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  = 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  = 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  = 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.