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Robert B. Scott and Brian K. Arbic

Abstract

The energy pathways in geostrophic turbulence are explored using a two-layer, flat-bottom, f-plane, quasigeostrophic model forced by an imposed, horizontally homogenous, baroclinically unstable mean flow and damped by bottom Ekman friction. A systematic presentation of the spectral energy fluxes, the mean flow forcing, and dissipation terms allows for a comprehensive understanding of the sources and sinks for baroclinic and barotropic energy as a function of length scale. The key new result is a robust inverse cascade of kinetic energy for both the baroclinic mode and the upper layer. This is consistent with recent observations of satellite altimeter data over the South Pacific Ocean. The well-known forward cascade of baroclinic potential and total energy was found to be very robust. Decomposing the spectral fluxes into contributions from different terms provided further insight. The inverse baroclinic kinetic energy cascade is driven mostly by an efficient interaction between the baroclinic velocity and the barotropic vorticity, the latter playing a crucial catalytic role. This cascade can be further enhanced by the baroclinic mode self-interaction, which is only present with nonuniform stratification (unequal layer depths). When model parameters are set such that modeled eddies compare favorably with observations, the inverse baroclinic kinetic energy cascade is actually much stronger than the well-known inverse cascade in the barotropic mode. The upper-layer kinetic energy cascade was found to dominate the lower-layer cascade over a wide range of parameters, suggesting that the surface cascade and time mean density stratification may be sufficient for estimating the depth-integrated cascade from ocean observations. This may find useful application in inferring the kinetic to gravitational potential energy conversion rate from satellite measurements.

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Brian K. Arbic and Glenn R. Flierl

Abstract

The effects of mean flow direction on statistically steady, baroclinically unstable, beta-plane quasigeostrophic (QG) turbulence are examined in a two-layer numerical model. The turbulence is forced by an imposed, horizontally homogeneous, vertically sheared mean flow and dissipated by bottom Ekman friction. The model is meant to be an idealization of the midocean eddy field, which generally has kinetic energies larger than the mean and is isotropic. Energetic eddies can be generated even when planetary beta (β) dominates gradients of mean potential vorticity (PV; also, q), as long as the mean shear has a substantial meridional component. However, eddies are isotropic only when the angle between layer mean PV gradients exceeds approximately 90°. This occurs when planetary and shear-induced gradients are comparable. Maps of PV indicate that these gradients may indeed be comparable over much of the midocean. Coherent jets form when the mean flow has a substantial meridional component and β is large. When β is nonzero, but small enough to permit isotropy, and the zonal component of the mean flow is not strongly eastward, lattices of like-signed coherent vortices develop. Like-signed vortex formation from initial and forcing conditions without a vorticity preference has not been observed before in QG systems. The vortex arrays are sensitive to the details of small-scale dissipation. Both cyclonic and anticyclonic fields arise in the simulations, depending on initial conditions, but they have different energies, consistent with broken symmetries in the governing equations.

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Brian K. Arbic and W. Brechner Owens

Abstract

Interdecadal temperature variability of the Atlantic Ocean is investigated by differencing hydrographic sections taken from the 1920s through the 1990s. A comprehensive reanalysis of North Atlantic sections and the inclusion of South Atlantic sections show that warming seen previously in the North Atlantic extends to the South Atlantic. The largest statistically significant changes occur on pressure surfaces between 1000 and 2000 decibars (db). Over this pressure range and for latitudes between 32°S and 36°N, temperatures have warmed by ∼0.5°C century−1. At 48°N a cooling of ∼3°C century−1 occurred between the 1950s and 1980s.

These isobaric temperature trends are decomposed into ones along surfaces of constant neutral density, and ones due to the vertical movement of neutral surfaces. The two components are associated with different processes. In the southern North Atlantic (8°–36°N) the subthermocline warming between the 1950s and 1980s appears to be due primarily to downward displacements of neutral surfaces, while the South Atlantic changes occur primarily along density surfaces. The downward displacements in the North Atlantic occur throughout the 1000–2000-db layer, suggesting a volumetric increase (decrease) in the water masses above (below) the intermediate layer. Since calculated wind-driven displacements of the thermocline do not agree with this analysis, a change in deep water formation rates is the most likely explanation. The South Atlantic warming trend can be extended further back in time and is due to isopycnal advection, which has a much slower signal propagation speed than does the displacement mechanism for the North Atlantic changes.

This suggests that warming in Atlantic intermediate waters is due not only to climatic forcing changes over the last four decades, but also to changes on centennial timescales. These oceanic climate changes have origins in both the northern and southern polar seas.

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Brian K. Arbic and Robert B. Scott

Abstract

Many investigators have idealized the oceanic mesoscale eddy field with numerical simulations of geostrophic turbulence forced by a horizontally homogeneous, baroclinically unstable mean flow. To date such studies have employed linear bottom Ekman friction (hereinafter, linear drag). This paper presents simulations of two-layer baroclinically unstable geostrophic turbulence damped by quadratic bottom drag, which is generally thought to be more realistic. The goals of the paper are 1) to describe the behavior of quadratically damped turbulence as drag strength changes, using previously reported behaviors of linearly damped turbulence as a point of comparison, and 2) to compare the eddy energies, baroclinicities, and horizontal scales in both quadratic and linear drag simulations with observations and to discuss the constraints these comparisons place on the form and strength of bottom drag in the ocean. In both quadratic and linear drag simulations, large barotropic eddies develop with weak damping, large equivalent barotropic eddies develop with strong damping, and the comparison in goal 2 above is closest when the nondimensional friction strength parameter is of order 1. Typical values of the quadratic drag coefficient (cd ∼ 0.0025) and of boundary layer depths (Hb ∼ 50 m) imply that the quadratic friction strength parameter cdLd/Hb, where Ld is the deformation radius, may indeed be of order 1 in the ocean. Model eddies are realistic over a wider range of friction strengths when drag is quadratic, because of a reduced sensitivity to friction strength in that case. The quadratic parameter is independent of the mean shear, in contrast to the linear parameter. Plots of eddy length scales, computed from satellite altimeter data, versus mean shear and versus rough estimates of the friction strength parameters suggest that both linear and quadratic bottom drag may be active in the ocean. Topographic wave drag contains terms that are linear in the bottom flow, thus providing some justification for the use of linear bottom drag in models.

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Brian K. Arbic and Glenn R. Flierl

Abstract

This paper examines the plausibility of mesoscale eddy generation through local baroclinic instability of weak midocean gyre flows. The main tool is a statistically steady, two-layer quasigeostrophic turbulence model driven by an imposed, horizontally homogeneous, vertically sheared mean flow and dissipated by bottom Ekman friction. A wide range of friction strengths is investigated. In the weakly damped limit, flow is nearly barotropic, and the horizontal length scale of barotropic energy increases with decreasing friction, consistent with previous studies. The strongly damped limit, explored here for the first time, is equivalent barotropic (lower-layer velocities are nearly zero) and features an increase in the horizontal scale of potential energy with increasing friction. Current-meter data suggest that midocean eddies lie between the barotropic and equivalent barotropic limits. In accord with this suggestion, the moderately damped regime of the model compares well to observations of eddy amplitude, vertical structure, and horizontal scale, especially when stratification is surface intensified. A review of pertinent observations suggests that mesoscale eddies may indeed lie in the moderately damped limit. These arguments are first developed in f-plane simulations. Previous studies of beta-plane turbulence have had eastward mean flows, and in this case eddy energy has little sensitivity to friction. However, midocean gyre flows are generally nonzonal, and this nonzonality appears to be a significant factor in the production of energetic eddies. Beta-plane turbulence driven by nonzonal mean flows is sensitive to bottom friction, such that moderate damping is required for model eddies to compare well to observations, as on the f plane. A heuristic argument is presented in support of this similarity.

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Amanda K. O’Rourke, Brian K. Arbic, and Stephen M. Griffies

Abstract

Low-frequency variability at the ocean surface can be excited both by atmospheric forcing, such as in exchanges of heat and momentum, and by the intrinsic nonlinear transfer of energy between mesoscale ocean eddies. Recent studies have shown that nonlinear eddy interactions can excite an energy transfer from high to low frequencies analogous to the transfer of energy from high to low wavenumbers (small to large spatial scales) in quasi-two-dimensional turbulence. As the spatial inverse cascade is driven by oceanic eddies, the process of energy exchange across frequencies may be sensitive to ocean model resolution. Here a cross-spectrum diagnostic is applied to the oceanic component in a hierarchy of fully coupled ocean–atmosphere models to address the transfer of ocean surface kinetic energy between high and low frequencies. The cross-spectral diagnostic allows for a comparison of the relative contributions of coupled atmospheric forcing through wind stress and the intrinsic advection to low-frequency ocean surface kinetic energy. Diagnostics of energy flux and transfer within the frequency domain are compared between three coupled models with ocean model horizontal resolutions of 1°, 1/4°, and 1/10° to address the importance of resolving eddies in the driving of energy to low frequencies in coupled models.

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Paige E. Martin, Brian K. Arbic, and Andrew McC. Hogg

Abstract

Ocean-atmosphere coupling modifies the variability of Earth’s climate over a wide range of timescales. However, attribution of the processes that generate this variability remains an outstanding problem. In this manuscript, air-sea coupling is investigated in an eddy-resolving, medium-complexity, idealized, ocean-atmosphere model. The model is run in three configurations: fully coupled, partially coupled (where the effect of the ocean geostrophic velocity on the sea surface temperature field is minimal), and atmosphere-only. A surface boundary layer temperature variance budget analysis computed in the frequency domain is shown to be a powerful tool for studying air-sea interactions, as it differentiates the relative contributions to the variability in the temperature field from each process across a range of timescales (from daily to multidecadal). This method compares terms in the ocean and atmosphere across the different model configurations to infer the underlying mechanisms driving temperature variability. Horizontal advection plays a dominant role in driving temperature variance in both the ocean and atmosphere, particularly at timescales shorter than annual. At longer timescales, the temperature variance is dominated by strong coupling between atmosphere and ocean. Furthermore, the Ekman transport contribution to the ocean’s horizontal advection is found to underlie the low-frequency behavior in the atmosphere. The ocean geostrophic eddy field is an important driver of ocean variability across all frequencies and is reflected in the atmospheric variability in the western boundary current separation region at longer timescales.

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Callum J. Shakespeare, Brian K. Arbic, and Andrew McC. Hogg

Abstract

The interaction of a barotropic flow with topography generates baroclinic motion that exerts a stress on the barotropic flow. Here, explicit solutions are calculated for the spatial-mean flow (i.e., the barotropic tide) resulting from a spatially uniform but time-varying body force (i.e., astronomical forcing) acting over rough topography. This approach of prescribing the force contrasts with that of previous authors who have prescribed the barotropic flow. It is found that the topographic stress, and thus the impact on the spatial-mean flow, depend on the nature of the baroclinic motion that is generated. Two types of stress are identified: (i) a “wave drag” force associated with propagating wave motion, which extracts energy from the spatial-mean flow, and (ii) a topographic “spring” force associated with standing motion at the seafloor, including bottom-trapped internal tides and propagating low-mode internal tides, which significantly damps the time-mean kinetic energy of the spatial-mean flow but extracts no energy in the time-mean. The topographic spring force is shown to be analogous to the force exerted by a mechanical spring in a forced-dissipative harmonic oscillator. Expressions for the topographic stresses appropriate for implementation as baroclinic drag parameterizations in global models are presented.

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Brian K. Arbic, Glenn R. Flierl, and Robert B. Scott

Abstract

Analysis of spectral kinetic energy fluxes in satellite altimetry data has demonstrated that an inverse cascade of kinetic energy is ubiquitous in the ocean. In geostrophic turbulence models, a fully developed inverse cascade results in barotropic eddies with large horizontal scales. However, midocean eddies contain substantial energy in the baroclinic mode and in compact horizontal scales (scales comparable to the deformation radius Ld). This paper examines the possibility that relatively strong bottom friction prevents the oceanic cascade from becoming fully developed. The importance of the vertical structure of friction is demonstrated by contrasting numerical simulations of two-layer quasigeostrophic turbulence forced by a baroclinically unstable mean flow and damped by bottom Ekman friction with turbulence damped by vertically symmetric Ekman friction (equal decay rates in the two layers). “Cascade inequalities” derived from the energy and enstrophy equations are used to interpret the numerical results. In the symmetric system, the inequality formally requires a cascade to large-scale barotropic flow, independent of the stratification. The inequality is less strict when friction is in the bottom layer only, especially when stratification is surface intensified. Accordingly, model runs with surface-intensified stratification and relatively strong bottom friction retain substantial small-scale baroclinic energy. Altimetric data show that the symmetric inequality is violated in the low- and midlatitude ocean, again suggesting the potential impact of the “bottomness” of friction on eddies. Inequalities developed for multilayer turbulence suggest that high baroclinic modes in the mean shear also enhance small-scale baroclinic eddy energy. The inequalities motivate a new interpretation of barotropization in weakly damped turbulence. In that limit the barotropic mode dominates the spatial average of kinetic energy density because large values of barotropic density are found throughout the model domain, consistent with the barotropic cascade to large horizontal scales, while baroclinic density is spatially localized.

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Aaron W. Skiba, Libo Zeng, Brian K. Arbic, Malte Müller, and William J. Godwin

Abstract

The resonance of diurnal tidal elevations is investigated with a forward ocean tide model run in a realistic near-global domain and a synthesis of free oscillations (normal modes) computed for realistic global ocean geometries and ocean physics. As a prelude to performing the forward ocean tide simulations, the topographic wave drag, which is now commonly employed in forward ocean tide models, is tuned specifically for diurnal tides. The synthesis of global free oscillations predicts reasonably well the forward ocean diurnal tide model sensitivity to changes in the frequency, zonal structure, and meridional structure of the astronomical diurnal tidal forcing. Three global free oscillations that are important for understanding diurnal tides as a superposition of forced-damped, resonant, free oscillations are identified. An admittance analysis of the frequency sweep experiments demonstrates that some coastal locations such as the Sea of Okhotsk are resonant to diurnal tidal forcing. As in earlier work done with semidiurnal tides, a series of simulations are performed in which regions possessing significant coastal diurnal tides are blocked out. The largest perturbations to the open-ocean diurnal tides take place in Blocked Sea of Okhotsk experiments. Lesser but still significant perturbations also arise from the blocking out of other regions of large diurnal tidal elevations or dissipation. Interpretation of the results is made more complex, however, by the fact that substantial perturbations also arise from blocking out regions where neither tidal elevations nor dissipation are large. The “blocking” experiments are relevant to understanding tides of the ice age, during which lower sea levels entail a reduced area of continental shelves.

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