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## Abstract

Local velocities and the trajectories of fluid parcels forced by wind blowing over a continental shelf, in the vicinity of a headland, are described with a linear, steady, three-dimensional barotropic model. The dynamical balance that governs the transport is similar to the wind-driven general circulation, because the varying bottom depth acts in the same way as meridional variation in the rotation rate. Far from the headland the circulation is independent of alongshore position, and the transport is parallel to the coast. The alongshore pressure gradient is a significant term in the alongshore momentum balance. Near the headland, the amplitude of the circulation, including the vertical motion, is larger on the upwave side (the side toward which a Kelvin wave would travel) than on the downwave side. On the upwave side, the flow adjusts to the presence of the headland over a distance of order *δ _{E}B**, where

*δ*is the ratio of the Ekman depth to the maximum shelf depth and

_{E}*B** is the width of the shelf. Fluid parcels that upwell on the upwave side are drawn from deeper depths than parcels that upwell at other alongshore locations. On the downwave side the flow adjusts over a relatively long distance, of order

*δ*

^{−1}

**.*

_{E}B## Abstract

Local velocities and the trajectories of fluid parcels forced by wind blowing over a continental shelf, in the vicinity of a headland, are described with a linear, steady, three-dimensional barotropic model. The dynamical balance that governs the transport is similar to the wind-driven general circulation, because the varying bottom depth acts in the same way as meridional variation in the rotation rate. Far from the headland the circulation is independent of alongshore position, and the transport is parallel to the coast. The alongshore pressure gradient is a significant term in the alongshore momentum balance. Near the headland, the amplitude of the circulation, including the vertical motion, is larger on the upwave side (the side toward which a Kelvin wave would travel) than on the downwave side. On the upwave side, the flow adjusts to the presence of the headland over a distance of order *δ _{E}B**, where

*δ*is the ratio of the Ekman depth to the maximum shelf depth and

_{E}*B** is the width of the shelf. Fluid parcels that upwell on the upwave side are drawn from deeper depths than parcels that upwell at other alongshore locations. On the downwave side the flow adjusts over a relatively long distance, of order

*δ*

^{−1}

**.*

_{E}B## Abstract

The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a coupled barotropic and baroclinic two-layer model on the *f* plane. As long as friction is not dominant, near-standing waves are present on the interface as well as on the surface. The surface pattern is principally determined by the product of the tidal barotropic wavenumber by the basin length. The interface deformation is determined by a baroclinic equivalent, usually a much larger number. As a result, the shape of the interface is characterized by horizontally smaller features than the surface. If the product of the tidal baroclinic wavenumber by the basin width is greater than one, both lateral and axial modes can be excited at the interface. If these modes are near resonant, large internal tides can be forced directly by the co-oscillating surface tide at the basin entrance. The amplitude and phase of the baroclinic component are sensitive functions of the density anomaly and the interface depth. As a result, the phase and amplitude of the interface vary by large amounts with comparatively small changes in those parameters. The model behavior is qualitatively consistent with observations in fjords and straits.

## Abstract

The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a coupled barotropic and baroclinic two-layer model on the *f* plane. As long as friction is not dominant, near-standing waves are present on the interface as well as on the surface. The surface pattern is principally determined by the product of the tidal barotropic wavenumber by the basin length. The interface deformation is determined by a baroclinic equivalent, usually a much larger number. As a result, the shape of the interface is characterized by horizontally smaller features than the surface. If the product of the tidal baroclinic wavenumber by the basin width is greater than one, both lateral and axial modes can be excited at the interface. If these modes are near resonant, large internal tides can be forced directly by the co-oscillating surface tide at the basin entrance. The amplitude and phase of the baroclinic component are sensitive functions of the density anomaly and the interface depth. As a result, the phase and amplitude of the interface vary by large amounts with comparatively small changes in those parameters. The model behavior is qualitatively consistent with observations in fjords and straits.

## Abstract

Coastal downwelling events, induced by tropical storms which travel up along the coast, occur regularly during the summer over the shelf of Southern California. Large vertical velocities (0.5 cm s^{−1}) are observed over the very narrow (3.6 km) shelf. Simultaneous observations of longshore current and cross-shelf pressure gradient indicate the cross-shelf momentum balance is geostrophic. Heat balance computations reveal that the increase in mean temperature over the shelf is mostly caused by cross-shelf advection of heat. Large longshore accelerations occurring simultaneously at all depths in the shallower part of the shelf may be explained by longshore sea surface slopes contributing, along with the wind stress, to the longshore momentum balance. Profiles of temperature and velocity are consistent with a two-layer description of the vertical structure, these layers being separated by a thin, turbulent mixing layer.

## Abstract

Coastal downwelling events, induced by tropical storms which travel up along the coast, occur regularly during the summer over the shelf of Southern California. Large vertical velocities (0.5 cm s^{−1}) are observed over the very narrow (3.6 km) shelf. Simultaneous observations of longshore current and cross-shelf pressure gradient indicate the cross-shelf momentum balance is geostrophic. Heat balance computations reveal that the increase in mean temperature over the shelf is mostly caused by cross-shelf advection of heat. Large longshore accelerations occurring simultaneously at all depths in the shallower part of the shelf may be explained by longshore sea surface slopes contributing, along with the wind stress, to the longshore momentum balance. Profiles of temperature and velocity are consistent with a two-layer description of the vertical structure, these layers being separated by a thin, turbulent mixing layer.

## Abstract

The three-dimensional residual circulation driven by tides in an elongated basin of arbitrary depth is described with a small amplitude, constant density model on the *f* plane. The inclusion of rotation fundamentally alters the residual flow. With rotation, fluid is drawn into the basin on the right side of an observer looking toward the closed end (in the Northern Hemisphere) and the return flow is on the opposite side. A lateral circulation is superposed on the axial flow, with upwelling over the deeper part of each section and downwelling near the sides. The residual flow is driven by a combination of advective terms, including the lateral advection of axial momentum associated with the Coriolis acceleration and Stokes forcing. Tidally averaged fluid parcel trajectories are determined by integrating the Lagrangian mean velocities. With or without rotation these trajectories vary considerably depending on small differences in initial position as well as on basin shape and other parameters of the problem.

## Abstract

The three-dimensional residual circulation driven by tides in an elongated basin of arbitrary depth is described with a small amplitude, constant density model on the *f* plane. The inclusion of rotation fundamentally alters the residual flow. With rotation, fluid is drawn into the basin on the right side of an observer looking toward the closed end (in the Northern Hemisphere) and the return flow is on the opposite side. A lateral circulation is superposed on the axial flow, with upwelling over the deeper part of each section and downwelling near the sides. The residual flow is driven by a combination of advective terms, including the lateral advection of axial momentum associated with the Coriolis acceleration and Stokes forcing. Tidally averaged fluid parcel trajectories are determined by integrating the Lagrangian mean velocities. With or without rotation these trajectories vary considerably depending on small differences in initial position as well as on basin shape and other parameters of the problem.

## Abstract

The wind-driven circulation in lakes, lagoons, estuaries, or coastal embayments is described with a linear, steady, three-dimensional barotropic model in an elongated basin of arbitrary depth distribution, on an *f* plane. With rotation, the vertically averaged velocity scales with the Ekman depth rather than the maximum depth *h*
_{0} as in the case without rotation. Near the closed ends of the basin, the flow turns in viscous boundary layers. Because the length of the turning areas depends on the sign of the bottom slope and on *δ,* the ratio of the Ekman depth to *h*
_{0}, there is a striking contrast between the turning areas on either side of an observer looking toward the end of the basin. In the Northern Hemisphere, the turning area on the left is broad, of order *δ*
^{−1}
*B**, where *B** is the basin half-width. The turning area on the right is narrow, of order *δB**, and dynamically equivalent to the western boundary current in models of the wind-driven ocean circulation. Ekman solutions are used to describe the vertical structure of the corresponding three-dimensional flow. The axial flow is qualitatively similar to the flow without rotation, but with reduced amplitude. The lateral circulation consists of two superposed gyres. The upper gyre rotates in the sense expected for Ekman transport: the surface flow is to the right of the wind. In the lower gyre, the circulation is in the opposite sense, driven by the veering in the bottom Ekman layer. The largest horizontal and vertical velocities occur in the narrow boundary layer near the end of the basin. Near midbasin, fluid parcels spiral downwind in a sheath surrounding a central core that rotates in the lateral plane, in the sense expected from Ekman dynamics. After turning at the end of the basin, some parcels travel upwind in the central core, while others return in the lower gyre.

## Abstract

The wind-driven circulation in lakes, lagoons, estuaries, or coastal embayments is described with a linear, steady, three-dimensional barotropic model in an elongated basin of arbitrary depth distribution, on an *f* plane. With rotation, the vertically averaged velocity scales with the Ekman depth rather than the maximum depth *h*
_{0} as in the case without rotation. Near the closed ends of the basin, the flow turns in viscous boundary layers. Because the length of the turning areas depends on the sign of the bottom slope and on *δ,* the ratio of the Ekman depth to *h*
_{0}, there is a striking contrast between the turning areas on either side of an observer looking toward the end of the basin. In the Northern Hemisphere, the turning area on the left is broad, of order *δ*
^{−1}
*B**, where *B** is the basin half-width. The turning area on the right is narrow, of order *δB**, and dynamically equivalent to the western boundary current in models of the wind-driven ocean circulation. Ekman solutions are used to describe the vertical structure of the corresponding three-dimensional flow. The axial flow is qualitatively similar to the flow without rotation, but with reduced amplitude. The lateral circulation consists of two superposed gyres. The upper gyre rotates in the sense expected for Ekman transport: the surface flow is to the right of the wind. In the lower gyre, the circulation is in the opposite sense, driven by the veering in the bottom Ekman layer. The largest horizontal and vertical velocities occur in the narrow boundary layer near the end of the basin. Near midbasin, fluid parcels spiral downwind in a sheath surrounding a central core that rotates in the lateral plane, in the sense expected from Ekman dynamics. After turning at the end of the basin, some parcels travel upwind in the central core, while others return in the lower gyre.

## Abstract

The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a linear, constant-density model on the *f* plane. Rotation fundamentally alters the lateral flow, introducing a lateral recirculation comparable in magnitude to the axial flow, as long as friction is not too large. This circulation is due to the imbalance between the cross-channel sea level gradient, which is in near-geostrophic balance with the Coriolis acceleration associated with the vertically averaged axial flow, and the Coriolis acceleration associated with the vertically sheared axial flow. During flood condition, for example, the lateral Coriolis acceleration near the surface exceeds the pressure gradient, tending to accelerate the lateral flow, while the converse is true near the bottom. As a result, with rotation, fluid parcels tend to corkscrew into and out of the basin in a tidal period. The axial flow is only weakly modified by rotation. When friction is small, the axial velocity is uniform in each section, except in a narrow bottom boundary layer where it decreases to zero. The boundary layer thickness increases with friction, so that with moderate or large friction, axial velocities are sheared from bottom to surface. When friction is large, the local and Coriolis accelerations are both small and the dynamics are governed by a balance between friction and the pressure gradient.

## Abstract

The three-dimensional tidal circulation in an elongated basin of arbitrary depth is described with a linear, constant-density model on the *f* plane. Rotation fundamentally alters the lateral flow, introducing a lateral recirculation comparable in magnitude to the axial flow, as long as friction is not too large. This circulation is due to the imbalance between the cross-channel sea level gradient, which is in near-geostrophic balance with the Coriolis acceleration associated with the vertically averaged axial flow, and the Coriolis acceleration associated with the vertically sheared axial flow. During flood condition, for example, the lateral Coriolis acceleration near the surface exceeds the pressure gradient, tending to accelerate the lateral flow, while the converse is true near the bottom. As a result, with rotation, fluid parcels tend to corkscrew into and out of the basin in a tidal period. The axial flow is only weakly modified by rotation. When friction is small, the axial velocity is uniform in each section, except in a narrow bottom boundary layer where it decreases to zero. The boundary layer thickness increases with friction, so that with moderate or large friction, axial velocities are sheared from bottom to surface. When friction is large, the local and Coriolis accelerations are both small and the dynamics are governed by a balance between friction and the pressure gradient.

## Abstract

Synthetic subsurface pressure (SSP) can be formed from tide gauge records and from bottom pressure measurements to provide a consistent and convenient basis for comparison of these two different types of observations. Common methods for this estimation are reviewed, and their accuracy is evaluated. Calculations show that subtidal SSP estimates from sea level (SSP_{SL}) and from bottom pressure observations (SSP_{BP}) at close sites agree only in a finite band of frequencies, corresponding to periods between 3.5 and 30 days. At the lower frequencies (periods longer than 30 days), sea level observations are subject to errors induced by the daily measure of staff height. At higher frequencies (periods between 1.5 and 3.5 days), the amplitude of fluctuations is too small to be resolved by a sea level gauge.

## Abstract

Synthetic subsurface pressure (SSP) can be formed from tide gauge records and from bottom pressure measurements to provide a consistent and convenient basis for comparison of these two different types of observations. Common methods for this estimation are reviewed, and their accuracy is evaluated. Calculations show that subtidal SSP estimates from sea level (SSP_{SL}) and from bottom pressure observations (SSP_{BP}) at close sites agree only in a finite band of frequencies, corresponding to periods between 3.5 and 30 days. At the lower frequencies (periods longer than 30 days), sea level observations are subject to errors induced by the daily measure of staff height. At higher frequencies (periods between 1.5 and 3.5 days), the amplitude of fluctuations is too small to be resolved by a sea level gauge.

## Abstract

The tidal and residual circulations in Laguna San Ignacio (LSI), a well-mixed evaporative lagoon located on the Pacific coast of the Baja California peninsula in Mexico, is described based on surveys and moored observations. At tidal periods pressure and axial current fluctuations are about one-quarter of a period out of phase, and so the tidal wave is close to standing. Pressure fluctuations increase and axial currents decrease with distance from the ocean. The fluctuating axial momentum balance is nonlinear and involves local acceleration, advection, barotropic pressure gradients, and friction. The structure of the residual circulation depends on the internal Froude number Fr_{i}, a measure of the relative strength of tidal and buoyancy forcing. Most of the time, Fr_{i} is large and the residual flow is laterally variable, driven by the tidally averaged nonlinear advective terms. The sense of this residual circulation is shown to depend on the lateral structure of the tidal stress and is away from the ocean in the deep channels when the tidal wave is standing, as in LSI, and in the opposite direction for a progressive wave. During neap tides, when Fr_{i} is small, the residual circulation is vertically stratified, with a dense near-bottom flow toward the ocean and relatively fresh inflow at the surface.

## Abstract

The tidal and residual circulations in Laguna San Ignacio (LSI), a well-mixed evaporative lagoon located on the Pacific coast of the Baja California peninsula in Mexico, is described based on surveys and moored observations. At tidal periods pressure and axial current fluctuations are about one-quarter of a period out of phase, and so the tidal wave is close to standing. Pressure fluctuations increase and axial currents decrease with distance from the ocean. The fluctuating axial momentum balance is nonlinear and involves local acceleration, advection, barotropic pressure gradients, and friction. The structure of the residual circulation depends on the internal Froude number Fr_{i}, a measure of the relative strength of tidal and buoyancy forcing. Most of the time, Fr_{i} is large and the residual flow is laterally variable, driven by the tidally averaged nonlinear advective terms. The sense of this residual circulation is shown to depend on the lateral structure of the tidal stress and is away from the ocean in the deep channels when the tidal wave is standing, as in LSI, and in the opposite direction for a progressive wave. During neap tides, when Fr_{i} is small, the residual circulation is vertically stratified, with a dense near-bottom flow toward the ocean and relatively fresh inflow at the surface.

## Abstract

Near the ocean, the residual circulation in Laguna San Ignacio, located on the Pacific coast of Baja California in Mexico, has been shown to be driven by tides. Here the subtidal circulation in the portion of the lagoon farther from the ocean is shown to be driven by the wind. The pressure difference between two stations, one near the closed end and the other midway along the central axis, is correlated well with the wind stress, in the sense that sea level rises downwind. Where the bathymetry is relatively simple, with a deep channel separating two shoal areas, the flow is upwind at the deepest part of the section, driven by the axial pressure gradient. In areas where the bathymetry is more complex, the direction of the observed flow is parallel neither to the local bathymetry nor to the applied wind stress. Linear theory qualitatively explains the major features of the wind-driven flow, including the relative strength of the pressure gradient to the wind stress, the direction of the flow, and the vertical structure, even in topographically complex areas. The residual circulation, after the wind-driven component has been removed, is assumed to be driven by the salinity gradient. That flow changes direction with depth. Where the bathymetry is simple, the near-bottom flow is toward relatively fresh water; flow is in the opposite direction closer to the surface. A linear model driven by a prescribed horizontal density gradient predicts downgradient flow at all depths near the deepest point of any section—a prediction that is qualitatively different from the observed flow.

## Abstract

Near the ocean, the residual circulation in Laguna San Ignacio, located on the Pacific coast of Baja California in Mexico, has been shown to be driven by tides. Here the subtidal circulation in the portion of the lagoon farther from the ocean is shown to be driven by the wind. The pressure difference between two stations, one near the closed end and the other midway along the central axis, is correlated well with the wind stress, in the sense that sea level rises downwind. Where the bathymetry is relatively simple, with a deep channel separating two shoal areas, the flow is upwind at the deepest part of the section, driven by the axial pressure gradient. In areas where the bathymetry is more complex, the direction of the observed flow is parallel neither to the local bathymetry nor to the applied wind stress. Linear theory qualitatively explains the major features of the wind-driven flow, including the relative strength of the pressure gradient to the wind stress, the direction of the flow, and the vertical structure, even in topographically complex areas. The residual circulation, after the wind-driven component has been removed, is assumed to be driven by the salinity gradient. That flow changes direction with depth. Where the bathymetry is simple, the near-bottom flow is toward relatively fresh water; flow is in the opposite direction closer to the surface. A linear model driven by a prescribed horizontal density gradient predicts downgradient flow at all depths near the deepest point of any section—a prediction that is qualitatively different from the observed flow.

## Abstract

Temperature and horizontal current observations at three water depths (15, 30 and 60 m) over the Southern California shelf are reported for four discrete periods during 1978–79, roughly corresponding to each of the principal seasons. The vertical structure of temperature changes markedly during the year; the water over the shelf is weakly stratified in the winter (*N* = 50 cpd) but stratification is stronger in the summer (*N* = 250 cpd). Seasonal changes in vertically averaged temperature are comparatively unimportant. Long-term averages of the longshore currents are to the south near the surface in all seasons, with amplitudes ranging up to 10 cm s^{−1} in the winter. During spring and summer, the stratification is accompanied by shear in the vertical structure of these long-term current averages, with surface currents sweeping to the south, but with deeper, colder water flowing in the opposite direction. Currents fluctuating at subtidal frequencies are predominantly alongshore and are strongest during the winter. The major fluctuations in this frequency band may he decomposed into barotropic and baroclinic components; the latter reach their maximum amplitudes during the summer. Relations between the barotropic currents, longshore wind stress, and synthetic bottom pressure are remarkably similar to those defined previously off Oregon, although the amplitude of currents is observed to increase with distance offshore. At tidal frequencies, both cross-shelf and longshore modes of fluctuation are important. Neither is well correlated to tidal sea surface elevation over long periods. The principal mode of variability associated with longshore tidal currents is barotropic, while that associated with cross-shelf currents is baroclinic. The motion in the cross-shelf plane resembles that due to a standing gravest-mode internal wave. At supratidal frequencies, internal waves travel onshore during those seasons when the water column is strongly stratified. The propagation characteristics of these high-frequency currents are similar to those expected for shoaling interfacial waves.

## Abstract

Temperature and horizontal current observations at three water depths (15, 30 and 60 m) over the Southern California shelf are reported for four discrete periods during 1978–79, roughly corresponding to each of the principal seasons. The vertical structure of temperature changes markedly during the year; the water over the shelf is weakly stratified in the winter (*N* = 50 cpd) but stratification is stronger in the summer (*N* = 250 cpd). Seasonal changes in vertically averaged temperature are comparatively unimportant. Long-term averages of the longshore currents are to the south near the surface in all seasons, with amplitudes ranging up to 10 cm s^{−1} in the winter. During spring and summer, the stratification is accompanied by shear in the vertical structure of these long-term current averages, with surface currents sweeping to the south, but with deeper, colder water flowing in the opposite direction. Currents fluctuating at subtidal frequencies are predominantly alongshore and are strongest during the winter. The major fluctuations in this frequency band may he decomposed into barotropic and baroclinic components; the latter reach their maximum amplitudes during the summer. Relations between the barotropic currents, longshore wind stress, and synthetic bottom pressure are remarkably similar to those defined previously off Oregon, although the amplitude of currents is observed to increase with distance offshore. At tidal frequencies, both cross-shelf and longshore modes of fluctuation are important. Neither is well correlated to tidal sea surface elevation over long periods. The principal mode of variability associated with longshore tidal currents is barotropic, while that associated with cross-shelf currents is baroclinic. The motion in the cross-shelf plane resembles that due to a standing gravest-mode internal wave. At supratidal frequencies, internal waves travel onshore during those seasons when the water column is strongly stratified. The propagation characteristics of these high-frequency currents are similar to those expected for shoaling interfacial waves.