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  • 1
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 636-655, doi:10.1175/2009JPO4267.1.
    Description: The effects of a sloping bottom and stratification on a turbulent bottom boundary layer are investigated for cases where the interior flow oscillates monochromatically with frequency ω. At higher frequencies, or small slope Burger numbers s = αN/f (where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter), the bottom boundary layer is well mixed and the bottom stress is nearly what it would be over a flat bottom. For lower frequencies, or larger slope Burger number, the bottom boundary layer consists of a thick, weakly stratified outer layer and a thinner, more strongly stratified inner layer. Approximate expressions are derived for the different boundary layer thicknesses as functions of s and σ = ω/f. Further, buoyancy arrest causes the amplitude of the fluctuating bottom stress to decrease with decreasing σ (the s dependence, although important, is more complicated). For typical oceanic parameters, arrest is unimportant for fluctuation periods shorter than a few days. Substantial positive (toward the right when looking toward deeper water in the Northern Hemisphere) time-mean flows develop within the well-mixed boundary layer, and negative mean flows exist in the weakly stratified outer boundary layer for lower frequencies and larger s. If the interior flow is realistically broad band in frequency, the numerical model predicts stress reduction over all frequencies because of the nonlinearity associated with a quadratic bottom stress. It appears that the present one-dimensional model is reliable only for time scales less than the advective time scale that governs interior stratification.
    Description: This research was sponsored by the National Science Foundation, Physical Oceanography Program through Grant OCE 0647050.
    Keywords: Ekman pumping/transport ; Buoyancy
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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  • 2
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2010. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 40 (2010): 621-635, doi:10.1175/2009JPO4266.1.
    Description: It is well known that along-isobath flow above a sloping bottom gives rise to cross-isobath Ekman transport and therefore sets up horizontal density gradients if the ocean is stratified. These transports in turn eventually bring the along-isobath bottom velocity, hence bottom stress, to rest (“buoyancy arrest”) simply by means of the thermal wind shear. This problem is revisited here. A modified expression for Ekman transport is rationalized, and general expressions for buoyancy arrest time scales are presented. Theory and numerical calculations are used to define a new formula for boundary layer thickness for the case of downslope Ekman transport, where a thick, weakly stratified arrested boundary layer results. For upslope Ekman transport, where advection leads to enhanced stability, expressions are derived for both the weakly sloping (in the sense of slope Burger number s = αN/f, where α is the bottom slope, N is the interior buoyancy frequency, and f is the Coriolis parameter) case where a capped boundary layer evolves and the larger s case where a nearly linearly stratified boundary layer joins smoothly to the interior density profile. Consistent estimates for the buoyancy arrest time scale are found for each case.
    Description: This research was supported by the National Science Foundation Physical Oceanography program through Grant OCE 0647050.
    Keywords: Ekman pumping/transport ; Buoyancy
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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  • 3
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 551-568, doi:10.1175/JPO-D-15-0047.1.
    Description: There exists a good deal of indirect evidence, from several locations around the world, that there is a substantial eddy field over continental shelves. These eddies appear to have typical swirl velocities of a few centimeters per second and have horizontal scales of perhaps 5–10 km. These eddies are weak compared to typical, wind-driven, alongshore flows but often seem to dominate middepth cross-shelf flows. The idea that motivates the present contribution is that the alongshore wind stress ultimately energizes these eddies by means of baroclinic instabilities, even in cases where obvious intense fronts do not exist. The proposed sequence is that alongshore winds over a stratified ocean cause upwelling or downwelling, and the resulting horizontal density gradients are strong enough to fuel baroclinic instabilities of the requisite energy levels. This idea is explored here by means of a sequence of idealized primitive equation numerical model studies, each driven by a modest, nearly steady, alongshore wind stress applied for about 5–10 days. Different runs vary wind forcing, stratification, bottom slope, bottom friction, and Coriolis parameter. All runs, both upwelling and downwelling, are found to be baroclinically unstable and to have scales compatible with the underlying hypothesis. The model results, combined with physically based scalings, show that eddy kinetic energy generally increases with bottom slope, stratification, wind impulse (time integral of the wind stress), and inverse Coriolis parameter. The dominant length scale of the eddies is found to increase with increasing eddy kinetic energy and to decrease with Coriolis parameter.
    Description: This work was supported by the Woods Hole Oceanographic Institution and by the National Science Foundation, Physical Oceanography section through Grant OCE-1433953.
    Description: 2016-06-09
    Keywords: Geographic location/entity ; Continental shelf/slope ; Variability ; Oceanic variability
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 4
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2015. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 569-582, doi:10.1175/JPO-D-15-0048.1.
    Description: Continental shelf baroclinic instability energized by fluctuating alongshore winds is treated using idealized primitive equation numerical model experiments. A spatially uniform alongshore wind, sinusoidal in time, alternately drives upwelling and downwelling and so creates highly variable, but slowly increasing, available potential energy. For all of the 30 model runs, conducted with a wide range of parameters (varying Coriolis parameter, initial stratification, bottom friction, forcing period, wind strength, and bottom slope), a baroclinic instability and subsequent eddy field develop. Model results and scalings show that the eddy kinetic energy increases with wind amplitude, forcing period, stratification, and bottom slope. The dominant alongshore length scale of the eddy field is essentially an internal Rossby radius of deformation. The resulting depth-averaged alongshore flow field is dominated by the large-scale, periodic wind forcing, while the cross-shelf flow field is dominated by the eddy variability. The result is that correlation length scales for alongshore flow are far greater than those for cross-shelf velocity. This scale discrepancy is qualitatively consistent with midshelf observations by Kundu and Allen, among others.
    Description: This work was funded by the Woods Hole Oceanographic Institution and by the National Science Foundation, Physical Oceanography section through Grant OCE-1433953.
    Description: 2016-06-09
    Keywords: Geographic location/entity ; Continental shelf/slope ; Variability ; Oceanic variability
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 5
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    American Meteorological Society
    Publication Date: 2022-06-03
    Description: Author Posting. © American Meteorological Society, 2021. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 51(9), (2021): 2721–2733, https://doi.org/10.1175/JPO-D-20-0298.1.
    Description: A linear numerical model of an island or a tall seamount is used to explore superinertial leaky resonances forced by ambient vertically and horizontally uniform current fluctuations. The model assumes a circularly symmetric topography (including a shallow reef) and allows realistic stratification and bottom friction. As long as there is substantial stratification, a number of leaky resonances are found, and when the island’s flanks are narrow relative to the internal Rossby radius, some of the near-resonant modes resemble leaky internal Kelvin waves. Other “resonances” resemble higher radial mode long gravity waves as explored by Chambers. The near-resonances amplify the cross-reef velocities that help fuel biological activity. Results for cases with the central island replaced by a lagoon do not differ greatly from the island case which has land at the center. As an aside, insight is provided on the question of offshore boundary conditions for superinertial nearly trapped waves along a straight coast.
    Keywords: Baroclinic flows ; Internal waves ; Kelvin waves
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 6
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    American Meteorological Society
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2017. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 47 (2017): 879-894, doi:10.1175/JPO-D-16-0196.1.
    Description: Models show that surface cooling over a sloping continental shelf should give rise to baroclinic instability and thus tend toward gravitationally stable density stratification. Less is known about how alongshore winds affect this process, so the role of surface momentum input is treated here by means of a sequence of idealized, primitive equation numerical model calculations. The effects of cooling rate, wind amplitude and direction, bottom slope, bottom friction, and rotation rate are all considered. All model runs lead to instability and an eddy field. While instability is not strongly affected by upwelling-favorable alongshore winds, wind-driven downwelling substantially reduces eddy kinetic energy, largely because the downwelling circulation plays a similar role to baroclinic instability by flattening isotherms and so reducing available potential energy. Not surprisingly, cross-shelf winds appear to have little effect. Analysis of the model runs leads to quantitative relations for the wind effect on eddy kinetic energy for the equilibrium density stratification (which increases as the cooling rate increases) and for eddy length scale.
    Description: This research was supported by the National Science Foundation Physical Oceanography Program through Grant OCE-1433953.
    Keywords: Continental shelf/slope ; Baroclinic flows ; Eddies ; Instability
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 7
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2018. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 48 (2018): 2209-2219, doi:10.1175/JPO-D-18-0070.1.
    Description: Published observations of subinertial ocean current variability show that the vertical structure is often well described by a vertical mode that has a node of horizontal velocity at the bottom rather than the traditional node of vertical velocity. The theory of forced and free linear Rossby waves in a continuously stratified ocean with a sloping bottom and bottom friction is treated here to see if frictional effects can plausibly contribute to this phenomenon. For parameter values representative of the mesoscale, bottom dissipation by itself appears to be too weak to be an explanation, although caution is required because the present approach uses a linear model to address a nonlinear phenomenon. One novel outcome is the emergence of a short-wave, bottom-trapped, strongly damped mode that is present even with a flat bottom.
    Description: Partial funding for this article is provided by the National Science Foundation Physical Oceanography section through Award OCE-1433953.
    Description: 2019-03-17
    Keywords: Baroclinic flows ; Ekman pumping/transport ; Rossby waves
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 8
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    American Meteorological Society
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2016. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 46 (2016): 3599-3621, doi:10.1175/JPO-D-16-0085.1.
    Description: At continental margins, energetic deep-ocean eddies can transport shelf water offshore in filaments that wrap around the eddy. One example is that of Gulf Stream warm-core rings interacting with the Mid-Atlantic Bight shelf. The rate at which shelf water is exported in these filaments is a major unknown in regional budgets of volume, heat, and salt. This unknown transport is constrained using a series of idealized primitive equation numerical experiments wherein a surface-intensified anticyclonic eddy interacts with idealized shelf–slope topography. There is no shelfbreak front in these experiments, and shelf water is tracked using a passive tracer. When anticyclones interact with shelf–slope topography, they suffer apparent intrusions of shelf–slope water, resulting in a subsurface maximum in offshore transport. The simulations help construct an approximate model for the filament of exported water that originates inshore of any given isobath. This model is then used to derive an expression for the total volume of shelf–slope water transported by the eddy across that isobath. The transport scales with water depth, radius, and azimuthal velocity scale of the eddy. The resulting expression can be used with satellite-derived eddy properties to estimate approximate real-world transports ignoring the presence of a shelfbreak front. The expression assumes that the eddy’s edge is at the shelf break, a condition not always satisfied by real eddies.
    Description: The research presented here was funded by NSF Grants OCE-1059632 and OCE-1433953. Funding support from the Academic Programs Office, and WHOI is also gratefully acknowledged.
    Description: 2017-06-08
    Keywords: Continental shelf/slope ; Advection ; Dynamics ; Eddies ; Topographic effects
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 9
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    American Meteorological Society
    Publication Date: 2022-05-26
    Description: Author Posting. © American Meteorological Society, 2012. This article is posted here by permission of American Meteorological Society for personal use, not for redistribution. The definitive version was published in Journal of Physical Oceanography 42 (2012): 644–658, doi:10.1175/JPO-D-11-0143.1.
    Description: When steady flow in a stratified ocean passes between the continental slope and open ocean, its ability to cross isobaths is potentially limited by buoyancy arrest. If the bottom Ekman transport vanishes and there are no interior stresses, then steady linear flow on an f plane must be geostrophic and follow isobaths exactly. The influence of arrest on cross-shelf transport is investigated here to establish 1) whether there are substantial penetration asymmetries between cases with upwelling and downwelling in the bottom boundary layer; 2) over what spatial scales, hence in what parameter regime, buoyancy arrest is important; and 3) the effects of depth-dependent interior flow. The problem is approached using scalings and idealized numerical models. The results show that there is little or no asymmetry introduced by bottom boundary layer behavior. Further, if the stratification is weak or moderate, as measured by a slope Burger number s = αN/f (where α is the bottom slope, N is buoyancy frequency, and f is the Coriolis parameter), buoyancy arrest does not exert a strong constraint on cross-isobath exchange.
    Description: This research was supported by the National Science Foundation Physical Oceanography program through Grant OCE-0849498.
    Description: 2012-10-01
    Keywords: Coastal flows ; Ekman pumping/transport
    Repository Name: Woods Hole Open Access Server
    Type: Article
    Format: application/pdf
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