of great importance to understand and quantify eddy vertical tilts in global oceans, and seek rules between eddy vertical tilt and background oceanic environments.…”

Skills and Limitations of the Adiabatic Omega Equation: How Effective Is It to Retrieve Oceanic Vertical Circulation at Mesoscale and Submesoscale?

“…Again this is presumably the signature of near-inertial wave activity. But contrary to the AZO case, the horizontal patterns visible in w fields are consistent with the structuring role of the (sub)mesoscale activity particularly during summer:presence of multipolar w patterns (Lapeyre and Klein 2006b;Viúdez 2018), that could be the signature of eddy-induced Ekman pumping and/or vortex Rossby waves (Mcwilliams et al 2003;Buongiorno Nardelli 2013;Barceló-Llull et al 2017), as in the left corner of Fig. 1c; elongated filaments of elevated w .…”

“…These model-based assessments of ω reconstructions were typically performed in simplified flow conditions, composed of a single coherent eddy or front, with a marked preference for the early stages of destabilisation of baroclinic zones (Strass 1994;Pinot et al 1996;Allen et al 2001;Rixen et al 2003;Viúdez 2018). More recently, the omega equation has been used to determine oceanic vertical velocity fields over larger domains and extended time periods from observationbased gridded reconstructions of temperature and salinity fields (Pascual et al 2015;Barceló-Llull et al 2016;Buongiorno Nardelli et al 2018).…”