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In inertial-range turbulence, structure functions can diagnose transfer or dissipation rates of energy and enstrophy, which are difficult to calculate directly in flows with complex geometry or sparse sampling. However, existing relations between third-order structure functions and these rates only apply under isotropic conditions. We propose new relations to diagnose energy and enstrophy dissipation rates in anisotropic two-dimensional (2-D) turbulence. These relations use second-order advective structure functions that depend on spatial increments of vorticity, velocity, and their advection. Numerical simulations of forced-dissipative anisotropic 2-D turbulence are used to compare new and existing relations against model-diagnosed dissipation rates of energy and enstrophy. These simulations permit a dual cascade where forcing is applied at an intermediate scale, energy is dissipated at large scales, and enstrophy is dissipated at small scales. New relations to estimate energy and enstrophy dissipation rates show improvement over existing methods through increased accuracy, insensitivity to sampling direction, and lower temporal and spatial variability. These benefits of advective structure functions are present under weakly anisotropic conditions, and increase with the flow anisotropy as third-order structure functions become increasingly inappropriate. Several of the structure functions also show promise for diagnosing the forcing scale of 2-D turbulence. Velocity-based advective structure functions show particular promise as they can diagnose both enstrophy and energy cascade rates, and are robust to changes in the effective resolution of local derivatives. Some existing and future datasets that are amenable to advective structure function analysis are discussed. 

Abstract Coastal hypoxia—harmfully low levels of oxygen—is a mounting problem that jeopardizes coastal ecosystems and economies. The northern Indian Ocean is particularly susceptible due to human‐induced impacts, vast naturally occurring oxygen minimum zones, and strong variability associated with the seasonal monsoons and interannual Indian Ocean Dipole (IOD). We assess hownaturalfactors influence the risk of coastal hypoxia by combining a large set of oxygen measurements with satellite observations to examine how the IOD amplifies or suppresses seasonal hypoxia tied to the Asian Monsoon. We show that on both seasonal and interannual timescales hypoxia is controlled by wind‐ and coastal Kelvin wave‐driven upwelling of oxygen‐poor waters onto the continental shelf and reinforcing biological feedbacks (increased subsurface oxygen demand). Seasonally, the risk of hypoxia is highest in the western Arabian Sea in summer/fall (71% probability of hypoxia). Major year‐to‐year impacts attributed to the IOD occur during positive phases along the eastern Bay of Bengal (EBoB), where the risk of coastal hypoxia increases from moderate to high in summer/fall (21%–46%) and winter/spring (31%–42%), and along the eastern Arabian Sea (i.e., India, Pakistan) where the risk drops from high to moderate in summer/fall (53%–34%). Strong effects are also seen in the EBoB during negative IOD phases, when the risk reduces from moderate to low year‐round (∼25% to ∼5%). This basin‐scale mapping of hypoxic risk is key to aid national and international efforts that monitor, forecast, and mitigate the impacts of hypoxia on coastal ecosystems and ecosystem services.