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- Author or Editor: David C. Chapman x
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Abstract
The scattering of freely-propapting coastal-trapped waves (CTWs) by large variations in coastline and topography is studied using a numerical model which accomodates arbitrary density stratification, bathymetry and coastline. Particular attention is paid to the role of stratification which in moderate amounts can eliminate backscattered free-waves which occur. theoretically, in a barotropic ocean.
Numerical simulations using widening and narrowing shelf topographies show that the strength of the forward scattering into transmitted CTW modes is proportional to a topographic warp factor which estimates the severity of the topographic irregularities. The forward-scattering is further amplified by density stratification. Within the scattering region itself, the strengths of the scattered-wave-induced currents exhibit substantial variation over short spatial scales. There is generally a marked intensification of the flow within the scattering region, and rapid variations in phase. On narrowing shelves, the influence of the scattering can extend upstream into the region of uniform topography even when no freely-propagating backscattered waves exist.
A simulation is conducted of CTW scattering at a site on the East Coast of Australia where observations suggest the presence of scattered freely-propagating CTWs. The success of the model simulation in reproducing, features of observations supports the notion that realistic shelf geometries can matter significant levels of CTW energy, and that the watered waves can have an appreciable signal in current-meter observations made on the continental shelf. This suggests that along irregular coastlines, it is important to account for the possibility that CTW scattering may be occurring if oceanographic observations are to be interpreted correctly.
Abstract
The scattering of freely-propapting coastal-trapped waves (CTWs) by large variations in coastline and topography is studied using a numerical model which accomodates arbitrary density stratification, bathymetry and coastline. Particular attention is paid to the role of stratification which in moderate amounts can eliminate backscattered free-waves which occur. theoretically, in a barotropic ocean.
Numerical simulations using widening and narrowing shelf topographies show that the strength of the forward scattering into transmitted CTW modes is proportional to a topographic warp factor which estimates the severity of the topographic irregularities. The forward-scattering is further amplified by density stratification. Within the scattering region itself, the strengths of the scattered-wave-induced currents exhibit substantial variation over short spatial scales. There is generally a marked intensification of the flow within the scattering region, and rapid variations in phase. On narrowing shelves, the influence of the scattering can extend upstream into the region of uniform topography even when no freely-propagating backscattered waves exist.
A simulation is conducted of CTW scattering at a site on the East Coast of Australia where observations suggest the presence of scattered freely-propagating CTWs. The success of the model simulation in reproducing, features of observations supports the notion that realistic shelf geometries can matter significant levels of CTW energy, and that the watered waves can have an appreciable signal in current-meter observations made on the continental shelf. This suggests that along irregular coastlines, it is important to account for the possibility that CTW scattering may be occurring if oceanographic observations are to be interpreted correctly.
Abstract
Abstract
Abstract
There are three possible scenarios. 1) If the predicted h b is shallower than the inflow depth, then the bottom boundary layer does not transport buoyancy offshore, and a purely surface-advected plume forms, which extends offshore a minimum of more than four Rossby radii. 2) If the h b isobath is farther offshore than y s , then transport in the bottom boundary layer dominates and a purely bottom-advected plume forms, which is trapped along the h b isobath. 3) If the h b isobath is deeper than the inflow depth but shoreward of y s , then an intermediate plume forms in which the plume detaches from the bottom at h b and spreads offshore at the surface to y s .
The theory is tested using a primitive equation numerical model. All three plume types are reproduced with scales that agree well with the theory. The theory is compared to a number of observational examples. In all cases, the prediction of plume type is correct, and the length scales are consistent with the theory.
Abstract
There are three possible scenarios. 1) If the predicted h b is shallower than the inflow depth, then the bottom boundary layer does not transport buoyancy offshore, and a purely surface-advected plume forms, which extends offshore a minimum of more than four Rossby radii. 2) If the h b isobath is farther offshore than y s , then transport in the bottom boundary layer dominates and a purely bottom-advected plume forms, which is trapped along the h b isobath. 3) If the h b isobath is deeper than the inflow depth but shoreward of y s , then an intermediate plume forms in which the plume detaches from the bottom at h b and spreads offshore at the surface to y s .
The theory is tested using a primitive equation numerical model. All three plume types are reproduced with scales that agree well with the theory. The theory is compared to a number of observational examples. In all cases, the prediction of plume type is correct, and the length scales are consistent with the theory.
Abstract
The dynamics of a surface-to-bottom density front on a uniformly sloping continental shelf and the role of density advection in the bottom boundary layer are examined using a three-dimensional, primitive equation numerical model. The front is formed by prescribing a localized freshwater inflow through the coastal boundary. The resulting freshwater plume turns anticyclonically and moves along the coast, generating offshore transport in the bottom boundary layer, which advects freshwater offshore and creates a sharp surface-to-bottom density front with a surface-intensified alongshelf jet over the front. The offshore buoyancy flux in the bottom boundary layer moves the front offshore until it reaches a depth where the vertical shear within the front leads to a reversal in the cross-shelf velocity at the shoreward edge of the front. Consequently, the offshore buoyancy flux in the bottom boundary layer vanishes shoreward of the front. Within the front, a steady balance is established in the bottom boundary layer between vertical mixing and onshore advection of density. At this point, the front is “trapped” to an isobath; that is, the front remains parallel to the isobath and does not move farther offshore. The location of the trapped front is consistent with simple thermal wind dynamics. The basic frontal-trapping mechanism dominates the dynamics for a wide range of inflow velocities and densities (including very weak density anomalies), indicating that the advection of density in the bottom boundary layer may play a major role in the circulation on many continental shelves, even when the bottom boundary layer is thin compared to the total water depth.
Abstract
The dynamics of a surface-to-bottom density front on a uniformly sloping continental shelf and the role of density advection in the bottom boundary layer are examined using a three-dimensional, primitive equation numerical model. The front is formed by prescribing a localized freshwater inflow through the coastal boundary. The resulting freshwater plume turns anticyclonically and moves along the coast, generating offshore transport in the bottom boundary layer, which advects freshwater offshore and creates a sharp surface-to-bottom density front with a surface-intensified alongshelf jet over the front. The offshore buoyancy flux in the bottom boundary layer moves the front offshore until it reaches a depth where the vertical shear within the front leads to a reversal in the cross-shelf velocity at the shoreward edge of the front. Consequently, the offshore buoyancy flux in the bottom boundary layer vanishes shoreward of the front. Within the front, a steady balance is established in the bottom boundary layer between vertical mixing and onshore advection of density. At this point, the front is “trapped” to an isobath; that is, the front remains parallel to the isobath and does not move farther offshore. The location of the trapped front is consistent with simple thermal wind dynamics. The basic frontal-trapping mechanism dominates the dynamics for a wide range of inflow velocities and densities (including very weak density anomalies), indicating that the advection of density in the bottom boundary layer may play a major role in the circulation on many continental shelves, even when the bottom boundary layer is thin compared to the total water depth.
Abstract
Abstract
Abstract
The evolution of a steady stratified along-isobath current flowing cyclonically (shallower water on the right looking downstream) over a sloping frictional bottom is examined using an idealized model. The flow is assumed to consist of an inviscid vertically uniform geostrophic interior above a bottom boundary layer in which density is vertically well mixed. Within the bottom boundary layer, vertical shear in the horizontal velocities is assumed to result only from horizontal density gradients. Density advection is included in the model, but momentum advection is not. The downstream evolution of the current is described by two coupled nonlinear partial differential equations for surface pressure and boundary layer thickness, each of which is first order in the along-isobath coordinate and can be easily integrated numerically.
An initially narrow along-isobath current over a uniformly sloping bottom spreads and slows rapidly owing to the effects of bottom friction, much like the unstratified case. However, as the bottom boundary layer grows, the resulting horizontal density gradients reduce the bottom velocity, which in turn, decreases both the transport in the bottom boundary layer and the spreading of the current. An equilibrium is reached downstream in which the bottom velocity vanishes everywhere and the current stops spreading. This equilibrium flow persists indefinitely despite the presence of a frictional bottom. The width of the equilibrium current scales as W ∼ (f/N α)(F 0/f)½, where f is the Coriolis parameter, N the buoyancy frequency, α the bottom slope, and F 0 the inflow volume flux per unit depth. The thickness of the bottom boundary layer scales as α W, while the along-isobath velocity scales as (N α/f)(F 0 f)½. Surprisingly, the downstream equilibrium flow is independent of the magnitude of bottom friction. Good approximations for the equilibrium scales are obtained analytically by imposing conservation of mass and buoyancy transports. Generalizations to variable bottom slope, nonuniform stratification, and coastal currents are also presented.
Abstract
The evolution of a steady stratified along-isobath current flowing cyclonically (shallower water on the right looking downstream) over a sloping frictional bottom is examined using an idealized model. The flow is assumed to consist of an inviscid vertically uniform geostrophic interior above a bottom boundary layer in which density is vertically well mixed. Within the bottom boundary layer, vertical shear in the horizontal velocities is assumed to result only from horizontal density gradients. Density advection is included in the model, but momentum advection is not. The downstream evolution of the current is described by two coupled nonlinear partial differential equations for surface pressure and boundary layer thickness, each of which is first order in the along-isobath coordinate and can be easily integrated numerically.
An initially narrow along-isobath current over a uniformly sloping bottom spreads and slows rapidly owing to the effects of bottom friction, much like the unstratified case. However, as the bottom boundary layer grows, the resulting horizontal density gradients reduce the bottom velocity, which in turn, decreases both the transport in the bottom boundary layer and the spreading of the current. An equilibrium is reached downstream in which the bottom velocity vanishes everywhere and the current stops spreading. This equilibrium flow persists indefinitely despite the presence of a frictional bottom. The width of the equilibrium current scales as W ∼ (f/N α)(F 0/f)½, where f is the Coriolis parameter, N the buoyancy frequency, α the bottom slope, and F 0 the inflow volume flux per unit depth. The thickness of the bottom boundary layer scales as α W, while the along-isobath velocity scales as (N α/f)(F 0 f)½. Surprisingly, the downstream equilibrium flow is independent of the magnitude of bottom friction. Good approximations for the equilibrium scales are obtained analytically by imposing conservation of mass and buoyancy transports. Generalizations to variable bottom slope, nonuniform stratification, and coastal currents are also presented.
Abstract
An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S > 0.2) has a major impact. These results are supported by numerical model calculations.
Abstract
An idealized theoretical model is developed for the acceleration of a two-dimensional, stratified current over a uniformly sloping bottom, driven by an imposed alongshelf pressure gradient and taking into account the effects of buoyancy advection in the bottom boundary layer. Both downwelling and upwelling pressure gradients are considered. For a specified pressure gradient, the model response depends primarily on the Burger number S = Nα/f, where N is the initial buoyancy frequency, α is the bottom slope, and f is the Coriolis parameter. Without stratification (S = 0), buoyancy advection is absent, and the alongshelf flow accelerates until bottom stress balances the imposed pressure gradient. The e-folding time scale to reach this steady state is the friction time, h/r, where h is the water depth and r is a linear bottom friction coefficient. With stratification (S ≠ 0), buoyancy advection in the bottom boundary layer produces vertical shear, which prevents the bottom stress from becoming large enough to balance the imposed pressure gradient for many friction time scales. Thus, the alongshelf flow continues to accelerate, potentially producing large velocities. The acceleration increases rapidly with increasing S, such that even relatively weak stratification (S > 0.2) has a major impact. These results are supported by numerical model calculations.
Abstract
A simple theory is proposed for steady, two-dimensional, wind-driven coastal upwelling that relates the dynamics and the structure of the cross-shelf circulation to the stratification, bathymetry, and wind stress. The new element is an estimate of the nonlinear cross-shelf momentum flux divergence due to the wind-driven cross-shelf circulation acting on the vertically sheared geostrophic alongshelf flow. The theory predicts that the magnitude of the cross-shelf momentum flux divergence relative to the wind stress depends on the Burger number S = αN/f, where α is the bottom slope, N is the buoyancy frequency, and f is the Coriolis parameter. For S ≪ 1 (weak stratification), the cross-shelf momentum flux divergence is small, the bottom stress balances the wind stress, and the onshore return flow is primarily in the bottom boundary layer. For S ≈ 1 or larger (strong stratification), the cross-shelf momentum flux divergence balances the wind stress, the bottom stress is small, and the onshore return flow is in the interior. Estimates of the cross-shelf momentum flux divergence using moored observations from four coastal upwelling regions (0.2 ≤ S ≤ 1.5) are substantial relative to the wind stress when S ≈ 1 and exhibit a dependence on S that is consistent with the theory. Two-dimensional numerical model results indicate that the cross-shelf momentum flux divergence can be substantial for the time-dependent response and that the onshore return flow shifts from the bottom boundary layer for small S to just below the surface boundary layer for S ≈ 1.5–2.
Abstract
A simple theory is proposed for steady, two-dimensional, wind-driven coastal upwelling that relates the dynamics and the structure of the cross-shelf circulation to the stratification, bathymetry, and wind stress. The new element is an estimate of the nonlinear cross-shelf momentum flux divergence due to the wind-driven cross-shelf circulation acting on the vertically sheared geostrophic alongshelf flow. The theory predicts that the magnitude of the cross-shelf momentum flux divergence relative to the wind stress depends on the Burger number S = αN/f, where α is the bottom slope, N is the buoyancy frequency, and f is the Coriolis parameter. For S ≪ 1 (weak stratification), the cross-shelf momentum flux divergence is small, the bottom stress balances the wind stress, and the onshore return flow is primarily in the bottom boundary layer. For S ≈ 1 or larger (strong stratification), the cross-shelf momentum flux divergence balances the wind stress, the bottom stress is small, and the onshore return flow is in the interior. Estimates of the cross-shelf momentum flux divergence using moored observations from four coastal upwelling regions (0.2 ≤ S ≤ 1.5) are substantial relative to the wind stress when S ≈ 1 and exhibit a dependence on S that is consistent with the theory. Two-dimensional numerical model results indicate that the cross-shelf momentum flux divergence can be substantial for the time-dependent response and that the onshore return flow shifts from the bottom boundary layer for small S to just below the surface boundary layer for S ≈ 1.5–2.
Abstract
Long-term current observations at 45 and 75 m at one location on the southern flank of Georges Bank in water 85 m deep were examined for evidence of tidal rectification. Loder has shown analytically that rectification of the strong semidiurnal tidal current can cause a mean along-bank flow, and thus may partially drive the observed clockwise circulation around Georges Bank. The amplitude of the tidally rectified along-bank flow is proportional to the squared amplitude of the cross-bank tidal current. A simply extension of Loder's model to include the weaker N2 and S2 tidal components suggests that fortnightly (354 h) and monthly (661 h) variations of the square of the cross-bank tidal current should cause a modulation of the subtidal along-bank flow. The predicted ratio (R) of the fortnightly and monthly modulation of the along-bank flow to the mean along-bank flow on the southern flank was a function of position and ranged from ∼0.1–0.5. The amplitude of modulation of the along-bank flow at 360 and 648 h, estimated from the (weak) coherence between the observed along-bank flow and the subtidal envelope of a simulated surface tide, was less than ∼1.1 and 0.9 cm s−1, respectively, at 45 m. The amplitude of the modulation which can be attributed to tidal rectification may be in error by the astronomically forced Mm and MSf tidal currents, which are undescribed in this region. However, the magnitude of the mean along-bank tidally rectified current determined from the observed modulation and R predicted by the analytical model was ∼2.0 cm s−1 at 45 m (36% of the observed mean current in winter) and less than 1.6 cm s−1 at 75 m (43% of the observed mean current). Although R may change in a more realistic model, this analysis suggests that only part of the seasonal-mean along-bank flow on the southern flank of Georges Bank may be caused by tidal rectification.
Abstract
Long-term current observations at 45 and 75 m at one location on the southern flank of Georges Bank in water 85 m deep were examined for evidence of tidal rectification. Loder has shown analytically that rectification of the strong semidiurnal tidal current can cause a mean along-bank flow, and thus may partially drive the observed clockwise circulation around Georges Bank. The amplitude of the tidally rectified along-bank flow is proportional to the squared amplitude of the cross-bank tidal current. A simply extension of Loder's model to include the weaker N2 and S2 tidal components suggests that fortnightly (354 h) and monthly (661 h) variations of the square of the cross-bank tidal current should cause a modulation of the subtidal along-bank flow. The predicted ratio (R) of the fortnightly and monthly modulation of the along-bank flow to the mean along-bank flow on the southern flank was a function of position and ranged from ∼0.1–0.5. The amplitude of modulation of the along-bank flow at 360 and 648 h, estimated from the (weak) coherence between the observed along-bank flow and the subtidal envelope of a simulated surface tide, was less than ∼1.1 and 0.9 cm s−1, respectively, at 45 m. The amplitude of the modulation which can be attributed to tidal rectification may be in error by the astronomically forced Mm and MSf tidal currents, which are undescribed in this region. However, the magnitude of the mean along-bank tidally rectified current determined from the observed modulation and R predicted by the analytical model was ∼2.0 cm s−1 at 45 m (36% of the observed mean current in winter) and less than 1.6 cm s−1 at 75 m (43% of the observed mean current). Although R may change in a more realistic model, this analysis suggests that only part of the seasonal-mean along-bank flow on the southern flank of Georges Bank may be caused by tidal rectification.
Abstract
Most of the water that eventually flows northward through Bering Strait originates about 500 km south, seaward of the shelfbreak in the Bering Sea. Cumulative observational evidence supports the idea that most of this northward flow across the gently shoaling eastern Bering Sea continental shelf occurs as a western boundary current along the Siberian coast. A homogeneous rotating laboratory model and a barotropic numerical model each demonstrate this westward intensification of the mean flow. The intensification results from the well-known topographic β-effect: the combination of rotation and the depth decrease in the direction of flow acts in a similar fashion to the meridional gradient of the Coriolis parameter. For reasonable values of Bering Strait transport and shelf bottom friction, current speeds of 10–20 cm s−1 and a current width of ∼50 km are predicted.
Abstract
Most of the water that eventually flows northward through Bering Strait originates about 500 km south, seaward of the shelfbreak in the Bering Sea. Cumulative observational evidence supports the idea that most of this northward flow across the gently shoaling eastern Bering Sea continental shelf occurs as a western boundary current along the Siberian coast. A homogeneous rotating laboratory model and a barotropic numerical model each demonstrate this westward intensification of the mean flow. The intensification results from the well-known topographic β-effect: the combination of rotation and the depth decrease in the direction of flow acts in a similar fashion to the meridional gradient of the Coriolis parameter. For reasonable values of Bering Strait transport and shelf bottom friction, current speeds of 10–20 cm s−1 and a current width of ∼50 km are predicted.
