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## Abstract

Recent studies have shown that the sensitivity of the circumpolar transport of channels to the westerlies is controlled by wind-driven gyre circulations. Although the form stress associated with the gyres has been shown to be controlled by eddies, bottom friction, and topographic width, the role of inertial effects has not been fully understood. In this study, we conduct a series of sensitivity analyses using the barotropic model with and without the advection term (hereinafter, the model without the advection term is denoted as *linear model*). Experiments showed that the sensitivity of the circumpolar transport decreased under the westerly winds compared to the linear model, while it increased under the easterly winds. We show that the inertial effect of western boundary currents generates anomalous anticyclonic circulations over the topography, producing the westward topographic form stress anomalies regardless of the wind directions. In addition, we discuss the sensitivity of the inertial effect mechanism to topographic height, width, and geometries. The inertial effect mechanism is robust as long as the gyre circulations dominate while its relative importance changes. We also found that the dynamics of the barotropic channel strongly depend on the geometries of geostrophic contours, *f/h*. Therefore, we conclude that the dynamics of barotropic channel models might be interpreted with caution to understand the dynamics of the Southern Ocean.

## Abstract

Recent studies have shown that the sensitivity of the circumpolar transport of channels to the westerlies is controlled by wind-driven gyre circulations. Although the form stress associated with the gyres has been shown to be controlled by eddies, bottom friction, and topographic width, the role of inertial effects has not been fully understood. In this study, we conduct a series of sensitivity analyses using the barotropic model with and without the advection term (hereinafter, the model without the advection term is denoted as *linear model*). Experiments showed that the sensitivity of the circumpolar transport decreased under the westerly winds compared to the linear model, while it increased under the easterly winds. We show that the inertial effect of western boundary currents generates anomalous anticyclonic circulations over the topography, producing the westward topographic form stress anomalies regardless of the wind directions. In addition, we discuss the sensitivity of the inertial effect mechanism to topographic height, width, and geometries. The inertial effect mechanism is robust as long as the gyre circulations dominate while its relative importance changes. We also found that the dynamics of the barotropic channel strongly depend on the geometries of geostrophic contours, *f/h*. Therefore, we conclude that the dynamics of barotropic channel models might be interpreted with caution to understand the dynamics of the Southern Ocean.

## Abstract

Observations from a tidal estuary show that tidal intrusion fronts occur regularly during flood tides near topographic features including constrictions and bends. A realistic model is used to study the generation of these fronts and their influence on stratification and mixing in the estuary. At the constriction, flow separation occurs on both sides of the jet flow downstream of the narrow opening, leading to sharp lateral salinity gradients and baroclinic secondary circulation. A tidal intrusion front, with a V-shaped convergence zone on the surface, is generated by the interaction between secondary circulation and the jet flow. Stratification is created at the front due to the straining of lateral salinity gradients by secondary circulation. Though stratification is expected to suppress turbulence, strong turbulent mixing is found near the surface front. The intense mixing is attributed to enhanced vertical shear due to both frontal baroclinicity and the twisting of lateral shear by secondary circulation. In the bend, flow separation occurs along the inner bank, resulting in lateral salinity gradients, secondary circulation, frontogenesis, and enhanced mixing near the front. In contrast to the V-shaped front at the constriction, an oblique linear surface convergence front occurs in the bend, which resembles a one-sided tidal intrusion front. Moreover, in addition to baroclinicity, channel curvature also affects secondary circulation, frontogenesis, and mixing in the bend. Overall in the estuary, the near-surface mixing associated with tidal intrusion fronts during flood tides is similar in magnitude to bottom boundary layer mixing that occurs primarily during ebbs.

## Abstract

Observations from a tidal estuary show that tidal intrusion fronts occur regularly during flood tides near topographic features including constrictions and bends. A realistic model is used to study the generation of these fronts and their influence on stratification and mixing in the estuary. At the constriction, flow separation occurs on both sides of the jet flow downstream of the narrow opening, leading to sharp lateral salinity gradients and baroclinic secondary circulation. A tidal intrusion front, with a V-shaped convergence zone on the surface, is generated by the interaction between secondary circulation and the jet flow. Stratification is created at the front due to the straining of lateral salinity gradients by secondary circulation. Though stratification is expected to suppress turbulence, strong turbulent mixing is found near the surface front. The intense mixing is attributed to enhanced vertical shear due to both frontal baroclinicity and the twisting of lateral shear by secondary circulation. In the bend, flow separation occurs along the inner bank, resulting in lateral salinity gradients, secondary circulation, frontogenesis, and enhanced mixing near the front. In contrast to the V-shaped front at the constriction, an oblique linear surface convergence front occurs in the bend, which resembles a one-sided tidal intrusion front. Moreover, in addition to baroclinicity, channel curvature also affects secondary circulation, frontogenesis, and mixing in the bend. Overall in the estuary, the near-surface mixing associated with tidal intrusion fronts during flood tides is similar in magnitude to bottom boundary layer mixing that occurs primarily during ebbs.

## Abstract

Generating mechanisms and parameterizations for enhanced turbulence in the wake of a seamount in the path of the Kuroshio are investigated. Full-depth profiles of finescale temperature, salinity, horizontal velocity, and microscale thermal-variance dissipation rate up- and downstream of the ∼10-km-wide seamount were measured with EM-APEX profiling floats and ADCP moorings. Energetic turbulent kinetic energy dissipation rates *N*
^{−1} ∼ 100 s and the 0.5 m s^{−1} Kuroshio flow speed. Thus, the turbulent wake must be maintained by continuous replenishment which might arise from (i) nonlinear instability of a marginally unstable vortex wake, (ii) anisotropic stratified turbulence with expected downstream decay scales of 10–100 km, and/or (iii) lee-wave critical-layer trapping at the base of the Kuroshio. Three turbulence parameterizations operating on different scales, (i) finescale, (ii) large-eddy, and (iii) reduced-shear, are tested. Average *ε* vertical profiles are well reproduced by all three parameterizations. Vertical wavenumber spectra for shear and strain are saturated over 10–100 m vertical wavelengths comparable to water depth with spectral levels independent of *ε* and spectral slopes of −1, indicating that the wake flows are strongly nonlinear. In contrast, vertical divergence spectral levels increase with *ε*.

## Abstract

Generating mechanisms and parameterizations for enhanced turbulence in the wake of a seamount in the path of the Kuroshio are investigated. Full-depth profiles of finescale temperature, salinity, horizontal velocity, and microscale thermal-variance dissipation rate up- and downstream of the ∼10-km-wide seamount were measured with EM-APEX profiling floats and ADCP moorings. Energetic turbulent kinetic energy dissipation rates *N*
^{−1} ∼ 100 s and the 0.5 m s^{−1} Kuroshio flow speed. Thus, the turbulent wake must be maintained by continuous replenishment which might arise from (i) nonlinear instability of a marginally unstable vortex wake, (ii) anisotropic stratified turbulence with expected downstream decay scales of 10–100 km, and/or (iii) lee-wave critical-layer trapping at the base of the Kuroshio. Three turbulence parameterizations operating on different scales, (i) finescale, (ii) large-eddy, and (iii) reduced-shear, are tested. Average *ε* vertical profiles are well reproduced by all three parameterizations. Vertical wavenumber spectra for shear and strain are saturated over 10–100 m vertical wavelengths comparable to water depth with spectral levels independent of *ε* and spectral slopes of −1, indicating that the wake flows are strongly nonlinear. In contrast, vertical divergence spectral levels increase with *ε*.

## 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 *κ* ≡ *r*/(*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.

## 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 *κ* ≡ *r*/(*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.

## 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

## 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

## 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.

## 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.

## 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.

## 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.

## 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 (*Nh*/*u*
_{0} (linear wave dynamics) to a linear drag law (*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.

## 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 (*Nh*/*u*
_{0} (linear wave dynamics) to a linear drag law (*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.

## 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.

## 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.

## 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 Pe_{β}, termed the *β* Péclet number, signifies the characteristics of open ocean–shelf interaction. The Pe_{β} ≡ *D*_{β}/*α* is determined by the ratio of long-wave-limit planetary to topographic Rossby wave speeds, i.e., the *β* drift *D*_{β}, and the linear Ekman number *α*. On the western boundary shelf, due to the westward planetary Rossby wave, open ocean pressure propagates shoreward as Pe_{β} > 1, and shelf circulation peaks where Pe_{β} drops to 1. At this location, the planetary *β* effect is balanced by the bottom friction. The Pe_{β} = 1 must occur either on the shelf or on the coastal wall when Pe_{β} > 1 is observed at the shelf edge. On the eastern boundary shelf, however, Pe_{β} < 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.

## 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 Pe_{β}, termed the *β* Péclet number, signifies the characteristics of open ocean–shelf interaction. The Pe_{β} ≡ *D*_{β}/*α* is determined by the ratio of long-wave-limit planetary to topographic Rossby wave speeds, i.e., the *β* drift *D*_{β}, and the linear Ekman number *α*. On the western boundary shelf, due to the westward planetary Rossby wave, open ocean pressure propagates shoreward as Pe_{β} > 1, and shelf circulation peaks where Pe_{β} drops to 1. At this location, the planetary *β* effect is balanced by the bottom friction. The Pe_{β} = 1 must occur either on the shelf or on the coastal wall when Pe_{β} > 1 is observed at the shelf edge. On the eastern boundary shelf, however, Pe_{β} < 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.