UNIVERSITY OF CALIFORNIA Los Angeles Topographic effects on mesoscale ocean circulation A dissertation submitted in partial satisfaction of the requirements for the degree Doctor of Philosophy in Atmospheric and Oceanic Sciences by Aviv Solodoch 2020 © Copyright by Aviv Solodoch 2020 Abstract of the Dissertation Topographic effects on mesoscale ocean circulation by Aviv Solodoch Doctor of Philosophy in Atmospheric and Oceanic Sciences University of California, Los Angeles, 2020 Professor James C. McWilliams, Co-chair Professor Andrew L. Stewart, Co-chair The trajectories and stability of boundary currents, of mesoscale vortices, and of recirculations, are often largely imposed by ocean bottom topography. Here several related questions in the influence of topography on mesoscale ocean circulation are investigated, largely motivated by observed circulation features in the sub-polar North Atlantic ocean. Observations show that boundary currents tend to become highly variable and shed material near sharp topographic variations, such as peninsula edges or corners of underwater capes. Baroclinic instability is understood to be one of the main causes of internal variability of large scale ocean circulation. Therefore the influence of horizontally curving topography on baroclinic instability is studied, under the hypothesis that the curvature may cause a higher tendency towards insta- bility. That is done within a minimum complexity model, a two-layer quasi-geostrophic model, and compared with the classic rectilinear model. First necessary conditions for instability as well as growth rate bounds are derived. Growth rates are calculated analytically or numerically for several flow and topography profiles. The growth rate in uniform azimuthal flow is similar to that in uniform rectilinear azimuthal flow, but decreases with increasing depth-averaged flow component amplitude. That is recognized as a generalization of the so called “barotropic gov- ernor” effect. Instability growth rate is nonetheless higher with uniform azimuthal flow when isopycnal slope is similar to the topographic slope magnitude, a common scenario in the ocean. ii Non-normal instability is studied as well, and is generally intensified with uniform azimuthal flow. Thus a complex picture emerges as to the influence of horizontal curvature on baroclinic instability. The Deep Western Boundary Current (DWBC) carries water masses formed in deep convection sites southward, as part of the Atlantic Overturning Meridional Circulation (AMOC), a circula- tion pattern of climatic importance. Observations show that the DWBC “leaks” material at an anomalously high rate in its path along two underwater capes in the Newfoundland Basin. The leakiness, resulting in water masses dilution, and in AMOC alternative (interior) pathways south- ward, has not been studied extensively from a dynamical perspective before. A high-resolution realistic regional numerical model configuration and a particle advection model are developed for this purpose. The numerical results, as well as two datasets of ocean float trajectories, are analyzed to determine the dynamical causes of leakiness and its phenomenology. It is found that leakiness is concentrated in three “hotspots”, in which topography turns and steepens. Mean Lagrangian velocity is offshore at these locations, showing that leakiness occurs by mean separa- tion. The mean velocity does not have a substantial eddy-rectified component at the two north- ern hotspots, where most of the mean leakiness happens. Likewise, energetic analysis shows ed- dies do not locally force the mean offshore flow. Furthermore, potential vorticity is not diluted substantially by eddies along mean separating streamlines. These results are consistent with mean leakiness occurring by inertial separation. A scaling analysis also suggests that bathymet- ric conditions near the leakiness hotspots are supportive of inertial separation. Eddy processes also contribute substantially to leakiness, partially through chaotic advection. In several North Atlantic basins semi-stationary anticyclonic vortices (ACs) have been repeat- edly observed for decades, within areas with bowl-like topography. These basins play significant parts in AMOC transport and transformations, and previous evidence suggests these ACs con- tribute to these processes. Therefore the formation processes of ACs above topographic bowls is studied here using idealized free evolution simulations in one or two isopycnal layers. It is demonstrated that ACs readily form under different (bowl-like) topographies and initial condi- iii tions. A non-dimensional nonlinearity parameter (ϵ ∼ ratio of vorticity to bowl PV gradient), or a potential vorticity (PV) inhomogeneity (PVI) parameter, largely determine if a trapped AC is formed from random mesoscale-like initial conditions. Trapped ACs form and stay close to bowl-center for ϵ . 0:5 (PVI ∼ 1). For ϵ & 1 (PVI ∼ 0) vortices freely cross the topography by mutual interactions. For intermediate ϵ or PVI values, trapped ACs can form at different bowl radii since the PV gradient is nullified by the presence of a slope current. Trapped ACs generally form by repeated mergers of ACs within the bowl, and have anomalously low PV. Tracer analysis shows that ACs which eventually merge into the trapped AC are sourced from within (outside) the bowl in low (high) energy cases. Two different cross-bowl propagation mechanisms are ex- amined. Monopole beta drift as well as dipole self propagation can both contribute to cross-bowl AC material transport, but the latter appears faster in relevant cases. The vertical structure of the trapped AC is studied as well. It is shown that it is top (bottom) intensified for top (bottom) in- tensified domain-mean initial conditions. That is consistent with observational structure but in contrast with the common vertical structure in Taylor Caps and of the slope current in our sim- ulations, which remain bottom-intensified in all cases. Scaling laws for vertical structures are suggested in several cases. The robustness of AC formation to topographic complexity is studied, as well as its long-term evolution, and the results are contrasted with topographic turbulence theories, which predict a slope current but not a bowl-trapped AC. iv The dissertation of Aviv Solodoch is approved. Jonathan Aurnou Gang Chen Andrew L. Stewart, Committee Co-chair James C. McWilliams, Committee Co-chair University of California, Los Angeles 2020 v I dedicate this work to my family. To my loving parents, Hana and Israel Solodoch, who imparted in me curiosity and the confidence to follow it. To my brothers, Dror and Omer, for always being there. To my wife, Gali, for lovingly making every day happier. To my daughter, Lia, for making everything worthwhile. vi Table of Contents 1 Introduction :::::::::::::::::::::::::::::::::::: 1 1.1 Topographic control in mesoscale ocean circulation . .1 1.2 Leakiness of the Deep Western Boundary Current . .4 1.3 Baroclinic instability on curved isobaths . .6 1.4 DWBC leakiness in a realistic regional numerical model . .7 1.5 Formation of Anticyclones above topographic depressions . .8 2 Baroclinic Instability Of Axially-Symmetric Flow Over Sloping Bathymetry ::: 10 2.1 Introduction . 10 2.2 Linear model of baroclinic growth in an annular channel . 13 2.2.1 Quasi-geostrophic model equations in cylindrical coordinates . 14 2.2.2 Method of solution . 17 2.2.3 Energy equation . 18 2.2.4 Mean flow profiles . 19 vii 2.3 Integral constraints on baroclinic growth . 21 2.3.1 Derivation of the Rayleigh theorem . 22 2.3.2 Stability bounds for solid-body rotation and uniform azimuthal flow . 23 2.4 Stability of flows in solid-body rotation . 24 2.5 Stability of uniform azimuthal flow . 28 2.5.1 Normal modes . 28 2.5.2 Non-normal growth . 36 2.5.3 Convex and concave cases . 38 2.6 Relation between baroclinic instability in straight and curved geometries . 39 2.7 Summary and Discussion . 41 2.8 Supplement . 45 2.8.1 Numerical verification and sensitivity tests . 45 2.8.2 Straight channel equations . 48 2.8.3 Semicircle theorem . 50 3 Why Does the Deep Western Boundary Current “Leak” Around Flemish Cap? :: 53 viii 3.1 Introduction . 53 3.2 Methods . 57 3.2.1 Numerical Model . 57 3.2.2 Float datasets . 61 3.2.3 Particle advection . 62 3.3 Results . 64 3.3.1 Lagrangian leakiness pathways . 64 3.3.2 Eulerian characterization of leakiness . 69 3.3.3 Robustness of spatial patterns of separation . 72 3.3.4 PV distribution and balance . 76 3.3.5 Energy conversions . 79 3.4 Discussion . 82 3.4.1 Mechanism of DWBC leakiness . 82 3.4.2 A scaling analysis of inertial separation . 86 3.4.3 Sensitivity to model circulation and resolution . 91 ix 3.5 Summary and Conclusions . 92 3.5.1 Phenomenology . 92 3.5.2 Dynamics . 93 3.5.3 Outlook . 95 3.6 Supplement . 97 3.6.1 Terms and acronyms . 97 3.6.2 Tracer diffusion noise . 97 3.6.3 Numerical model validation . 100 3.6.4 EKE comparison with altimetry and degradation with resolution . 106 3.6.5 Statistical comparison of model and observed DWBC transports . 108 3.6.6 Additional model DWBC transport validation . 109 3.6.7 Loss of ExPath floats around Flemish Cap . 110 3.6.8 Statistical significance of Lagrangian velocity average . 110 3.6.9 Additional Lagrangian mean diagnostics for model particles . 111 3.6.10 Streamfunction calculation by a flood-fill algorithm . 113 x 3.6.11 Cluster analysis of the horizontal circulation pattern variability . 114 3.6.12 Correlations between offshore velocity and bathymetric variation . 117 4 Formation Of Anticyclones Above Topographic Depressions ::::::::::: 119 4.1 Introduction . 119 4.2 Methods . 123 4.2.1 Layered Primitive Equations model . 123 4.2.2 Main experiments . 124 4.2.3 Coherent monopole and dipole experiments . 128 4.2.4 Eddy Detection . 128 4.3 Emergence of barotropic bowl-trapped anticyclones . 129 4.3.1 Emergent circulation over a bowl — case study . 129 4.3.2 Regime diagram . 133 4.3.3 Long-term evolution . 136 4.3.4 Spin-up of the anticyclone and slope current: a vorticity budget .