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P. Tedesco, J. Gula, P. Penven, and C. Ménesguen

Abstract

Western boundary currents are hotspots of mesoscale variability and eddy–topography interactions, which channel energy toward smaller scales and eventually down to dissipation. Here, we assess the main mesoscale eddies energy sinks in the Agulhas Current region from a regional numerical simulation. We derive an eddy kinetic energy (EKE¯) budget in the framework of the vertical modes. It accounts for energy transfers between energy reservoirs and vertical modes, including transfers channeled by topography. The variability is dominated by mesoscale eddies (barotropic and first baroclinic modes) in the path of intense mean currents. Eddy–topography interactions result in a major mesoscale eddy energy sink, along three different energy routes, with comparable importance: transfers toward bottom-intensified time-mean currents, generation of higher baroclinic modes, and bottom friction. The generation of higher baroclinic modes takes different forms in the Northern Agulhas Current, where it corresponds to nonlinear transfers to smaller vertical eddies on the slope, and in the Southern Agulhas Current, where it is dominated by a (linear) generation of internal gravity waves over topography. Away from the shelf, mesoscale eddies gain energy by an inverse vertical turbulent cascade. However, the Agulhas Current region remains a net source of mesoscale eddy energy due to the strong generation of eddies, modulated by the topography, especially in the Southern Agulhas Current. It shows that the local generation of mesoscale eddies dominates the net EKE¯ budget, contrary to the paradigm of mesoscale eddies decay upon western boundaries.

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Lin Jiang, Wansuo Duan, and Hailong Liu

Abstract

We used the conditional nonlinear optimal perturbation (CNOP) approach to investigate the most sensitive initial error of sea surface height anomaly (SSHA) forecasts by using a two-layer quasigeostrophic model and revealed the importance of mesoscale eddies in initialization of the SSHA forecasts. Then, the CNOP-type initial errors for individual mesoscale eddies were calculated, revealing that the errors tend to occur in locations where the eddies present a clear high- to low-velocity gradient along the eddy rotation and the errors often have a shear SSHA structure present. Physically, we interpreted the rationality of the particular location and shear structure of the CNOP-type errors by barotropic instability from the perspective of the Lagrange expression of fluid motions. Numerically, we examined the sensitivity of the CNOP-type errors by using observing system simulation experiments (OSSEs). We concluded that if additional observations are preferentially implemented in the location where CNOP-type errors occur, especially with a particular array indicated by their shear structure, the forecast ability of the SSHA can be significantly improved. These results provide scientific guidance for the target observation of mesoscale eddies and therefore are very instructive for improving ocean state SSHA forecasts.

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Yu Gao, Igor Kamenkovich, Natalie Perlin, and Benjamin Kirtman

Abstract

We analyze the role of mesoscale heat advection in a mixed layer (ML) heat budget, using a regional high-resolution coupled model with realistic atmospheric forcing and an idealized ocean component. The model represents two regions in the Southern Ocean, one with strong ocean currents and the other with weak ocean currents. We conclude that heat advection by oceanic currents creates mesoscale anomalies in sea surface temperature (SST), while the atmospheric turbulent heat fluxes dampen these SST anomalies. This relationship depends on the spatial scale, the strength of the currents, and the mixed layer depth (MLD). At the oceanic mesoscale, there is a positive correlation between the advection and SST anomalies, especially when the currents are strong overall. For large-scale zonal anomalies, the ML-integrated advection determines the heating/cooling of the ML, while the SST anomalies tend to be larger in size than the advection and the spatial correlation between these two fields is weak. The effects of atmospheric forcing on the ocean are modulated by the MLD variability. The significance of Ekman advection and diabatic heating is secondary to geostrophic advection except in summer when the MLD is shallow. This study links heat advection, SST anomalies, and air–sea heat fluxes at ocean mesoscales, and emphasizes the overall dominance of intrinsic oceanic variability in mesoscale air–sea heat exchange in the Southern Ocean.

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Giovanni Dematteis, Kurt Polzin, and Yuri V. Lvov

Abstract

We provide a first-principles analysis of the energy fluxes in the oceanic internal wave field. The resulting formula is remarkably similar to the renowned phenomenological formula for the turbulent dissipation rate in the ocean, which is known as the finescale parameterization. The prediction is based on the wave turbulence theory of internal gravity waves and on a new methodology devised for the computation of the associated energy fluxes. In the standard spectral representation of the wave energy density, in the two-dimensional vertical wavenumber–frequency (mω) domain, the energy fluxes associated with the steady state are found to be directed downscale in both coordinates, closely matching the finescale parameterization formula in functional form and in magnitude. These energy transfers are composed of a “local” and a “scale-separated” contributions; while the former is quantified numerically, the latter is dominated by the induced diffusion process and is amenable to analytical treatment. Contrary to previous results indicating an inverse energy cascade from high frequency to low, at odds with observations, our analysis of all nonzero coefficients of the diffusion tensor predicts a direct energy cascade. Moreover, by the same analysis fundamental spectra that had been deemed “no-flux” solutions are reinstated to the status of “constant-downscale-flux” solutions. This is consequential for an understanding of energy fluxes, sources, and sinks that fits in the observational paradigm of the finescale parameterization, solving at once two long-standing paradoxes that had earned the name of “oceanic ultraviolet catastrophe.”

Significance Statement

The global circulation models cannot resolve the scales of the oceanic internal waves. The finescale parameterization of turbulent dissipation, a formula grounded in observations, is the standard tool by which the energy transfers due to internal waves are incorporated in the global models. Here, we provide an interpretation of this parameterization formula building on the first-principles statistical theory describing energy transfers between waves at different scales. Our result is in agreement with the finescale parameterization and points out a large contribution to the energy fluxes due to a type of wave interactions (local) usually disregarded. Moreover, the theory on which the traditional understanding of the parameterization is mainly built, a “diffusion approximation,” is known to be partly in contradiction with observations. We put forward a solution to this problem, visualized by means of “streamlines” that improve the intuition of the direction of the energy cascade.

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Chao Yan, James C. McWilliams, and Marcelo Chamecki

Abstract

Boundary layer turbulence in coastal regions differs from that in deep ocean because of bottom interactions. In this paper, we focus on the merging of surface and bottom boundary layers in a finite-depth coastal ocean by numerically solving the wave-averaged equations using a large-eddy simulation method. The ocean fluid is driven by combined effects of wind stress, surface wave, and a steady current in the presence of stable vertical stratification. The resulting flow consists of two overlapping boundary layers, i.e., surface and bottom boundary layers, separated by an interior stratification. The overlapping boundary layers evolve through three phases, i.e., a rapid deepening, an oscillatory equilibrium and a prompt merger, separated by two transitions. Before the merger, internal waves are observed in the stratified layer, and they are excited mainly by Langmuir turbulence in the surface boundary layer. These waves induce a clear modulation on the bottom-generated turbulence, facilitating the interaction between the surface and bottom boundary layers. After the merger, the Langmuir circulations originally confined to the surface layer are found to grow in size and extend down to the sea bottom (even though the surface waves do not feel the bottom), reminiscent of the well-organized Langmuir supercells. These full-depth Langmuir circulations promote the vertical mixing and enhance the bottom shear, leading to a significant enhancement of turbulence levels in the vertical column.

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Yu-Kun Qian, Shiqiu Peng, Xixi Wen, and Tongya Liu

Abstract

Based on the dispersion of Lagrangian particles relative to the contours of a quasi-conservative tracer field, the present study proposes two new diffusivity diagnostics: the local Lagrangian diffusivity K˜L and local effective diffusivity K˜eff, to quantify localized, instantaneous, irreversible mixing. The attractiveness of these two diagnostics is that 1) they both recover exactly the effective diffusivity K eff proposed by when averaged along a contour and 2) they share very similar spatial patterns at each time step and hence a local equivalence between particle-based and tracer-based diffusivities can be obtained instantaneously. From a particle perspective, K˜L represents the local magnifying of the mixing length; from a contour perspective, K˜eff represents the local strengthening of tracer gradient and elongation of the contour interface. Both of these enhancements are relative to an unstirred (meridionally sorted) state. While K eff cannot quantify the along-contour variation of irreversible mixing, K˜L is able to identify the portion of a (quasi-conservative) contour where it is leaky and thus easily penetrated through by Lagrangian particles. Also, unlike traditional Lagrangian diffusivity, K˜L is able to capture the fine-scale spatial structure of mixing. These two new diagnostics allows one to explore the interrelations among three types (Eulerian, Lagrangian, and tracer-based) of mixing diagnostics. Through a time mean, K˜eff has a very similar expression with the Eulerian Osborn–Cox diffusivity. The main difference lies in the definition of their denominators. That is, the non-eddying tracer background state, representing the lowest mixing efficiency, differs in each definition. Discrepancies between these three types of diffusivities are then reconciled both theoretically and practically.

Significance Statement

Large discrepancies are reported in the estimates of mixing using different types of diffusivity diagnostics, specifically the particle-based, tracer-based, and Eulerian-based diffusivities, as their definitions are quite different from each other. Here we propose two local mixing diagnostics according to the particle- and tracer-based diffusivities. It is then shown that the theoretical discrepancies between the three types of mixing diagnostics can be clearly reconciled based on these two local diagnostics. Therefore, an updated, consistent, and unified view of different mixing models becomes clear and discrepancies between different estimates can be minimized.

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Henry G. Peterson and Jörn Callies

Abstract

The near-bottom mixing that allows abyssal waters to upwell tilts isopycnals and spins up flow over the flanks of midocean ridges. Meso- and large-scale currents along sloping topography are subjected to a delicate balance of Ekman arrest and spindown. These two seemingly disparate oceanographic phenomena share a common theory, which is based on a one-dimensional model of rotating, stratified flow over a sloping, insulated boundary. This commonly used model, however, lacks rapid adjustment of interior flows, limiting its ability to capture the full physics of spinup and spindown of along-slope flow. Motivated by two-dimensional dynamics, the present work extends the one-dimensional model by constraining the vertically integrated cross-slope transport and allowing for a barotropic cross-slope pressure gradient. This produces a closed secondary circulation by forcing Ekman transport in the bottom boundary layer to return in the interior. The extended model can thus capture Ekman spinup and spindown physics: the interior return flow is turned by the Coriolis acceleration, leading to rapid rather than slow diffusive adjustment of the along-slope flow. This transport-constrained one-dimensional model accurately describes two-dimensional mixing-generated spinup over an idealized ridge and provides a unified framework for understanding the relative importance of Ekman arrest and spindown of flow along a slope.

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Hailu Kong and Malte F. Jansen

Abstract

Changes in the Southern Ocean (SO) surface wind stress influence both the meridional overturning circulation (MOC) and stratification not only in the SO but in the global oceans, which can take multiple millennia to fully equilibrate. We use a hierarchy of models to investigate the time-dependent response of the MOC and low-latitude pycnocline depth (which quantifies the stratification) to SO wind stress changes: a two-layer analytical theory, a multicolumn model (PyMOC), and an idealized general circulation model (GCM). We find that in both the GCM and PyMOC, the MOC has a multidecadal adjustment time scale while the pycnocline depth has a multicentennial time scale. The two-layer theory instead predicts the MOC and pycnocline depth to adjust on the same, multidecadal time scale. We argue that this discrepancy arises because the pycnocline depth depends on the bulk stratification, while the MOC amplitude is sensitive mostly to isopycnals within the overturning cell. We can reconcile the discrepancy by interpreting the “pycnocline depth” in the theory as the depth of a specific isopycnal near the maximum of the MOC. We also find that SO stationary eddies respond very quickly to a sudden wind stress change, compensating for most of the change in the Ekman-driven MOC. This effect is missing in the theory, where the eddy-induced MOC only follows the adjustment of the pycnocline depth. Our results emphasize the importance of depth dependence in the oceans’ transient response to changes in surface boundary conditions, and the distinct role played by stationary eddies in the SO.

Significance Statement

Our work resolves the question of why previous theories predict the ocean density structure to adjust to a change in the winds over the Southern Ocean within centuries, while climate models indicate that this adjustment takes thousands of years. The question is important because it is related to our understanding of how the ocean responds to potential climate change scenarios. Our results emphasize the importance of depth dependence in the density response (i.e., the upper ocean adjusts faster than the deep ocean), suggesting that future theoretical advancement should be made with careful considerations of the ocean’s vertical structure. Our results also highlight the role of stationary meanders in the Southern Ocean’s Antarctic Circumpolar Current, whose influence has not been included in the existing theories.

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Paul A. Hwang

Abstract

Wind-wave development is governed by the fetch- or duration-limited growth principle that is expressed as a pair of similarity functions relating the dimensionless elevation variance (wave energy) and spectral peak frequency to fetch or duration. Combining the pair of similarity functions, the fetch or duration variable can be removed to form a dimensionless function of elevation variance and spectral peak frequency, which is interpreted as the wave energy evolution with wave age. The relationship is initially developed for quasi-neural stability and quasi-steady wind forcing conditions. Further analyses show that the same fetch, duration, and wave-age similarity functions are applicable to unsteady wind forcing conditions, including rapidly accelerating and decelerating mountain gap wind episodes and tropical cyclone (TC) wind fields. Here it is shown that with the dimensionless frequency converted to dimensionless wavenumber using the surface wave dispersion relationship, the same similarity function is applicable in all water depths. Field data collected in shallow to deep waters and mild to TC wind conditions and synthetic data generated by spectrum model computations are assembled to illustrate the applicability. For the simulation work, the finite-depth wind-wave spectrum model and its shoaling function are formulated for variable spectral slopes. Given wind speed, wave age, and water depth, the measured and spectrum-computed significant wave heights and the associated growth parameters are in good agreement in forcing conditions from mild to TC winds and in all depths from deep ocean to shallow lake.

Significance Statement

This paper presents a growth function and spectrum model to describe wind-wave development in all water depths. Their applicability covers a wide range of wind forcing conditions including steady, accelerating, decelerating, and tropical cyclone events. Support for the unified spectrum model and growth function is presented with field observations and numerical computations.

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Zimeng Li and Hidenori Aiki

Abstract

The present study investigates the interannual variability of the tropical Indian Ocean (IO) based on the transfer routes of wave energy in a set of 61-yr hindcast experiments using a linear ocean model. To understand the basic feature of the IO dipole mode, this paper focuses on the 1994 pure positive event. Two sets of westward transfer episodes in the energy flux associated with Rossby waves (RWs) are identified along the equator during 1994. One set represents the same phase speed as the linear theory of equatorial RWs, while the other set is slightly slower than the theoretical phase speed. The first set originates from the reflection of equatorial Kelvin waves at the eastern boundary of the IO. On the other hand, the second set is found to be associated with off-equatorial RWs generated by southeasterly winds in the southeastern IO, which may account for the appearance of the slower group velocity. A combined empirical orthogonal function (EOF) analysis of energy-flux streamfunction and potential reveals the intense westward signals of energy flux are attributed to off-equatorial RWs associated with predominant wind input in the southeastern IO corresponding to the positive IO dipole event.

Significance Statement

The present study gains a new insight into the mechanism of the Indian Ocean dipole events using a new diagnostic scheme for wave energy based on 61-yr hindcast experiments. The results have shown the existence of two sets of westward transfer of wave energy at the equator during 1994. One set of westward signals shows the same group velocity with theoretical equatorial Rossby waves that appear reasonably along the equator. The other set of westward signals at the equator represents a slightly slower group velocity than the theoretical equatorial Rossby waves, which is associated with abnormally extended southeasterly winds during the Indian Ocean dipole event.

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