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Hui Wu

Abstract

The response of a wide shelf to subinertial and barotropic offshore pressure signals from the shelf edge was investigated. By relaxing the semigeostrophic approximation, an elliptical wave structure equation was formulated and solved with the integral transform method. It was found that when the imposed offshore signal has an along-shelf length scale similar to the shelf width, it can efficiently break the potential vorticity barrier and propagate toward the coast, producing a significant coastal sea level setup. Thereafter, the pressure signal reflects from the coast or the sloping topography, producing a transient eddy and propagates to the downshelf. The intensities of the coastal setup and the eddy increase as the along-shelf scale of the subinertial signal decreases or when its time scale is close to the inertial period. For a signal with longer time scale, the eddy is insignificant. The nature of the shelf response is controlled by the shelf conductivity κr/(fsB), in which r is the Rayleigh friction coefficient, f is the Coriolis parameter, s is the shelf slope, and B is the shelf width, respectively. For a given offshore signal, coastal setup increases with κ. For large κ, the eddy energy is concentrated at low modes, producing a large eddy, whereas a small κ produces a small eddy. The proposed theory can explain coastal sea level fluctuations under eddy impingement in the Mid-Atlantic Bight or other similar areas.

Significance Statement

Coastal sea level and shelf circulation are greatly affected by offshore pressure signals, e.g., mesoscale eddy impingements or boundary current fluctuations. It is often assumed that the along-shelf length scale of the forcing is much larger than the shelf width, i.e., the semigeostrophic approximation. Here in this study, we found this approximation significantly underestimates the shelf–ocean interaction. A general shelf wave equation was developed that relaxed the semigeostrophic approximation and was solved analytically with a novel mathematical method. The solution can characterize the shelf response to subinertial offshore forcing at arbitrary spatiotemporal scales. It was found that for a subinertial signal with scale close to or smaller than the shelf width, significant coastal sea level setup and transient eddy can be formed, which was consistent with realistic phenomena. The new theory could promote the understanding of coastal sea level variations and along-/cross-shelf transports at synoptic and intermediate scales.

Restricted access
Gunnar Voet
,
Matthew H. Alford
,
Jesse M. Cusack
,
Larry J. Pratt
,
James B. Girton
,
Glenn S. Carter
,
Jody M. Klymak
,
Shuwen Tan
, and
Andreas M. Thurnherr

Abstract

The energy and momentum balance of an abyssal overflow across a major sill in the Samoan Passage is estimated from two highly resolved towed sections, set 16 months apart, and results from a two-dimensional numerical simulation. Driven by the density anomaly across the sill, the flow is relatively steady. The system gains energy from divergence of horizontal pressure work O ( 5 ) kW m 1 and flux of available potential energy O ( 2 ) kW m 1 . Approximately half of these gains are transferred into kinetic energy while the other half is lost to turbulent dissipation, bottom drag, and divergence in vertical pressure work. Small-scale internal waves emanating downstream of the sill within the overflow layer radiate O ( 1 ) kW m 1 upward but dissipate most of their energy within the dense overflow layer and at its upper interface. The strongly sheared and highly stratified upper interface acts as a critical layer inhibiting any appreciable upward radiation of energy via topographically generated lee waves. Form drag of O ( 2 ) N m 2 , estimated from the pressure drop across the sill, is consistent with energy lost to dissipation and internal wave fluxes. The topographic drag removes momentum from the mean flow, slowing it down and feeding a countercurrent aloft. The processes discussed in this study combine to convert about one-third of the energy released from the cross-sill density difference into turbulent mixing within the overflow and at its upper interface. The observed and modeled vertical momentum flux divergence sustains gradients in shear and stratification, thereby maintaining an efficient route for abyssal water mass transformation downstream of this Samoan Passage sill.

Restricted access
Yue Bai
,
Yan Wang
, and
Andrew L. Stewart

Abstract

Topographic form stress (TFS) plays a central role in constraining the transport of the Antarctic Circumpolar Current (ACC), and thus the rate of exchange between the major ocean basins. Topographic form stress generation in the ACC has been linked to the formation of standing Rossby waves, which occur because the current is retrograde (opposing the direction of Rossby wave propagation). However, it is unclear whether TFS similarly retards current systems that are prograde (in the direction of Rossby wave propagation), which cannot arrest Rossby waves. An isopycnal model is used to investigate the momentum balance of wind-driven prograde and retrograde flows in a zonal channel, with bathymetry consisting of either a single ridge or a continental shelf and slope with a meridional excursion. Consistent with previous studies, retrograde flows are almost entirely impeded by TFS, except in the limit of flat bathymetry, whereas prograde flows are typically impeded by a combination of TFS and bottom friction. A barotropic theory for standing waves shows that bottom friction serves to shift the phase of the standing wave’s pressure field from that of the bathymetry, which is necessary to produce TFS. The mechanism is the same in prograde and retrograde flows, but is most efficient when the mean flow arrests a Rossby wave with a wavelength comparable to that of the bathymetry. The asymmetry between prograde and retrograde momentum balances implies that prograde current systems may be more sensitive to changes in wind forcing, for example associated with climate shifts.

Full access
Andrew L. Stewart
,
James C. McWilliams
, and
Aviv Solodoch

Abstract

Previous studies have concluded that the wind-input vorticity in ocean gyres is balanced by bottom pressure torques (BPT), when integrated over latitude bands. However, the BPT must vanish when integrated over any area enclosed by an isobath. This constraint raises ambiguities regarding the regions over which BPT should close the vorticity budget, and implies that BPT generated to balance a local wind stress curl necessitates the generation of a compensating, nonlocal BPT and thus nonlocal circulation. This study aims to clarify the role of BPT in wind-driven gyres using an idealized isopycnal model. Experiments performed with a single-signed wind stress curl in an enclosed, sloped basin reveal that BPT balances the winds only when integrated over latitude bands. Integrating over other, dynamically motivated definitions of the gyre, such as barotropic streamlines, yields a balance between wind stress curl and bottom frictional torques. This implies that bottom friction plays a nonnegligible role in structuring the gyre circulation. Nonlocal bottom pressure torques manifest in the form of along-slope pressure gradients associated with a weak basin-scale circulation, and are associated with a transition to a balance between wind stress and bottom friction around the coasts. Finally, a suite of perturbation experiments is used to investigate the dynamics of BPT. To predict the BPT, the authors extend a previous theory that describes propagation of surface pressure signals from the gyre interior toward the coast along planetary potential vorticity contours. This theory is shown to agree closely with the diagnosed contributions to the vorticity budget across the suite of model experiments.

Full access
Jody M. Klymak
,
Dhruv Balwada
,
Alberto Naveira Garabato
, and
Ryan Abernathey

Abstract

Slowly evolving stratified flow over rough topography is subject to substantial drag due to internal motions, but often numerical simulations are carried out at resolutions where this “wave” drag must be parameterized. Here we highlight the importance of internal drag from topography with scales that cannot radiate internal waves, but may be highly nonlinear, and we propose a simple parameterization of this drag that has a minimum of fit parameters compared to existing schemes. The parameterization smoothly transitions from a quadratic drag law ( ~ h u 0 2 ) for low Nh/u 0 (linear wave dynamics) to a linear drag law ( ~ h 2 u 0 N ) for high Nh/u 0 flows (nonlinear blocking and hydraulic dynamics), where N is the stratification, h is the height of the topography, and u 0 is the near-bottom velocity; the parameterization does not have a dependence on Coriolis frequency. Simulations carried out in a channel with synthetic bathymetry and steady body forcing indicate that this parameterization accurately predicts drag across a broad range of forcing parameters when the effect of reduced near-bottom mixing is taken into account by reducing the effective height of the topography. The parameterization is also tested in simulations of wind-driven channel flows that generate mesoscale eddy fields, a setup where the downstream transport is sensitive to the bottom drag parameterization and its effect on the eddies. In these simulations, the parameterization replicates the effect of rough bathymetry on the eddies. If extrapolated globally, the subinertial topographic scales can account for 2.7 TW of work done on the low-frequency circulation, an important sink that is redistributed to mixing in the open ocean.

Open access
Kristin L. Zeiden
,
Jennifer A. MacKinnon
,
Matthew H. Alford
,
Daniel L. Rudnick
,
Gunnar Voet
, and
Hemantha Wijesekera

Abstract

An array of moorings deployed off the coast of Palau is used to characterize submesoscale vorticity generated by broadband upper-ocean flows around the island. Palau is a steep-sided archipelago lying in the path of strong zonal geostrophic currents, but tides and inertial oscillations are energetic as well. Vorticity is correspondingly broadband, with both mean and variance O(f) in a surface and subsurface layer (where f is the local Coriolis frequency). However, while subinertial vorticity is linearly related to the incident subinertial current, the relationship between superinertial velocity and superinertial vorticity is weak. Instead, there is a strong nonlinear relationship between subinertial velocity and superinertial vorticity. A key observation of this study is that during periods of strong westward flow, vorticity in the tidal bands increases by an order of magnitude. Empirical orthogonal functions (EOFs) of velocity show this nonstationary, superinertial vorticity variance is due to eddy motion at the scale of the array. Comparison of kinetic energy and vorticity time series suggest that lateral shear against the island varies with the subinertial flow, while tidal currents lead to flow reversals inshore of the recirculating wake and possibly eddy shedding. This is a departure from the idealized analog typically drawn on in island wake studies: a cylinder in a steady flow. In that case, eddy formation occurs at a frequency dependent on the scale of the obstacle and strength of the flow alone. The observed tidal formation frequency likely modulates the strength of submesoscale wake eddies and thus their dynamic relationship to the mesoscale wake downstream of Palau.

Full access
Hui Wu

Abstract

Pressure anomaly set by the open ocean affects the dynamic topography and associated circulation over the continental shelf, which is explored here on a linearized β-plane arrested topographic wave framework that considers the variation in Coriolis parameter with latitude. It was found that on a meridional shelf, a nondimensional parameter Peβ, termed the β Péclet number, signifies the characteristics of open ocean–shelf interaction. The PeβDβ/α is determined by the ratio of long-wave-limit planetary to topographic Rossby wave speeds, i.e., the β drift Dβ, and the linear Ekman number α. On the western boundary shelf, due to the westward planetary Rossby wave, open ocean pressure propagates shoreward as Peβ > 1, and shelf circulation peaks where Peβ drops to 1. At this location, the planetary β effect is balanced by the bottom friction. The Peβ = 1 must occur either on the shelf or on the coastal wall when Peβ > 1 is observed at the shelf edge. On the eastern boundary shelf, however, Peβ < 0, the pressure anomaly is removed from the shelf, and hence the inductive circulation decays rapidly from the shelf edge. This β effect is robust on gently sloping meridional shelves. For zonal shelves, the planetary β increases the effective bottom slope on the northern boundary shelf but decreases it on the southern one, in a sense of potential vorticity conservation. However, this effect could be less significant in reality, given the complex dynamics involved. The above mechanism can explain the dynamics driving the Taiwan Warm Current in the East China Sea and its bifurcation around 28°N.

Full access
Madeleine M. Hamann
,
Matthew H. Alford
,
Andrew J. Lucas
,
Amy F. Waterhouse
, and
Gunnar Voet

Abstract

The La Jolla Canyon System (LJCS) is a small, steep, shelf-incising canyon offshore of San Diego, California. Observations conducted in the fall of 2016 capture the dynamics of internal tides and turbulence patterns. Semidiurnal (D2) energy flux was oriented up-canyon; 62% ± 20% of the signal was contained in mode 1 at the offshore mooring. The observed mode-1 D2 tide was partly standing based on the ratio of group speed times energy cgE and energy flux F. Enhanced dissipation occurred near the canyon head at middepths associated with elevated strain arising from the standing wave pattern. Modes 2–5 were progressive, and energy fluxes associated with these modes were oriented down-canyon, suggesting that incident mode-1 waves were back-reflected and scattered. Flux integrated over all modes across a given canyon cross section was always onshore and generally decreased moving shoreward (from 240 ± 15 to 5 ± 0.3 kW), with a 50-kW increase in flux occurring on a section inshore of the canyon’s major bend, possibly due to reflection of incident waves from the supercritical sidewalls of the bend. Flux convergence from canyon mouth to head was balanced by the volume-integrated dissipation observed. By comparing energy budgets from a global compendium of canyons with sufficient observations (six in total), a similar balance was found. One exception was Juan de Fuca Canyon, where such a balance was not found, likely due to its nontidal flows. These results suggest that internal tides incident at the mouth of a canyon system are dissipated therein rather than leaking over the sidewalls or siphoning energy to other wave frequencies.

Full access
Magdalena Andres
,
Ruth C. Musgrave
,
Daniel L. Rudnick
,
Kristin L. Zeiden
,
Thomas Peacock
, and
Jae-Hun Park

Abstract

As part of the Flow Encountering Abrupt Topography (FLEAT) program, an array of pressure-sensor equipped inverted echo sounders (PIESs) was deployed north of Palau where the westward-flowing North Equatorial Current encounters the southern end of the Kyushu–Palau Ridge in the tropical North Pacific. Capitalizing on concurrent observations from satellite altimetry, FLEAT Spray gliders, and shipboard hydrography, the PIESs’ 10-month duration hourly bottom pressure p and round-trip acoustic travel time τ records are used to examine the magnitude and predictability of sea level and pycnocline depth changes and to track signal propagations through the array. Sea level and pycnocline depth are found to vary in response to a range of ocean processes, with their magnitude and predictability strongly process dependent. Signals characterized here comprise the barotropic tides, semidiurnal and diurnal internal tides, southeastward-propagating superinertial waves, westward-propagating mesoscale eddies, and a strong signature of sea level increase and pycnocline deepening associated with the region’s relaxation from El Niño to La Niña conditions. The presence of a broad band of superinertial waves just above the inertial frequency was unexpected and the FLEAT observations and output from a numerical model suggest that these waves detected near Palau are forced by remote winds east of the Philippines. The PIES-based estimates of pycnocline displacement are found to have large uncertainties relative to overall variability in pycnocline depth, as localized deep current variations arising from interactions of the large-scale currents with the abrupt topography around Palau have significant travel time variability.

Open access
Gunnar Voet
,
Matthew H. Alford
,
Jennifer A. MacKinnon
, and
Jonathan D. Nash

Abstract

Towed shipboard and moored observations show internal gravity waves over a tall, supercritical submarine ridge that reaches to 1000 m below the ocean surface in the tropical western Pacific north of Palau. The lee-wave or topographic Froude number, Nh 0/U 0 (where N is the buoyancy frequency, h 0 the ridge height, and U 0 the farfield velocity), ranged between 25 and 140. The waves were generated by a superposition of tidal and low-frequency flows and thus had two distinct energy sources with combined amplitudes of up to 0.2 m s−1. Local breaking of the waves led to enhanced rates of dissipation of turbulent kinetic energy reaching above 10−6 W kg−1 in the lee of the ridge near topography. Turbulence observations showed a stark contrast between conditions at spring and neap tide. During spring tide, when the tidal flow dominated, turbulence was approximately equally distributed around both sides of the ridge. During neap tide, when the mean flow dominated over tidal oscillations, turbulence was mostly observed on the downstream side of the ridge relative to the mean flow. The drag exerted by the ridge on the flow, estimated to O ( 10 4 ) N m 1 for individual ridge crossings, and the associated power loss, thus provide an energy sink both for the low-frequency ocean circulation and the tidal flow.

Free access