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David N. Straub

Abstract

Simple inverted reduced-gravity models of flow over deep ocean sills are considered, with emphasis placed on the case for which sills are wide with respect to the abyssal Rossby radius. When the length scale of the flow is also large compared to the Rossby radius, an f-plane version of the planetary geostrophic (PG) equations applies. These equations, however, predict a collapse in scale of the flow so that the PG approximation breaks down and higher-order dynamics must be evoked. Whether or not the collapsing PG dynamics give way to semigeostrophy (SG) or to some other balance regime is also discussed.

Next, the steady semigeostrophic equations typically used in rotating hydraulics studies are considered. For relatively wide sills, as well as for narrow sills that are not elongated, the path taken by the overflow is not well constrained by the sill geometry alone. The collapsing PG problem, however, suggests that the appropriate axis of flow follows a branch of the seperatrix isobath. Also suggested by the PG dynamics is that there may be a mass of quiescent water adjacent to the overflow current. Dependence of the maximum flux across the sill on assumptions regarding the flow path and the presence or absence of a quiescent water mass are therefore considered. These are compared with dependencies on sill width and the potential vorticity of the overflow. Finally, flow upstream and downstream of the sill is considered. In particular, a case in which multiple equilibria exist downstream of the sill is discussed.

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Mitsuhiro Kawase and David Straub

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Spinup of the circulation driven by an inflow into an abyssal basin containing a simple large-scale topographic feature is studied, using an inverted one-and-a-half-layer shallow-water model. Two types of topography, one a plateau and the other a depression, are considered. In both cases, the topography gives rise to a region of closed geostrophic contours. The character of the adjustment and the resultant flow differ markedly between the closed geostrophic contour region and the region outside. Long-wave processes set up a modified Stommel–Arons flow outside the closed contour region, while inside the closed contour region “frictional spinup” leads to a vigorous recirculation. It is shown that the ratio of the velocity of the recirculation to that of the Stommet–Arons flow is equal to half the ratio of the radius of the closed contour region to the Stommel boundary-layer thickness. Moreover, it is shown that the recirculation inside the closed contour region is always cyclonic, whether the topography is a plateau or a depression. The shape of the topography is important, however, to the formation of meanders in the flow around the rim of the closed contour region.

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David N. Straub

Abstract

Angular momentum balances are discussed, both in general as well as in the context of simple channel models of the Antarctic Circumpolar Current (ACC). Particular emphasis is placed on the close relationship between the angular momentum balance and the meridional circulation. It is found that topographic form drag is established very early in the integration, whereas interfacial form drag can take much longer to develop.

Restrictions on the geostrophic portion of the meridional circulation imposed by zonally reconnecting potential vorticity contours in the upper ocean allow derivation of an estimate for the steady-state transport. The estimate assumes there to be little or no circumpolar flow at great depth, an assumption that stems from the belief that the band of zonally reconnecting geostrophic contours in the Southern Ocean does not extend to the ocean floor. The predicted transport is proportional to the strength of the stratification and compares favorably with numerical results in the literature. Interaction of the ACC with the two adjoining gyres, however, is not accounted for by this estimate. The implications of this for the total transport through Drake Passage are discussed.

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Stephanne Taylor and David Straub

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Using primitive equation simulations, a zonally periodic channel is considered. The channel flow is forced by a combination of steady and high-frequency winds. The high-frequency forcing excites near-inertial motion, and the focus is on how this influences the low-frequency, nearly geostrophic part of the flow. In particular, this study seeks to clarify how Reynolds stresses exerted by the near-inertial modes affect the low-frequency kinetic energy. In the system considered, the near-inertial Reynolds stresses (i) serve as a sink term in the low-frequency kinetic energy budget and (ii) transfer low-frequency kinetic energy downward from the mixed layer. Transfer spectra show the bulk of this sink to occur at relatively small horizontal wavenumber (i.e., in the mesoscale, not the submesoscale). The presence of near-inertial motion can also affect the kinetic-to-potential energy exchanges, especially within the low-frequency band.

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David N. Straub

Abstract

Considered here is the evolution of three-dimensional perturbations to the hydrostatic equations linearized about a two-dimensional base state U. Motivated by an argument by T. Warn, this study begins with the nonrotating, unstratified case, and draws analogies between the perturbation equations and equations describing evolution of material line elements and scalar gradients embedded in the same 2D flow. When U is chaotic, both scalar gradients and line elements are characterized by rapid growth, and this leads one to suspect that the perturbations behave similarly. A generalized Okubo–Weiss parameter is proposed, and it is argued that this gives a reasonable litmus test for identifying regions where growth is most probable. Rotation modifies the generalized Okubo–Weiss parameter and tends to curb growth of the perturbation fields, as expected. It is also pointed out that, in realistic geophysical settings, the stability parameter can be suggestive of growth locally, even when a globally defined Rossby number is small.

Also considered is the effect of a constant stratification. The perturbation equations can then be separated into vertical modes that have simple sinusoidal structures. The equations describing the evolution of a given mode take a form analogous to the shallow water equations, linearized about U. Numerical simulations of these, assuming a simple but chaotic prescription of U, are carried out. For sufficiently strong stratification, a balance dynamics similar to that suggested by Riley, Metcalfe, and Weissman is recovered. For a given value of the buoyancy frequency N, however, this balance breaks down at high vertical wavenumbers. For high vertical wavenumbers, the modified Okubo–Weiss parameter once again appears to give a potentially useful indication of when growth should be expected. When the Rossby number is small, this criterion predicts stability, and growth occurs only when stratification effects are comparable to or larger than rotational effects. More specifically, growth is seen when the relevant Rossby radius is comparable to or larger than the characteristic length scale of U. It is also found in this limit that approximate geostrophic adjustment occurs prior to growth.

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Stephanne Taylor and David Straub

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An eddy-resolving primitive equation ocean model is used to examine energy transfers between frequency bands. Steady wind forcing is used to drive a geostrophic channel to which high-frequency winds are added. This excites near-inertial motion, which exerts a Reynolds stress on the slowly varying flow and acts to transfer kinetic energy between low and high frequencies. These transfers extract balanced energy primarily from the mesoscale. A frequency analysis of the transfers shows the bulk of the energy to be extracted from an intermediate range of frequencies that are large relative to the dominant kinetic energy–containing frequencies and small relative to the spectral gap separating high- and low-frequency bands. This phenomenon is robust and is found in systems spanning two orders of magnitude of kinetic energy. Direct calculation of potential energy transfers proved more difficult but nonetheless shows a similar low-to-high frequency transfer. For the parameter range considered, the ratio of potential-to-kinetic energy transfers is slightly larger than unity, and as such is consistent with balanced energy being extracted from horizontal scales that are somewhat larger than the relevant deformation radius.

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Aaron Gertz and David N. Straub

Abstract

The classic wind-driven double-gyre problem for a homogeneous (unstratified) thin aspect ratio fluid is considered, but allowing for the flow to be depth dependent. Linear free modes for which the vertical wavenumber kz ≠ 0 are inertial oscillations, and they are excited with a large-scale stochastic forcing. This produces a background sea of near-inertial oscillations and their interaction with the vertically averaged flow is the focus of this study. In the absence of 3D forcing, the near-inertial motion vanishes and the barotropic quasigeostrophic system is recovered. With 3D forcing, 2D-to-3D energy transfers—coupled with a forward cascade of 3D energy and scale-selective dissipation—provide an energy dissipation mechanism for the gyres. The relative strength of this mechanism and a Rayleigh drag applied to the 2D flow depends on both the 3D forcing strength and the Rayleigh drag coefficient.

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N. Robb McDonald and David N. Straub

Abstract

A two-layer model of anticyclonic eddy propagation including the effects of diapycnal mixing is presented. The lower layer is assumed to be of finite volume, whereas the upper layer is infinite in horizontal extent, and its dynamics are quasigeostrophic and wavelike. Integral expressions for the zonal and meridional velocity am obtained using center of mass calculations. The meridional motion is a result of both southward and northward velocities in the upper layer generated by Sverdrup forcing due to diapycnal mixing and stretching of vortex lines by the collapsing eddy. Net meridional motion of the eddy arises by requiring the mixing eddy to collapse both vertically and horizontally as it adjusts cyclostrophically. Moreover, it is shown for anticyclones in solid body rotation such motion must be equatorward. The specific case of a parabolic eddy is used to illustrate the theory, and application is made to Mediterranean salt lenses and warm core rings.

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Olivier Asselin, Peter Bartello, and David N. Straub

Abstract

The near-tropopause energy spectrum closely follows a −5/3 power law at mesoscales. Most theories addressing the mesoscale spectrum assume unbalanced dynamics but ignore the tropopause (near which the bulk of the data were collected). Conversely, it has also been proposed that the mesoscale spectrum results from tropopause-induced alterations of geostrophic turbulence. This paper seeks to reconcile these a priori mutually exclusive theories by presenting simulations that permit both unbalanced motion and tropopause-induced effects. The model integrates the nonhydrostatic Boussinesq equations in the presence of a rapidly varying background stratification profile (an idealized tropopause). Decaying turbulence simulations were performed over a wide range of Rossby numbers. In the limit of weak flow (U ≲ 1 m s−1), the essential features of the Boussinesq simulations are well captured by a quasigeostrophic version of the model: secondary roll-ups of filaments and shallow spectral slopes are observed near the tropopause but not elsewhere. However, these tropopause-induced effects rapidly disappear with increasing flow strength. For flow strengths more typical of the tropopause (U ~ 10 m s−1), the spectrum develops a shallow, near −5/3 tail associated with fast-time-scale, unbalanced motion. In contrast to weak flows, this spectral shallowing is evident at any altitude and regardless of the presence of a tropopause. Diagnostics of the fast component of motion reveal significant inertia–gravity wave activity at large horizontal scales (where the balanced flow dominates). However, no evidence points to such activity in the shallow range. That is, the mesoscale of the model is dominated by unbalanced turbulence, not waves. Implications and limitations of these findings are discussed.

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Louis-Philippe Nadeau and David N. Straub

Abstract

The idea that basinlike dynamics may play a major role in determining the Antarctic Circumpolar Current (ACC) transport is revisited. A simple analytic model is developed to describe the relationship between the wind stress and transport. At very low-wind stress, a nonzero minimum is predicted. This is followed by two distinct dynamical regimes for stronger forcing: 1) a Stommel regime in which transport increases linearly with forcing strength; and 2) a saturation regime in which the transport levels off. The baroclinic structure of the Sverdrup flux into the Drake Passage latitude band is central to the analytic model, and the geometry of characteristics, or geostrophic contours, is key to predicting the transition between the two regimes. A robustness analysis is performed using an eddy-permitting quasigeostrophic model in idealized geometries. Many simulations were carried out in large domains across a range of forcing strengths. The simulations agree qualitatively with the analytic model, with two main discrepancies being related to zonal jet structures and to a western boundary inertial recirculation. Eddy fluxes associated with zonal jets modify the baroclinic structure and lower the saturation transport value. Inertial effects increase the transport, although this effect is mainly limited to smaller domains.

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