Publications
Papers
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Climatic reach of small-scale turbulence in the ocean interior
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Direct observations of strong jets transporting deep and bottom water into the Indian Ocean through the fracture zones of the Southwest Indian Ridge
The Indian Ocean plays a crucial role in the abyssal overturning circulation, transforming Antarctic Bottom Water (AABW) into lighter water. In the western Indian Ocean, the only path for AABW to reach the subtropics as part of the global overturning is through the fracture zones of the Southwest Indian Ridge. This mid-ocean ridge has seven known fracture zones in this area, but until recently, only Atlantis II has been investigated, given the historical shortage of in situ observations in the region. To address this gap, we collected as part of the Deep Madagascar Basin (DMB) Experiment (DMB) the first comprehensive surface-to-bottom measurements of velocities, water properties, and tracers at four fracture zones deemed to transport AABW northward - Gallieni, Atlantis II, Novara, and Melville. Based on these new observations, we estimate the relative contributions of each fracture zone to the overall northward transport in the abyss and assess the strength of diapycnal turbulent mixing. Our observations reveal two strong northward deep jets transporting AABW, one at the Novara (46.0 cm/s at 4,370 dbar) and another at the Melville (23.8 cm/s at 4,360 dbar) fracture zones, and provide evidence of the persistence of the previously observed Atlantis II jet. Contrary to earlier assumptions, we find that the Melville fracture zone, rather than the Atlantis II, is the primary contributor to the northward transport of deep and bottom water, at least during the DMB period.
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Efficient Lagrangian averaging with exponential filters
Lagrangian averaging is a valuable tool for the analysis and modeling of multiscale processes in fluid dynamics. The numerical computation of Lagrangian (time) averages from simulation data is challenging, however. It can be carried out by tracking a large number of particles or, following a recent approach, by solving a dedicated set of partial differential equations (PDEs). Both approaches are computationally demanding because they require an entirely new computation for each time at which the Lagrangian mean fields are desired. We overcome this drawback by developing a PDE-based method that delivers Lagrangian mean fields for all times through the single solution of evolutionary PDEs. This allows for an on-the-fly implementation, in which Lagrangian averages are computed along with the dynamical variables. This is made possible by the use of a special class of temporal filters whose kernels are sums of exponential functions. We focus on two specific kernels involving one and two exponential functions. We implement these in the rotating shallow-water model and demonstrate their effectiveness at filtering out large-amplitude Poincaré waves while retaining the salient features of an underlying slowly evolving turbulent flow.
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Lagrangian filtering for wave–mean flow decomposition
Geophysical flows are typically composed of wave and mean motions with a wide range of overlapping temporal scales, making separation between the two types of motion in wave-resolving numerical simulations challenging. Lagrangian filtering – whereby a temporal filter is applied in the frame of the flow – is an effective way to overcome this challenge, allowing clean separation of waves from mean flow based on frequency separation in a Lagrangian frame. Previous implementations of Lagrangian filtering have used particle tracking approaches, which are subject to large memory requirements or difficulties with particle clustering. Kafiabad & Vanneste (2023) recently proposed a novel method for finding Lagrangian means without particle tracking by solving a set of partial differential equations alongside the governing equations of the flow. In this work, we adapt the approach of KV23 to develop a flexible, on-the-fly, PDE-based method for Lagrangian filtering using arbitrary convolutional filters. We present several different wave–mean decompositions, demonstrating that our Lagrangian methods are capable of recovering a clean wave-field from a nonlinear simulation of geostrophic turbulence interacting with Poincaré waves.
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Near-resonant generation of internal tide superharmonics: comparing theoretical predictions with a global ocean model
Internal tides are generated in the stratified ocean interior by the interaction of barotropic tidal currents with rough bathymetry. Low-vertical-mode internal tides can transport energy far from their generation site, but it remains unclear how and where this energy is eventually dissipated at small scales. A potential mechanism for the transfer of energy from low-mode internal tides to smaller scales in equatorial regions is superharmonic generation, whereby nonlinear self-interaction of internal tides in non-uniform stratification excites waves with shorter wavelengths and higher frequencies. Here, we use a realistically forced global configuration of the Massachusetts Institute of Technology general circulation model to investigate an enhanced superharmonic signal in the equatorial Pacific Ocean. Using existing theory, we demonstrate that the superharmonic amplitude is consistent with nonlinear self-interaction of the original baroclinic tide, providing strong evidence for an energy pathway from the mode-1 semidiurnal internal tide to smaller horizontal scales.
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On the role of seamounts in upwelling deep-ocean waters through turbulent mixing
Turbulent mixing in the ocean exerts an important control on the rate and structure of the overturning circulation. However, the balance of processes underpinning this mixing is subject to significant uncertainties, limiting our understanding of the overturning’s deep upwelling limb. Here, we investigate the hitherto primarily neglected role of tens of thousands of seamounts in sustaining deep-ocean upwelling. Dynamical theory indicates that seamounts may stir and mix deep waters by generating lee waves and topographic wake vortices. At low latitudes, stirring and mixing are predicted to be enhanced by a layered vortex regime in the wakes. Using three realistic regional simulations spanning equatorial to middle latitudes, we show that layered wake vortices and elevated mixing are widespread around seamounts. We identify scalings that relate mixing rate within seamount wakes to topographic and hydrographic parameters. We then apply such scalings to a global seamount dataset and an ocean climatology to show that seamount-generated mixing makes an important contribution to the upwelling of deep waters. Our work thus brings seamounts to the fore of the deep-ocean mixing problem and urges observational, theoretical, and modeling efforts toward incorporating the seamounts’ mixing effects in conceptual and numerical ocean circulation models.
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Spatiotemporal characteristics of the near-surface turbulent cascade at the submesoscale in the Drake Passage
Submesoscale currents and internal gravity waves achieve an intense turbulent cascade near the ocean surface [depth of 0–O(100) m], which is thought to give rise to significant energy sources and sinks for mesoscale eddies. Here, we characterize the contributions of nonwave currents (NWCs; including eddies and fronts) and internal gravity waves (IGWs; including near-inertial motions, lee waves, and the internal wave continuum) to near-surface submesoscale turbulence in the Drake Passage. Using a numerical simulation, we combine Lagrangian filtering and a Helmholtz decomposition to identify NWCs and IGWs and to characterize their dynamics (rotational versus divergent). We show that NWCs and IGWs contribute in different proportions to the inverse and forward turbulent kinetic energy cascades, based on their dynamics and spatiotemporal scales. Purely rotational NWCs cause most of the inverse cascade, while coupled rotational–divergent components of NWCs and coupled NWC–IGWs cause the forward cascade. The cascade changes direction at a spatial scale at which motions become increasingly divergent. However, the forward cascade is ultimately limited by the motions’ spatiotemporal scales. The bulk of the forward cascade (80%–95%) is caused by NWCs and IGWs of small spatiotemporal scales (L < 10 km; T < 6 h), which are primarily rotational: submesoscale eddies, fronts, and the internal wave continuum. These motions also cause a significant part of the inverse cascade (30%). Our results highlight the requirement for high spatiotemporal resolutions to diagnose the properties and large-scale impacts of near-surface submesoscale turbulence accurately, with significant implications for ocean energy cycle study strategies.
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Boundary Upwelling of Antarctic Bottom Water by Topographic Turbulence
The lower cell of the meridional overturning circulation (MOC) is sourced by dense Antarctic Bottom Waters (AABWs), which form and sink around Antarctica and subsequently fill the abyssal ocean. For the MOC to “overturn,” these dense waters must upwell via mixing with lighter waters above. Here, we investigate the processes underpinning such mixing, and the resulting water mass transformation, using an observationally forced, high-resolution numerical model of the Drake Passage in the Southern Ocean. In the Drake Passage, the mixing of dense AABW formed in the Weddell Sea with lighter deep waters transported from the Pacific Ocean by the Antarctic Circumpolar Current is catalyzed by energetic flows impinging on rough topography. We find that multiple topographic interaction processes facilitate the mixing of the two water masses, ultimately resulting in the upwelling of waters with neutral density greater than 28.19 kg m−3, and the downwelling of the lighter waters above. In particular, we identify the role of sharp density interfaces between AABW and overlying waters and find that the dynamics of the interfaces’ interaction with topography can modify many of the processes that generate mixing. Such sharp interfaces between water masses have been observed in several parts of the global ocean, but are unresolved and unrepresented in climate-scale ocean models. We suggest that they are likely to play an important role in abyssal dynamics and mixing, and therefore require further exploration.
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The Impact of Representations of Realistic Topography on Parameterized Oceanic Lee Wave Energy Flux
Oceanic lee waves are generated when quasi-steady flows interact with rough topography at the bottom of the ocean, providing an important sink of energy and momentum from the mean flow and a source of turbulent kinetic energy. Linear theory with a spectral representation of topography is typically used to inform parameterisations of lee wave generation. Here, we use a realistic wave resolving simulation of the Drake Passage, a hot-spot of lee wave generation, to investigate the utility of such parameterisations for areas of complex large scale topography. The flow is often blocked and split by large amplitude topographic features, creating an ‘effective topography’, and calling into question the spectral representation of small scale topography for lee wave generation. By comparing the resolved modelled wave field to parameterisations employing various representations of topography, we show that spectral methods may not be appropriate in areas of rough topography. We develop a simple topographic representation consisting of an ensemble of topographic peaks, which allows physical treatment of flow blocking at finite amplitude topography. This method allows better prediction of bottom vertical velocities and lee wave energy flux than spectral methods, and implies that the nature of lee waves in such regions can be misrepresented by a spectral approach to topographic representation. This leads to both an overestimate of wave energy flux and an underestimate of wave nonlinearity, with implications for the mechanisms by which lee waves break and mix in the abyssal ocean.
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TAO data support the existence of large high frequency variations in cross-equatorial overturning circulation
Large amplitude oscillations in the meridional overturning circulation (MOC) have been found near the equator in all major ocean basins in the NEMO ocean general circulation model. With periods of 3-15 days and amplitudes of ~ 100 Sv in the Pacific, these oscillations have been shown to correspond to zonally integrated equatorially trapped waves forced by winds within 10 degrees N/S of the equator. Observations of dynamic height from the Tropical Atmosphere Ocean (TAO) mooring array in the equatorial Pacific also exhibit spectral peaks consistent with the dispersion relation for equatorially trapped waves. Here, we revisit the TAO observations to confirm that the amplitude of the oscillations is consistent with the simulations, supporting the modelled large amplitude MOC oscillations. We also show that the zonal structure of the frequency spectrum in both observations and simulations is predicted by changes in the baroclinic wave speed with variation in stratification across the ocean basin.
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A Marginal Stability Paradigm for Shear-Induced Diapycnal Turbulent Mixing in the Ocean
Turbulent mixing induced by breaking internal waves is key to the ocean circulation and global tracer budgets. While the classic marginal shear instability of Richardson number ∼1/4 has been considered as potentially relevant to turbulent wave breaking, its relevance to flows that are not steady parallel shear flows has been suspect. We show that shear instability is indeed relevant in the ocean interior and propose a new marginal stability paradigm that relates the stability criterion based on Richardson number to one based on the ratio of Ozmidov and Thorpe turbulence scales. The new paradigm applies to both ocean interior and boundary layer flows. This allows for accurate quantification of the transition from downwelling to upwelling zones in a recently emerged paradigm of ocean circulation. Our results help climate models more accurately calculate the mixing-driven deep ocean circulation and fluxes of tracers in the ocean interior.
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Surface reflection of bottom generated oceanic lee waves
Lee waves generated by stratified flow over rough bottom topography in the ocean extract momentum and energy from the geostrophic flow, causing drag and enhancing turbulence and mixing in the interior ocean when they break. Inviscid linear theory is generally used to predict the generation rate of lee waves, but the location and mechanism of wave breaking leading to eventual dissipation of energy and irreversible mixing are poorly constrained. In this study, a linear model with viscosity, diffusivity, and an upper boundary is used to demonstrate the potential importance of the surface in reflecting lee wave energy back into the interior, making the case for treating lee waves as a full water column process. In the absence of critical levels, it is shown that lee waves can be expected to interact with the upper ocean, resulting in enhanced vertical velocities and dissipation and mixing near the surface. The impact of the typical oceanic conditions of increasing background velocity and stratification with height above bottom are investigated and shown to contribute to enhanced upper ocean vertical velocities and mixing.
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IPCC Special Report Meeting: Climate Change Around the Globe
Co-hosted by the Grantham Institute, a Royal Meteorological Society meeting was held on 18 November 2019 to discuss climate change around the globe and the two recently released Intergovernmental Panel on Climate Change (IPCC) Special reports (SR) (IPCC, 2019a,b). The meeting’s presentations and panel discussions covered the current state of knowledge on climate change and the options for action.
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The evolution of superharmonics excited by internal tides in non-uniform stratification
A weakly nonlinear time-dependent theory for the evolution of superharmonics generated by the nonlinear self-interaction of a mode-1 internal tide in non-uniform stratification is developed and compared to numerical simulations. The forcing by the internal tide is found to excite near-pure mode-1 superharmonics whose natural frequency is moderately different from twice the internal tide frequency. Consequently, the superharmonics undergo a slow periodic growth and decay that is comparable to an acoustic ‘beat’. At low latitudes the beat frequency is smaller and the superharmonics can grow to larger amplitude, allowing for the possibility of a superharmonic cascade.
Preprints
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Volume-preserving Lagrangian averaging using polar factorization
The generalised Lagrangian mean (GLM) theory of Andrews & McIntyre provides a powerful framework to study the interactions between waves and flows. A drawback of this theory is that the Lagrangian mean velocity is divergent even for incompressible fluids because the mean flow map, which sends the Lagrangian labels of fluid parcels to their mean positions, does not preserve volume. This results, for instance, in vortices shrinking under Lagrangian averaging. We overcome this drawback by revising the definition of the mean flow map, choosing it as the volume-preserving map closest to the “bare” GLM mean map. A standard result of optimal-transport theory then shows that the new mean map is the volume-preserving factor in the polar factorization of the GLM mean map. We develop and implement a numerical method for the computation of the corresponding Lagrangian mean fields from simulation data. The implementation builds on recently developed algorithms for the on-the-fly computation of Lagrangian means using the exponential and Butterworth filters. We demonstrate the value of volume-preserving Lagrangian averaging in simulations of the two-dimensional incompressible and shallow-water models. We compare the Lagrangian-mean fields obtained with and without the volume-preservation constraint.
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Characterisation of Topographically-Generated Internal Waves in the Arctic Ocean Northward of the Critical Latitude
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Oceanic internal tides: do they get phased at the Equator?
Low-mode baroclinic tides play a major role in ocean dynamics, especially for energy redistribution and deep ocean mixing. These internal waves, generated by tidal flow over submarine topography, can propagate for thousands of kilometres across ocean basins, and become unstable through wave-mean flow or wave-wave interactions. Satellite observations of internal tides have shown that part of their lunar semidiurnal (M2) altimetry signal loses phase coherence in equatorial regions, thus affecting how we interpret their dynamics and energy distribution (Buijsman et al. 2017). We investigate the interaction of a baroclinic M2 internal tide wavepacket with an equatorial zonal jet, possibly of any horizontal or vertical structure. The dynamics of the low modes are explored as well as the potential excitation of higher vertical modes and how these interactions can generate incoherences in the baroclinic tide signal. We develop an idealized linear model using modal decomposition (Kelly et al. 2016), which is solved using Dedalus, to study the dynamics of a mode 1 M2 internal wavepacket on an equatorial beta plane. A zonal jet, with a uniform or a sheared vertical structure, is added at the equator to investigate potential wave-mean flow interaction. We find that a vertically uniform zonal jet affects the propagation of the mode 1 wavepacket. Depending on the strength of the jet, this can cause total reflection or strong distortion of the wavepacket. In contrast, a wavepacket entering a vertically sheared jet shows energy scattering into higher modes, which have lower phase and group speeds, shorter wavelengths, and are thus more susceptible to dissipation (and critical layers for non-uniform stratification). As the wavepacket exits the jet, reverse energy transfer occurs and the phase speed difference between the modes may explain part of the phase incoherence observed in altimetry data.
Software products
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Online and Offline Lagrangian Filtering with PDEs: Theoretical Framework and Implementation in OceananigansLagrangianFilter.jl [software and dataset]
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Characterisation of Topographically-Generated Internal Waves in the Arctic Ocean Northward of the Critical Latitude [software and dataset]
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Code and data for “Volume preserving Lagrangian averaging using polar factorization”
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OceananigansLagrangianFilter.jl: A set of tools to perform online or offline Lagrangian filtering of Oceananigans.jl simulations
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Near-resonant generation of internal tide superharmonics: comparing theoretical predictions with a global ocean model [software and dataset]
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Code and data for “Efficient Lagrangian averaging with exponential filters”
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Lagrangian filtering for wave–mean flow decomposition [software and dataset]
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Seamount parameters used in Mashayek & Gula et al. PNAS 2024 [dataset]
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Boundary upwelling of Antarctic Bottom Water by topographic turbulence [dataset]
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lee-wave-solver: Surface reflection of bottom generated oceanic lee waves [software]
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The Impact of Representations of Realistic Topography on Parameterized Oceanic Lee Wave Energy Flux [software and data]
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TAO data support the existence of large high frequency variations in cross-equatorial overturning circulation [software and data]
Other
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Deep Madagascar Basin Expedition Cruise Report
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Editor's Highlight: Overturning Ocean Water by Turbulence
Our recent paper in AGU Advances was chosen as an Editor’s Highlight – as explained by Nicolas Gruber in Eos. -
Proceedings of the NFFDy Summer Programme on ‘Data in Fluids’
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The generation, propagation, and mixing of oceanic lee waves (PhD thesis)