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  • 1
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    Massachusetts Institute of Technology and Woods Hole Oceanographic Institution
    Publication Date: 2022-05-25
    Description: Submitted in partial fulfillment of the requirements for the degree of Doctor of Philosophy at the Massachusetts Institute of Technology and the Woods Hole Oceanographic Institution April 1982
    Description: The dynamics of steady and unsteady channel flow over large obstacles is studied analytically and numerically in an attempt to determine the applicability of classical hydraulic concepts to such flows. The study is motivated by a need to understand the influence of deep ocean straits and sills on the abyssal circulation. Three types of channel flow are considered: nonrotating one dimensional (Chapter 2); semigeostrophic, constant potential vorticity (Chapter 3); and dispersive, zero potential vorticity (Chapter 4). In each case the discussion centers around the time-dependent adjustment that occurs as a result of sudden obtrusion of an obstacle into a uniform initial flow or the oscillatory upstream forcing of a steady flow over topography. For nondispersive (nonrotating or semigeostrophic) flow, nonlinear adjustment to obstacle obtrusion is examined using a characteristic formulation and numerical results obtained from a Lax-Wendroff scheme. The adjustment process and asymptotic state are found to depend upon the height of the obstacle bO in relation to a critical height bc and a blocking height bb. For bO 〈 bc 〈 bb, isolated packets of nondispersive (long gravity or Kelvin) waves are generated which propagate away from the obstacle, leaving the far field unaffected. For bc 〈 bO 〈 bb, a bore is generated which moves upstream and partially blocks the flow. In the semigeostrophic case, the potential vorticity of the flow is changed by the bore at a rate proportional to the differential rate of energy dissipation along the line of breakage. For bb 〈 bO the flow is completely blocked. Dispersive results in the parameter range bO 〈 bc are obtained from a linear model of the adjustment that results from obstacle obtrusion into a uniform, rotating-channel flow. The results depend on the initial Froude number Fd (based on the Kelvin wave speed). The dispersive modes set up a decaying response about the obstacle if Fd 〈 1 and (possibly resonant) lee waves if Fd 〉 1. However, the far-field upstream response is found to depend on the behavior of the nondispersive Kelvin modes and is therefore nil. Nonlinear steady solutions to nondispersive flow are obtained through direct integration of the equations of motion. The characteristic formulation is used to evaluate the stability of various steady solutions with respect to small disturbances. Of the four types of steady solution, the one in which hydraulic control occurs is found to be the most stable. This is verified by numerical experiments in which the steady, controlled flow is perturbed by disturbances generated upstream. If the topography is complicated (contains more than sill, say), then controlled flows may become destabilized and oscillations may be excited near the topography. The transmission across the obstacle of energy associated with upstream-forced oscillations is studied using a reflection theory for small amplitude waves. The theory assumes quasi-steady flow over the obstacle and is accurate for waves long compared to the obstacle. For nonrotating flow, the reflection coefficients are bounded below by a value of 1/3. For semigeostrophic flow, however, the reflection coefficient can be arbitrarily small for large values of potential vorticity. This is explained as a result of the boundary-layer character of the semigeostrophic flow.
    Keywords: Hydraulics ; Channels ; Fluid dynamics ; Rotating masses of fluid
    Repository Name: Woods Hole Open Access Server
    Type: Thesis
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  • 2
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    Cambridge University Press
    Publication Date: 2022-05-25
    Description: Author Posting. © Cambridge University Press, 2008. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 602 (2008): 241-266, doi:10.1017/S0022112008000827.
    Description: The stability of a hydraulically driven sill flow in a rotating channel with smoothly varying cross-section is considered. The smooth topography forces the thickness of the moving layer to vanish at its two edges. The basic flow is assumed to have zero potential vorticity, as is the case in elementary models of the hydraulic behaviour of deep ocean straits. Such flows are found to always satisfy Ripa's necessary condition for instability. Direct calculation of the linear growth rates and numerical simulation of finite-amplitude behaviour suggests that the flows are, in fact, always unstable. The growth rates and nonlinear evolution depend largely on the dimensionless channel curvature κ=2αg′/f2, where 2α is the dimensional curvature, g′ is the reduced gravity, and f is the Coriolis parameter. Very small positive (or negative) values of κ correspond to dynamically wide channels and are associated with strong instability and the breakup of the basic flow into a train of eddies. For moderate or large values of κ, the instability widens the flow and increases its potential vorticity but does not destroy its character as a coherent stream. Ripa's condition for stability suggests a theory for the final width and potential vorticity that works moderately well. The observed and predicted growth in these quantities are minimal for κ≥1, suggesting that the zero-potential-vorticity approximation holds when the channel is narrower than a Rossby radius based on the initial maximum depth. The instability results from a resonant interaction between two waves trapped on opposite edges of the stream. Interactions can occur between two Kelvin-like frontal waves, between two inertia–gravity waves, or between one wave of each type. The growing disturbance has zero energy and extracts zero energy from the mean. At the same time, there is an overall conversion of kinetic energy to potential energy for κ〉0, with the reverse occurring for κ〈0. When it acts on a hydraulically controlled basic state, the instability tends to eliminate the band of counterflow that is predicted by hydraulic theory and that confounds hydraulic-based estimates of volume fluxes in the field. Eddy generation downstream of the controlling sill occurs if the downstream value of κ is sufficiently small.
    Description: This work was supported by the National Science Foundation (Grant OCE- 0525729).
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 3
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2013. 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 43 (2013): 418–431, doi:10.1175/JPO-D-12-087.1.
    Description: The overflow of the dense water mass across the Greenland–Scotland Ridge (GSR) from the Nordic Seas drives the Atlantic meridional overturning circulation (AMOC). The Nordic Seas is a large basin with an enormous reservoir capacity. The volume of the dense water above the GSR sill depth in the Nordic Seas, according to previous estimates, is sufficient to supply decades of overflow transport. This large capacity buffers overflow’s responses to atmospheric variations and prevents an abrupt shutdown of the AMOC. In this study, the authors use a numerical and an analytical model to show that the effective reservoir capacity of the Nordic Seas is actually much smaller than what was estimated previously. Basin-scale oceanic circulation is nearly geostrophic and its streamlines are basically the same as the isobaths. The vast majority of the dense water is stored inside closed geostrophic contours in the deep basin and thus is not freely available to the overflow. The positive wind stress curl in the Nordic Seas forces a convergence of the dense water toward the deep basin and makes the interior water even more removed from the overflow-feeding boundary current. Eddies generated by the baroclinic instability help transport the interior water mass to the boundary current. But in absence of a robust renewal of deep water, the boundary current weakens rapidly and the eddy-generating mechanism becomes less effective. This study indicates that the Nordic Seas has a relatively small capacity as a dense water reservoir and thus the overflow transport is sensitive to climate changes.
    Description: This study has been supported by National Science Foundation (OCE0927017,ARC1107412).
    Description: 2013-08-01
    Keywords: Bottom currents ; Drainage flow ; Meridional overturning circulation ; Ocean dynamics ; Potential vorticity ; Topographic effects
    Repository Name: Woods Hole Open Access Server
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  • 4
    Publication Date: 2022-05-25
    Description: © The Author(s), 2017. This is the author's version of the work. It is posted here under a nonexclusive, irrevocable, paid-up, worldwide license granted to WHOI. It is made available for personal use, not for redistribution. The definitive version was published in Ocean Modelling 113 (2017): 131-144, doi:10.1016/j.ocemod.2017.04.001.
    Description: Numerical models of ocean circulation often depend on parameters that must be tuned to match either results from laboratory experiments or field observations. This study demonstrates that an initial, suboptimal estimate of a parameter in a model of a small bay can be improved by assimilating observations of trajectories of passive drifters. The parameter of interest is the Manning's n coefficient of friction in a small inlet of the bay, which had been tuned to match velocity observations from 2011. In 2013, the geometry of the inlet had changed, and the friction parameter was no longer optimal. Results from synthetic experiments demonstrate that assimilation of drifter trajectories improves the estimate of n, both when the drifters are located in the same region as the parameter of interest and when the drifters are located in a different region of the bay. Real drifter trajectories from field experiments in 2013 also are assimilated, and results are compared with velocity observations. When the real drifters are located away from the region of interest, the results depend on the time interval (with respect to the full available trajectories) over which assimilation is performed. When the drifters are in the same region as the parameter of interest, the value of n estimated with assimilation yields improved estimates of velocity throughout the bay.
    Description: This work was supported by: Department of Defense Multidisciplinary University Research Initiative (MURI) [grant N000141110087], administered by the Office of Naval Research; the National Science Foundation (NSF); the National Oceanic and Atmospheric Administration (NOAA); NOAA's Climate Program Office; the Department of Energy's Office for Science (BER); and the Assistant Secretary of Defense (Research & Development).
    Keywords: Data assimilation ; Modelling ; Drag coefficient ; Drifters ; Tidal inlets
    Repository Name: Woods Hole Open Access Server
    Type: Preprint
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  • 5
    Publication Date: 2022-05-25
    Description: Author Posting. © Cambridge University Press, 2000. This article is posted here by permission of Cambridge University Press for personal use, not for redistribution. The definitive version was published in Journal of Fluid Mechanics 404 (2000):117-149, doi:10.1017/S0022112099007065.
    Description: In order to gain insight into the hydraulics of rotating-channel flow, a set of initial-value problems analogous to Long's towing experiments is considered. Specifically, we calculate the adjustment caused by the introduction of a stationary obstacle into a steady, single-layer flow in a rotating channel of infinite length. Using the semigeostrophic approximation and the assumption of uniform potential vorticity, we predict the critical obstacle height above which upstream influence occurs. This height is a function of the initial Froude number, the ratio of the channel width to an appropriately defined Rossby radius of deformation, and a third parameter governing how the initial volume flux in sidewall boundary layers is partitioned. (In all cases, the latter is held to a fixed value specifying zero flow in the right-hand (facing downstream) boundary layer.) The temporal development of the flow according to the full, two-dimensional shallow water equations is calculated numerically, revealing numerous interesting features such as upstream-propagating shocks and separated rarefying intrusions, downstream hydraulic jumps in both depth and stream width, flow separation, and two types of recirculations. The semigeostrophic prediction of the critical obstacle height proves accurate for relatively narrow channels and moderately accurate for wide channels. Significantly, we find that contact with the left-hand wall (facing downstream) is crucial to most of the interesting and important features. For example, no instances are found of hydraulic control of flow that is separated from the left-hand wall at the sill, despite the fact that such states have been predicted by previous semigeostrophic theories. The calculations result in a series of regime diagrams that should be very helpful for investigators who wish to gain insight into rotating, hydraulically driven flow.
    Description: The authors have been supported by the National Science Foundation through Grants (OCE-9810599 for L.J.P. and K.R.H. and OCE-9711186 for EPC). L.J.P. also received support from the Office of Naval Research under Grant N00014-95-1-0456 and K.R.H. under grant N00014-93-1-0263.
    Keywords: Rotating-channel flow ; Hydraulically driven flow
    Repository Name: Woods Hole Open Access Server
    Type: Article
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  • 6
    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): 1087-1105, doi:10.1175/2010JPO4312.1.
    Description: Hood Canal, a long fjord in Washington State, has strong tides but limited deep-water renewal landward of a complex constriction. Tide-resolving hydrographic and velocity observations at the constriction, with a depth-cycling towed body, varied markedly during three consecutive years, partly because of stratification variations. To determine whether hydraulic control is generally important and to interpret observations of lee waves, blocking, and other features, hydraulic criticality is estimated over full tidal cycles for channel wide internal wave modes 1, 2, and 3, at five cross-channel sections, using mode speeds from the extended Taylor–Goldstein equation. These modes were strongly supercritical during most of ebb and flood on the gentle seaward sill face and for part of flood at the base of the steep landward side. Examining local criticality along the thalweg found repeated changes between mode 1 being critical and supercritical approaching the sill crest during flood, unsurprising given local minima and maxima in the cross-sectional area, with the sill crest near a maximum. Density crossing the sill sometimes resembled an overflow with an internal hydraulic control at the sill, followed by a hydraulic jump or lee wave. Long-wave speeds, however, suggest cross waves, particularly along the shallower gentler side, where flow downstream of a large-amplitude wave was uniformly supercritical. Supercritical approaching the sill, peak ebb was critical to mode 1 and supercritical to modes 2 and 3 at the base while forming a sluggish dome of dense water over the sill. Full interpretation exceeds observations and existing theory.
    Description: Washington State Sea Grant funded collection of these observations and the Office of Naval Research their publication. Pratt’s efforts were supported by the National Science Foundation under Grant OCE-0525729.
    Keywords: Channel flows ; Field experiments ; Ship observations ; Tides
    Repository Name: Woods Hole Open Access Server
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  • 7
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2009. 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 39 (2009): 2779-2799, doi:10.1175/2009JPO4075.1.
    Description: The hydraulic state of the exchange circulation through the Strait of Gibraltar is defined using a recently developed critical condition that accounts for cross-channel variations in layer thickness and velocity, applied to the output of a high-resolution three-dimensional numerical model simulating the tidal exchange. The numerical model uses a coastal-following curvilinear orthogonal grid, which includes, in addition to the Strait of Gibraltar, the Gulf of Cadiz and the Alboran Sea. The model is forced at the open boundaries through the specification of the surface tidal elevation that is characterized by the two principal semidiurnal and two diurnal harmonics: M2, S2, O1, and K1. The simulation covers an entire tropical month. The hydraulic analysis is carried out approximating the continuous vertical stratification first as a two-layer system and then as a three-layer system. In the latter, the transition zone, generated by entrainment and mixing between the Atlantic and Mediterranean flows, is considered as an active layer in the hydraulic model. As result of these vertical approximations, two different hydraulic states have been found; however, the simulated behavior of the flow only supports the hydraulic state predicted by the three-layer case. Thus, analyzing the results obtained by means of the three-layer hydraulic model, the authors have found that the flow in the strait reaches maximal exchange about 76% of the tropical monthlong period.
    Keywords: Channel flows ; Seas/gulfs/bays ; Mediterranean Sea ; Tides ; Orographic effects
    Repository Name: Woods Hole Open Access Server
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  • 8
    Publication Date: 2022-05-25
    Description: Author Posting. © American Meteorological Society, 2005. 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 35 (2005): 1568–1592, doi:10.1175/JPO2775.1.
    Description: Rotating two-layer exchange flow over a sill in a strait separating two relatively deep and wide basins is analyzed. Upstream of the sill in the deep upstream basin, the infinitely deep dense lower layer is assumed to be inactive, while the relatively thin upper layer flowing away from the sill forms a detached boundary current in the upstream basin. This analysis emphasizes the importance of this upstream boundary current, incorporating its width as a key parameter in a formalism for deducing the volume exchange rate and discriminating between maximal and submaximal states. Hence, even for narrow straits in which rotation does not dominate the dynamics within the strait, the importance of rotation in the wide upstream basin can be exploited. It is shown that the maximal allowable exchange transport through straits wider than 1½ Rossby deformation radii increases as rotation increases, unlike for smaller rotations, where the exchange decreases as rotation increases. The theory is applied to the exchange flow through the Strait of Gibraltar. This application illustrates how images of the oceans taken from space showing the width of the upstream flow, in this case a space shuttle photograph, might be used to determine the exchange transport through a strait. Maximal exchange conditions in the Strait of Gibraltar are predicted to apply at the time the space shuttle photograph was taken.
    Repository Name: Woods Hole Open Access Server
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  • 9
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    Copernicus Publications on behalf of the European Geosciences Union and the American Geophysical Union
    Publication Date: 2022-05-25
    Description: © The Author(s), 2011. This article is distributed under the terms of the Creative Commons Attribution 3.0 License. The definitive version was published in Nonlinear Processes in Geophysics 18 (2011): 977-987, doi:10.5194/npg-18-977-2011.
    Description: It is argued that the complexity of fluid particle trajectories provides the basis for a new method, referred to as the Complexity Method (CM), for estimation of Lagrangian coherent structures in aperiodic flows that are measured over finite time intervals. The basic principles of the CM are explained and the CM is tested in a variety of examples, both idealized and realistic, and in different reference frames. Two measures of complexity are explored in detail: the correlation dimension of trajectory, and a new measure – the ergodicity defect. Both measures yield structures that strongly resemble Lagrangian coherent structures in all of the examples considered. Since the CM uses properties of individual trajectories, and not separation rates between closely spaced trajectories, it may have advantages for the analysis of ocean float and drifter data sets in which trajectories are typically widely and non-uniformly spaced.
    Description: Work supported by grants NSF-CMG- 82469600, NSF-CMG-0825547 and ONR-N00014-11-1-0087.
    Repository Name: Woods Hole Open Access Server
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  • 10
    Publication Date: 2022-05-25
    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): 2206–2228, doi:10.1175/JPO-D-11-0191.1.
    Description: This study investigates the anisotropic properties of the eddy-induced material transport in the near-surface North Atlantic from two independent datasets, one simulated from the sea surface height altimetry and one derived from real-ocean surface drifters, and systematically examines the interactions between the mean- and eddy-induced material transport in the region. The Lagrangian particle dispersion, which is widely used to characterize the eddy-induced tracer fluxes, is quantified by constructing the “spreading ellipses.” The analysis consistently demonstrates that this dispersion is spatially inhomogeneous and strongly anisotropic. The spreading is larger and more anisotropic in the subtropical than in the subpolar gyre, and the largest ellipses occur in the Gulf Stream vicinity. Even at times longer than half a year, the spreading exhibits significant nondiffusive behavior in some parts of the domain. The eddies in this study are defined as deviations from the long-term time-mean. The contributions from the climatological annual cycle, interannual, and subannual (shorter than one year) variability are investigated, and the latter is shown to have the strongest effect on the anisotropy of particle spreading. The influence of the mean advection on the eddy-induced particle spreading is investigated using the “eddy-following-full-trajectories” technique and is found to be significant. The role of the Ekman advection is, however, secondary. The pronounced anisotropy of particle dispersion is expected to have important implications for distributing oceanic tracers, and for parameterizing eddy-induced tracer transfer in non-eddy-resolving models.
    Description: IR was supported by Grant NSF-OCE-0725796. IK would like to acknowledge support by the National Science foundation Grant OCE-0842834.
    Description: 2013-06-01
    Keywords: North Atlantic Ocean ; Diffusion ; Dispersion ; Eddies ; Lagrangian circulation/transport ; Trajectories
    Repository Name: Woods Hole Open Access Server
    Type: Article
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