Coastal Baroclinic Two-Dimensional Turbulence. Part 2: Buoyancy Transport and Energy Transfer

This study demonstrates that large-scale coastal barotropic turbulence, rather than vortex dipoles, drives cross-shelf eddy buoyancy flux (EBF), with the eddies generated by an inverse energy cascade near the surface.Building on a companion paper (Part 1), we address three central questions: (1) What is the mechanism of EBF generation -large-scale barotropic stirring or vortex dipole interactions?(2) Do eddy-driven jets suppress EBF by forming transport barriers?(3) Does the inverse cascade of eddy kinetic energy in the coastal ocean conform to the dual-cascade theory?Our results show that barotropic eddies dominate EBF at scales near the energy containing scale, while eddy-driven jets locally reduce fluxes.The inverse cascade is confined to the upper layer due to the equivalent-barotropic state, while pressure work transmits energy downward to the bottom boundary layer, where it is dissipated through a "tele-friction" effect.The surface-intensified turbulence underscores the potential of high-resolution global sea surface height observations for quantifying cross-shelf transport and energy budgets.Finally, the convergence of scales identified in Part 1 emerges here as a direct consequence of the weak inverse cascade. IntroductionCross-shelf transport is a fundamental process in coastal oceans, mediating the exchange of heat, nutrients, and momentum between shelves and the open ocean.Understanding its driving mechanisms is essential for predicting coastal circulation, ecosystem dynamics, and regional climate.Two-dimensional (2D) baroclinic turbulence has been identified as one of the main drivers of cross-shelf transport, as shown in a companion manuscript by Hsu et al. (submitted; hereafter Part 1).Yet, the way the turbulence develops and controls transport remains uncertain, because many classical 2D turbulence theories were developed under weak-drag, flat-bottom assumptions that do not apply directly to coastal settings.Part 1 demonstrated that while classical scaling theories offer some explanation, non-negligible bottom drag in coastal regions fundamentally alters the dynamics.In particular, drag drives the system toward an equivalent-barotropic state (e.g., Arbic and Flierl 2004), in which turbulence is surface-intensified and near-bottom flow is nearly stagnant.This behavior contrasts sharply with quasi-geostrophic (QG) theories built for weak-drag flows, highlighting the need to reassess how coastal turbulence and transport should be interpreted within existing theoretical frameworks.Part 2 therefore focuses on identifying the mechanisms that generate cross-shelf eddy buoyancy flux (EBF) and clarifying how 2D turbulence in drag-dominated coastal regimes emerges to drive it.The physical mechanism of EBF remain uncertain in idealized QG models.Salmon (1980) and Larichev and Held (1995) proposed that barotropic turbulence stirs buoyancy as a passive tracer, producing flux in weak-drag regimes (i.e., , where is the Eady timescale and the Ekman timescale).In contrast, Thompson and Young (2006) argued that transport arises from interactions between isolated cyclonic (cold core) and anticyclonic (warm core) vortices, while Gallet and Ferrari (2020) emphasized the importance of vortex dipoles that strongly accelerate transport through circulation between paired vortices.However, these mechanisms may not directly apply to the coastal ocean.Friction is stronger than in the original weak-drag setups: Part 1 suggested / 0.47, a moderate-drag regime that falls near the edge of theoretical parameter space.For example, Gallet and Ferrari (2020)'s scaling starts diverging from model behavior when / (10 -1 -1) (see also Hadjerci and Gallet (2023, 2024); Chen (2023)).In addition, coastal length scales differ from theoretical assumptions.Larichev and Held (1995) assumed , where is the energy containing scale, and is