Snapshots of vertically integrated vorticity, normalized by fh m for solutions with no bottom drag: (a) h ^ = 1.6, (b) h ^ = 3.2, and (c) h ^ = 6.4. Values of the parameter h ^ are indicated inside each panel. (10) and (bottom) difference of BPT and BSDT, both time-averaged and normalized by fh m V 0 a −1. (top) Bottom pressure torque (BPT), defined in Eq. Values of the parameter h ^ are indicated inside each panel: (a) anticyclonic side and (b) cyclonic side. BSDT is the bottom stress divergence torque, VSVT denotes the net sum of vortex stretching and tilting terms, and EA is the eddy advection a is the ridge half-width and s/ a is the normalized distance along the streamline.
(18) to ω ¯ averaged separately on each of the cyclonic and anticyclonic sides across the streamlines depicted in Fig. Partial cumulative integrations of source terms on the RHS of Eq.
Each term has been normalized by fh m V 0 a −1: (a) h ^ = 3.2 and (b) h ^ = 6.4. VSVT is the sum of the vortex stretching (VS) and tilting (VT) terms. Time-averaged generation terms on the RHS of the integrated vorticity equation, Eq. The black and green contour lines are, respectively, streamlines of the barotropic transport U and bathymetry contours at z = 0.14 h m, z = 0.37 h m, and z = 0.9 h m. Time averages of vertically integrated vorticity, normalized by fh m for the ridge solutions. The subpanel columns in (a) and (b) depict the following vertical sections: (left) at encounter region y/ a = 10 and (right) averaged across the straight section of the ridge. (a) Stress divergence curl and (b) VS + VT, the sum of vortex stretching and tilting terms in Eq. (6), normalized by fV 0 a −1 and overlain by flow isopycnals for (top) h ^ = 1.6 and (bottom) h ^ = 6.4, indicated inside the leftmost panel. Time-averaged tendency terms in the 3D vertical vorticity equation, Eq. The dimensional h bbl are smaller for larger h ^. Note that u * here is taken to be the average friction velocity over the flat bottom, away from the ridge, for the respective h ^ cases. The time-mean BBL height h bbl normalized by 3 u * / N f at two different locations-one in the encounter region ( y/ a = 10) and the other further downstream ( y/ a = 34). Normalized, time-averaged boundary stress. Vertical sections of normalized, time-mean vertical vorticity ζ/ f overlain by isopycnals at successive downstream locations: (top) h ^ = 1.6 and (bottom) h ^ = 6.4. Vertical sections of normalized, time-mean along-slope velocity υ/ V 0 overlain by isopycnals at successive downstream locations: (top) h ^ = 1.6 and (bottom) h ^ = 6.4. Note that the panel aspect ratio (height-to-width) is smaller than the true aspect ratio. The geostrophically balanced background flow is from south to north. The green lines are bathymetry contours at z = 0.14 h m, z = 0.37 h m, and z = 0.9 h m. Snapshots of vertically integrated vorticity, normalized by fh m for barotropically forced flow past an elongated ridge.