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## Abstract

A remarkably consistent Lagrangian upwelling circulation at monthly and longer time scales is observed in a 17-yr time series of current profiles in 12 m of water on the southern New England inner shelf. The upwelling circulation is strongest in summer, with a current magnitude of ∼1 cm s^{−1}, which flushes the inner shelf in ∼2.5 days. The average winter upwelling circulation is about one-half of the average summer upwelling circulation, but with larger month-to-month variations driven, in part, by cross-shelf wind stresses. The persistent upwelling circulation is not wind-driven; it is driven by a cross-shelf buoyancy force associated with less-dense water near the coast. The cross-shelf density gradient is primarily due to temperature in summer, when strong surface heating warms shallower nearshore water more than deeper offshore water, and to salinity in winter, caused by fresher water near the coast. In the absence of turbulent stresses, the cross-shelf density gradient would be in a geostrophic, thermal-wind balance with the vertical shear in the along-shelf current. However, turbulent stresses over the inner shelf attributable to strong tidal currents and wind stress cause a partial breakdown of the thermal-wind balance that releases the buoyancy force, which drives the observed upwelling circulation. The presence of a cross-shelf density gradient has a profound impact on exchange across this inner shelf. Many inner shelves are characterized by turbulent stresses and cross-shelf density gradients with lighter water near the coast, suggesting turbulent thermal-wind-driven coastal upwelling may be a broadly important cross-shelf exchange mechanism.

### Significance Statement

A remarkably consistent upwelling circulation at monthly time scales is observed in a 17-yr time series of current profiles in shallow water off southern New England. This is not the traditional wind-driven coastal upwelling; instead, it is forced by cross-shelf buoyancy (density) gradients, released by turbulent stresses in shallow water. The persistent upwelling circulation is strongest in summer, when wind and wave forcing are weak, and flushes the inner portion of the continental shelf in a few days. Consequently, this buoyancy-driven coastal upwelling is important for cooling the inner shelf and provides a reliable mechanism for cross-shelf exchange. Many inner shelves are characterized by cross-shelf density gradients and turbulent stresses, suggesting this may be a broadly important cross-shelf exchange mechanism.

## Abstract

A remarkably consistent Lagrangian upwelling circulation at monthly and longer time scales is observed in a 17-yr time series of current profiles in 12 m of water on the southern New England inner shelf. The upwelling circulation is strongest in summer, with a current magnitude of ∼1 cm s^{−1}, which flushes the inner shelf in ∼2.5 days. The average winter upwelling circulation is about one-half of the average summer upwelling circulation, but with larger month-to-month variations driven, in part, by cross-shelf wind stresses. The persistent upwelling circulation is not wind-driven; it is driven by a cross-shelf buoyancy force associated with less-dense water near the coast. The cross-shelf density gradient is primarily due to temperature in summer, when strong surface heating warms shallower nearshore water more than deeper offshore water, and to salinity in winter, caused by fresher water near the coast. In the absence of turbulent stresses, the cross-shelf density gradient would be in a geostrophic, thermal-wind balance with the vertical shear in the along-shelf current. However, turbulent stresses over the inner shelf attributable to strong tidal currents and wind stress cause a partial breakdown of the thermal-wind balance that releases the buoyancy force, which drives the observed upwelling circulation. The presence of a cross-shelf density gradient has a profound impact on exchange across this inner shelf. Many inner shelves are characterized by turbulent stresses and cross-shelf density gradients with lighter water near the coast, suggesting turbulent thermal-wind-driven coastal upwelling may be a broadly important cross-shelf exchange mechanism.

### Significance Statement

A remarkably consistent upwelling circulation at monthly time scales is observed in a 17-yr time series of current profiles in shallow water off southern New England. This is not the traditional wind-driven coastal upwelling; instead, it is forced by cross-shelf buoyancy (density) gradients, released by turbulent stresses in shallow water. The persistent upwelling circulation is strongest in summer, when wind and wave forcing are weak, and flushes the inner portion of the continental shelf in a few days. Consequently, this buoyancy-driven coastal upwelling is important for cooling the inner shelf and provides a reliable mechanism for cross-shelf exchange. Many inner shelves are characterized by cross-shelf density gradients and turbulent stresses, suggesting this may be a broadly important cross-shelf exchange mechanism.

## Abstract

Time-series measurements of velocity, temperature, and conductivity on the northern California shelf during two winter seasons permit an observational test, in vertically integrated form, of a simple set of subinertial momentum and heat balances for the bottom boundary layer, which have resulted from recent theoretical work. These are 1) an along-isobath momentum equation that reduces to a classic Ekman balance; 2) a cross-isobath momentum equation in which the Ekman balance is modified by a buoyancy force caused by distortion of the isopycnal surfaces within the boundary layer; and 3) a heat balance in which variability of temperature is produced by cross-isobath advection. The measurements confirm the importance of buoyancy in the cross-isobath momentum equation, and, as has recently been predicted theoretically, they indicate that buoyancy is a dominant effect when the boundary layer is thick, which typically occurs during downwelling-favorable flows. An Ekman balance describes subinertial fluctuations in the along-isobath momentum equation with only moderate success. In contrast to idealizations made in most theoretical work, a buoyancy force caused by an along-isobath temperature gradient is as important as bottom stress in the mean along-isobath momentum equation, and along-isobath advection is as important as cross-isobath advection in the heat balance.

## Abstract

Time-series measurements of velocity, temperature, and conductivity on the northern California shelf during two winter seasons permit an observational test, in vertically integrated form, of a simple set of subinertial momentum and heat balances for the bottom boundary layer, which have resulted from recent theoretical work. These are 1) an along-isobath momentum equation that reduces to a classic Ekman balance; 2) a cross-isobath momentum equation in which the Ekman balance is modified by a buoyancy force caused by distortion of the isopycnal surfaces within the boundary layer; and 3) a heat balance in which variability of temperature is produced by cross-isobath advection. The measurements confirm the importance of buoyancy in the cross-isobath momentum equation, and, as has recently been predicted theoretically, they indicate that buoyancy is a dominant effect when the boundary layer is thick, which typically occurs during downwelling-favorable flows. An Ekman balance describes subinertial fluctuations in the along-isobath momentum equation with only moderate success. In contrast to idealizations made in most theoretical work, a buoyancy force caused by an along-isobath temperature gradient is as important as bottom stress in the mean along-isobath momentum equation, and along-isobath advection is as important as cross-isobath advection in the heat balance.

## Abstract

The effects of stratification, planetary rotation and a sloping bottom combine to produce an asymmetric response in which the characteristics of an oceanic bottom boundary layer depend on the direction, in addition to the magnitude, of the along-isobath velocity in the inviscid interior. The asymmetric response is examined theoretically under idealized conditions in which the motion begins from rest, the flow is uniform in the along-isobath and cross-isobath directions, and the water column is initially uniformly stratified. The analysis is based on an integrated model, in which the bottom stress is determined from a quadratic drag law, and the height of the boundary layer is determined from a Pollard–Rhines–Thompson mixing criterion. The model indicates rapid mixing at the onset of forcing to a height limited by planetary rotation and interior stratification, followed by evolution in which the height of the boundary layer may either increase or remain fixed near its initial value, depending on the behavior of the buoyancy within the boundary layer and the shear across the top of the layer. The model indicates reduction of the velocity within the boundary layer with increasing time, as a result of increasingly important buoyancy forces acting in opposition to the forcing by the dynamic pressure gradient. Model results compare favorably with previous turbulence closure computations, and the model reproduces the qualitative asymmetric behavior apparent in observations of boundary layer height.

## Abstract

The effects of stratification, planetary rotation and a sloping bottom combine to produce an asymmetric response in which the characteristics of an oceanic bottom boundary layer depend on the direction, in addition to the magnitude, of the along-isobath velocity in the inviscid interior. The asymmetric response is examined theoretically under idealized conditions in which the motion begins from rest, the flow is uniform in the along-isobath and cross-isobath directions, and the water column is initially uniformly stratified. The analysis is based on an integrated model, in which the bottom stress is determined from a quadratic drag law, and the height of the boundary layer is determined from a Pollard–Rhines–Thompson mixing criterion. The model indicates rapid mixing at the onset of forcing to a height limited by planetary rotation and interior stratification, followed by evolution in which the height of the boundary layer may either increase or remain fixed near its initial value, depending on the behavior of the buoyancy within the boundary layer and the shear across the top of the layer. The model indicates reduction of the velocity within the boundary layer with increasing time, as a result of increasingly important buoyancy forces acting in opposition to the forcing by the dynamic pressure gradient. Model results compare favorably with previous turbulence closure computations, and the model reproduces the qualitative asymmetric behavior apparent in observations of boundary layer height.

## Abstract

The horizontal momentum balance in the marine atmospheric boundary layer during the Coastal Ocean Dynamics Experiment (CODE) is analyzed, using meteorological data from an array of surface moorings. Previous studies have indicated the presence of orographically generated mesoscale features that are induced by strong southward flow around Point Arena. The present analysis demonstrates that during periods of strong southward flow, the cross-shore momentum equation is dominated by a balance between the ageostrophic acceleration associated with the flow curvature around Point Arena, and the cross-shore pressure gradient, while the along-shore momentum equation is dominated by a balance between vertical stress divergence and alongshore pressure gradient. These balances are consistent with results from a shallow water model of the marine layer. The calculations provide evidence for orographic modification of the horizontal structure of the boundary layer under a broader range of southward flow conditions than had been indicated by previous studies.

## Abstract

The horizontal momentum balance in the marine atmospheric boundary layer during the Coastal Ocean Dynamics Experiment (CODE) is analyzed, using meteorological data from an array of surface moorings. Previous studies have indicated the presence of orographically generated mesoscale features that are induced by strong southward flow around Point Arena. The present analysis demonstrates that during periods of strong southward flow, the cross-shore momentum equation is dominated by a balance between the ageostrophic acceleration associated with the flow curvature around Point Arena, and the cross-shore pressure gradient, while the along-shore momentum equation is dominated by a balance between vertical stress divergence and alongshore pressure gradient. These balances are consistent with results from a shallow water model of the marine layer. The calculations provide evidence for orographic modification of the horizontal structure of the boundary layer under a broader range of southward flow conditions than had been indicated by previous studies.

## Abstract

Subinertial currents on the southern California shelf are investigated using observations from a current meter array deployed near San Diego during the summer, fall and winter of 1978/79. This region is characterized by weak winds (order 1–2 m s^{−1}) and thus other driving mechanisms for the subinertial currents may be important. A simplified depth-averaged longshore momentum equation consisting of a balance between current accelerations, the adjusted sea level (ASL) gradient and the wind and bottom stress is examined. The ASL gradient is estimated using sea level and atmospheric pressure observations separated by 350 km. A linear parameterization of the bottom stress is used with a drag coefficient of 5 × 10^{−4} m s^{−1}. During fall and winter, the first-order balance of terms in the longshore momentum equation over the inner-shelf (15 m depth) is between the wind and bottom stress. Over the outer-shelf (60 m) the primary balance is between the ASL gradient and the bottom stress. At midshelf (30 m) both driving mechanisms are important. An estimate of the depth-average longshore velocity in turns of wind stress and the ASL gradient reproduce the major features of the observed depth-averaged velocity (correlations from 0.59 to 0.85). These simple dynamics fail to describe the summer observations, except during one strongly forced event. The vertical structure in summer is complicated by the presence of a thermocline and strong shears over the shelf. Examination of observed and estimated winds within the Southern California Bight and to the south along Baja California indicates that winds along Baja California (∼500 km south of San Diego) may play an important role in generating the ASL gradient fluctuations in the Southern California Bight.

## Abstract

Subinertial currents on the southern California shelf are investigated using observations from a current meter array deployed near San Diego during the summer, fall and winter of 1978/79. This region is characterized by weak winds (order 1–2 m s^{−1}) and thus other driving mechanisms for the subinertial currents may be important. A simplified depth-averaged longshore momentum equation consisting of a balance between current accelerations, the adjusted sea level (ASL) gradient and the wind and bottom stress is examined. The ASL gradient is estimated using sea level and atmospheric pressure observations separated by 350 km. A linear parameterization of the bottom stress is used with a drag coefficient of 5 × 10^{−4} m s^{−1}. During fall and winter, the first-order balance of terms in the longshore momentum equation over the inner-shelf (15 m depth) is between the wind and bottom stress. Over the outer-shelf (60 m) the primary balance is between the ASL gradient and the bottom stress. At midshelf (30 m) both driving mechanisms are important. An estimate of the depth-average longshore velocity in turns of wind stress and the ASL gradient reproduce the major features of the observed depth-averaged velocity (correlations from 0.59 to 0.85). These simple dynamics fail to describe the summer observations, except during one strongly forced event. The vertical structure in summer is complicated by the presence of a thermocline and strong shears over the shelf. Examination of observed and estimated winds within the Southern California Bight and to the south along Baja California indicates that winds along Baja California (∼500 km south of San Diego) may play an important role in generating the ASL gradient fluctuations in the Southern California Bight.

## Abstract

The effects of a sloping bottom and stratification on a turbulent bottom boundary layer are investigated for cases where the interior flow oscillates monochromatically with frequency *ω*. At higher frequencies, or small slope Burger numbers *s* = *αN*/*f* (where *α* is the bottom slope, *N* is the interior buoyancy frequency, and *f* is the Coriolis parameter), the bottom boundary layer is well mixed and the bottom stress is nearly what it would be over a flat bottom. For lower frequencies, or larger slope Burger number, the bottom boundary layer consists of a thick, weakly stratified outer layer and a thinner, more strongly stratified inner layer. Approximate expressions are derived for the different boundary layer thicknesses as functions of *s* and *σ* = *ω*/*f*. Further, buoyancy arrest causes the amplitude of the fluctuating bottom stress to decrease with decreasing *σ* (the *s* dependence, although important, is more complicated). For typical oceanic parameters, arrest is unimportant for fluctuation periods shorter than a few days. Substantial positive (toward the right when looking toward deeper water in the Northern Hemisphere) time-mean flows develop within the well-mixed boundary layer, and negative mean flows exist in the weakly stratified outer boundary layer for lower frequencies and larger *s*. If the interior flow is realistically broad band in frequency, the numerical model predicts stress reduction over all frequencies because of the nonlinearity associated with a quadratic bottom stress. It appears that the present one-dimensional model is reliable only for time scales less than the advective time scale that governs interior stratification.

## Abstract

The effects of a sloping bottom and stratification on a turbulent bottom boundary layer are investigated for cases where the interior flow oscillates monochromatically with frequency *ω*. At higher frequencies, or small slope Burger numbers *s* = *αN*/*f* (where *α* is the bottom slope, *N* is the interior buoyancy frequency, and *f* is the Coriolis parameter), the bottom boundary layer is well mixed and the bottom stress is nearly what it would be over a flat bottom. For lower frequencies, or larger slope Burger number, the bottom boundary layer consists of a thick, weakly stratified outer layer and a thinner, more strongly stratified inner layer. Approximate expressions are derived for the different boundary layer thicknesses as functions of *s* and *σ* = *ω*/*f*. Further, buoyancy arrest causes the amplitude of the fluctuating bottom stress to decrease with decreasing *σ* (the *s* dependence, although important, is more complicated). For typical oceanic parameters, arrest is unimportant for fluctuation periods shorter than a few days. Substantial positive (toward the right when looking toward deeper water in the Northern Hemisphere) time-mean flows develop within the well-mixed boundary layer, and negative mean flows exist in the weakly stratified outer boundary layer for lower frequencies and larger *s*. If the interior flow is realistically broad band in frequency, the numerical model predicts stress reduction over all frequencies because of the nonlinearity associated with a quadratic bottom stress. It appears that the present one-dimensional model is reliable only for time scales less than the advective time scale that governs interior stratification.

## Abstract

It is well known that along-isobath flow above a sloping bottom gives rise to cross-isobath Ekman transport and therefore sets up horizontal density gradients if the ocean is stratified. These transports in turn eventually bring the along-isobath bottom velocity, hence bottom stress, to rest (“buoyancy arrest”) simply by means of the thermal wind shear. This problem is revisited here. A modified expression for Ekman transport is rationalized, and general expressions for buoyancy arrest time scales are presented. Theory and numerical calculations are used to define a new formula for boundary layer thickness for the case of downslope Ekman transport, where a thick, weakly stratified arrested boundary layer results. For upslope Ekman transport, where advection leads to enhanced stability, expressions are derived for both the weakly sloping (in the sense of slope Burger number *s* = *αN*/*f*, where *α* is the bottom slope, *N* is the interior buoyancy frequency, and *f* is the Coriolis parameter) case where a capped boundary layer evolves and the larger *s* case where a nearly linearly stratified boundary layer joins smoothly to the interior density profile. Consistent estimates for the buoyancy arrest time scale are found for each case.

## Abstract

It is well known that along-isobath flow above a sloping bottom gives rise to cross-isobath Ekman transport and therefore sets up horizontal density gradients if the ocean is stratified. These transports in turn eventually bring the along-isobath bottom velocity, hence bottom stress, to rest (“buoyancy arrest”) simply by means of the thermal wind shear. This problem is revisited here. A modified expression for Ekman transport is rationalized, and general expressions for buoyancy arrest time scales are presented. Theory and numerical calculations are used to define a new formula for boundary layer thickness for the case of downslope Ekman transport, where a thick, weakly stratified arrested boundary layer results. For upslope Ekman transport, where advection leads to enhanced stability, expressions are derived for both the weakly sloping (in the sense of slope Burger number *s* = *αN*/*f*, where *α* is the bottom slope, *N* is the interior buoyancy frequency, and *f* is the Coriolis parameter) case where a capped boundary layer evolves and the larger *s* case where a nearly linearly stratified boundary layer joins smoothly to the interior density profile. Consistent estimates for the buoyancy arrest time scale are found for each case.

## Abstract

Acoustic Doppler current profilers (ADCPs) are widely used for routine measurements of ocean currents and waves in coastal environments. These instruments have the basic capability to measure surface wave frequency–directional spectra, but the quality of the estimates is not well understood because of the relatively high noise levels in the velocity measurements. In this study, wave data are evaluated from two 600-kHz ADCP instruments deployed at 20- and 45-m depths on the Southern California continental shelf. A simple parametric estimation technique is presented that provides robust estimates of the gross directional wave properties, even when the data quality is marginal, as was often the case in this benign wave environment. Good agreement of mean direction and (to a lesser degree) directional spreading estimates with measurements from a nearby surface-following buoy confirms that reliable wave information can generally be extracted from ADCP measurements on the continental shelf, supporting the instrument’s suitability for routine wave-monitoring applications.

## Abstract

Acoustic Doppler current profilers (ADCPs) are widely used for routine measurements of ocean currents and waves in coastal environments. These instruments have the basic capability to measure surface wave frequency–directional spectra, but the quality of the estimates is not well understood because of the relatively high noise levels in the velocity measurements. In this study, wave data are evaluated from two 600-kHz ADCP instruments deployed at 20- and 45-m depths on the Southern California continental shelf. A simple parametric estimation technique is presented that provides robust estimates of the gross directional wave properties, even when the data quality is marginal, as was often the case in this benign wave environment. Good agreement of mean direction and (to a lesser degree) directional spreading estimates with measurements from a nearby surface-following buoy confirms that reliable wave information can generally be extracted from ADCP measurements on the continental shelf, supporting the instrument’s suitability for routine wave-monitoring applications.

## Abstract

Onset's HOBO U22 Water Temp Pros are small, reliable, relatively inexpensive, self-contained temperature loggers that are widely used in studies of oceans, lakes, and streams. An in-house temperature bath calibration of 158 Temp Pros indicated root-mean-square (RMS) errors ranging from 0.01° to 0.14°C, with one value of 0.23°C, consistent with the factory specifications. Application of a quadratic calibration correction substantially reduced the RMS error to less than 0.009°C in all cases. The primary correction was a bias error typically between −0.1° and 0.15°C. Comparison of water temperature measurements from Temp Pros and more accurate temperature loggers during two oceanographic studies indicates that calibrated Temp Pros have an RMS error of ~0.02°C throughout the water column at night and beneath the surface layer influenced by penetrating solar radiation during the day. Larger RMS errors (up to 0.08°C) are observed near the surface during the day due to solar heating of the black Temp Pro housing. Errors due to solar heating are significantly reduced by wrapping the housing with white electrical tape.

## Abstract

Onset's HOBO U22 Water Temp Pros are small, reliable, relatively inexpensive, self-contained temperature loggers that are widely used in studies of oceans, lakes, and streams. An in-house temperature bath calibration of 158 Temp Pros indicated root-mean-square (RMS) errors ranging from 0.01° to 0.14°C, with one value of 0.23°C, consistent with the factory specifications. Application of a quadratic calibration correction substantially reduced the RMS error to less than 0.009°C in all cases. The primary correction was a bias error typically between −0.1° and 0.15°C. Comparison of water temperature measurements from Temp Pros and more accurate temperature loggers during two oceanographic studies indicates that calibrated Temp Pros have an RMS error of ~0.02°C throughout the water column at night and beneath the surface layer influenced by penetrating solar radiation during the day. Larger RMS errors (up to 0.08°C) are observed near the surface during the day due to solar heating of the black Temp Pro housing. Errors due to solar heating are significantly reduced by wrapping the housing with white electrical tape.

## Abstract

A primary challenge in modeling flow over shallow coral reefs is accurately characterizing the bottom drag. Previous studies over continental shelves and sandy beaches suggest surface gravity waves should enhance the drag on the circulation over coral reefs. The influence of surface gravity waves on drag over four platform reefs in the Red Sea is examined using observations from 6-month deployments of current and pressure sensors burst sampling at 1 Hz for 4–5 min. Depth-average current fluctuations *U*′ within each burst are dominated by wave orbital velocities *u*
_{
w
} that account for 80%–90% of the burst variance and have a magnitude of order 10 cm s^{−1}, similar to the lower-frequency depth-average current *U*
_{avg}. Previous studies have shown that the cross-reef bottom stress balances the pressure gradient over these reefs. A bottom stress estimate that neglects the waves (*ρC*
_{
da
}
*U*
_{avg}|*U*
_{avg}|, where *ρ* is water density and *C _{da}
* is a drag coefficient) balances the observed pressure gradient when

*u*

_{ w }is smaller than

*U*

_{avg}but underestimates the pressure gradient when

*u*

_{ w }is larger than

*U*

_{avg}(by a factor of 3–5 when

*u*

_{ w }= 2

*U*

_{avg}), indicating the neglected waves enhance the bottom stress. In contrast, a bottom stress estimate that includes the waves [

*ρC*

_{ da }(

*U*

_{avg}+

*U*′)

*|U*

_{avg}

*+ U*′|)] balances the observed pressure gradient independent of the relative size of

*u*

_{ w }and

*U*

_{avg}, indicating that this estimate accounts for the wave enhancement of the bottom stress. A parameterization proposed by Wright and Thompson provides a reasonable estimate of the total bottom stress (including the waves) given the burst-averaged current and the wave orbital velocity.

## Abstract

A primary challenge in modeling flow over shallow coral reefs is accurately characterizing the bottom drag. Previous studies over continental shelves and sandy beaches suggest surface gravity waves should enhance the drag on the circulation over coral reefs. The influence of surface gravity waves on drag over four platform reefs in the Red Sea is examined using observations from 6-month deployments of current and pressure sensors burst sampling at 1 Hz for 4–5 min. Depth-average current fluctuations *U*′ within each burst are dominated by wave orbital velocities *u*
_{
w
} that account for 80%–90% of the burst variance and have a magnitude of order 10 cm s^{−1}, similar to the lower-frequency depth-average current *U*
_{avg}. Previous studies have shown that the cross-reef bottom stress balances the pressure gradient over these reefs. A bottom stress estimate that neglects the waves (*ρC*
_{
da
}
*U*
_{avg}|*U*
_{avg}|, where *ρ* is water density and *C _{da}
* is a drag coefficient) balances the observed pressure gradient when

*u*

_{ w }is smaller than

*U*

_{avg}but underestimates the pressure gradient when

*u*

_{ w }is larger than

*U*

_{avg}(by a factor of 3–5 when

*u*

_{ w }= 2

*U*

_{avg}), indicating the neglected waves enhance the bottom stress. In contrast, a bottom stress estimate that includes the waves [

*ρC*

_{ da }(

*U*

_{avg}+

*U*′)

*|U*

_{avg}

*+ U*′|)] balances the observed pressure gradient independent of the relative size of

*u*

_{ w }and

*U*

_{avg}, indicating that this estimate accounts for the wave enhancement of the bottom stress. A parameterization proposed by Wright and Thompson provides a reasonable estimate of the total bottom stress (including the waves) given the burst-averaged current and the wave orbital velocity.