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• 1. [Article] Swash zone sediment suspension and transport and the importance of bore-generated turbulence

  copyrighted by American Geophysical Union

  Citation × Citation Citation Abstract Copy Title: Swash zone sediment suspension and transport and the importance of bore-generated turbulence Author: Puleo, J. A., Holman, Robert A., Allen, J. S., Beach, R. A. copyrighted by American Geophysical Union Title: Swash zone sediment suspension and transport and the importance of bore-generated turbulence Author: Puleo, J. A., Holman, Robert A., Allen, J. S., Beach, R. A. copyrighted by American Geophysical Union Close

• 2. [Article] On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part I: Formulation and Comparison of Exact Solutions

  Motivated by the general objective of pursuing oceanographic process and data assimilation studies of the complex, nonlinear eddy and jet current fields observed over the continental shelf and slope off ...

  Citation × Citation Citation Abstract Copy Title: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part I: Formulation and Comparison of Exact Solutions Author: Barth, J. A., Allen, J. S., Newberger, P. A. Motivated by the general objective of pursuing oceanographic process and data assimilation studies of the complex, nonlinear eddy and jet current fields observed over the continental shelf and slope off the west coast of the United States, we investigate the use of intermediate models for that purpose. Intermediate models contain physics between that in the primitive equations and that in the quasigeostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope, while filtering out high-frequency gravity-inertial waves. As an initial step, we compare and evaluate several intermediate models applied to the f-plane shallow-water equations for flows over topography. The accuracy and utility of the intermediate models are assessed by a comparison of exact analytical and numerical solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG). The intermediate models that we consider are based on the geostrophic momentum (GM) approximation, the derivation of Salmon (1983) utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), the slow equations (SE) of Lynch (1989), and the modified slow equations (MSE). In Part I, we discuss the intermediate models and develop formulations that are suitable for numerical solution in physical coordinates for use in Parts II and III. We investigate the capability of the intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, and demonstrate that they do so with accuracy consistent with standard linear low-frequency approximations. We also assess the accuracy of the models by a comparison of exact nonlinear analytical solutions to the SWE for steady flow in an elliptic paraboloid and for unsteady motion of elliptical vortices in a circular paraboloid with corresponding analytical solutions to the intermediate models and to QG. General results from the exact solution comparisons include the following. Many of the intermediate models are capable of producing more accurate solutions than QG over a range of Rossby numbers 0 < ϵ < 1. In some cases, the intermediate models provide accurate approximate solutions where QG is not applicable and fails to give a relevant solution. Considerable parameter-dependent variation in quality exists, however, among the different intermediate models. For the particular problems considered here, BE, HBE, BEM, NBE, and MSE reproduce the exact results of the SWE while LBE and LQBE give the same approximation as QG. The accuracy of the models is typically in the order GV, GM, IM, HP, and QG, with GV most accurate and IM and HP sometimes less accurate than QG. Title: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part I: Formulation and Comparison of Exact Solutions Author: Barth, J. A., Allen, J. S., Newberger, P. A. Motivated by the general objective of pursuing oceanographic process and data assimilation studies of the complex, nonlinear eddy and jet current fields observed over the continental shelf and slope off the west coast of the United States, we investigate the use of intermediate models for that purpose. Intermediate models contain physics between that in the primitive equations and that in the quasigeostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope, while filtering out high-frequency gravity-inertial waves. As an initial step, we compare and evaluate several intermediate models applied to the f-plane shallow-water equations for flows over topography. The accuracy and utility of the intermediate models are assessed by a comparison of exact analytical and numerical solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG). The intermediate models that we consider are based on the geostrophic momentum (GM) approximation, the derivation of Salmon (1983) utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), the slow equations (SE) of Lynch (1989), and the modified slow equations (MSE). In Part I, we discuss the intermediate models and develop formulations that are suitable for numerical solution in physical coordinates for use in Parts II and III. We investigate the capability of the intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, and demonstrate that they do so with accuracy consistent with standard linear low-frequency approximations. We also assess the accuracy of the models by a comparison of exact nonlinear analytical solutions to the SWE for steady flow in an elliptic paraboloid and for unsteady motion of elliptical vortices in a circular paraboloid with corresponding analytical solutions to the intermediate models and to QG. General results from the exact solution comparisons include the following. Many of the intermediate models are capable of producing more accurate solutions than QG over a range of Rossby numbers 0 < ϵ < 1. In some cases, the intermediate models provide accurate approximate solutions where QG is not applicable and fails to give a relevant solution. Considerable parameter-dependent variation in quality exists, however, among the different intermediate models. For the particular problems considered here, BE, HBE, BEM, NBE, and MSE reproduce the exact results of the SWE while LBE and LQBE give the same approximation as QG. The accuracy of the models is typically in the order GV, GM, IM, HP, and QG, with GV most accurate and IM and HP sometimes less accurate than QG. Close

• 3. [Article] On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part II: Comparison of Numerical Model Solutions in Doubly Periodic Domains

  As part of a program to improve understanding of the dynamics of the complicated, vigorous eddy and jet flow fields recently observed over the continental shelf and slope, we investigate the potential ...

  Citation × Citation Citation Abstract Copy Title: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part II: Comparison of Numerical Model Solutions in Doubly Periodic Domains Author: Newberger, P. A., Allen, J. S., Barth, J. A. As part of a program to improve understanding of the dynamics of the complicated, vigorous eddy and jet flow fields recently observed over the continental shelf and slope, we investigate the potential of intermediate models for use in both process and data assimilation studies of these flows. Intermediate models incorporate physics simpler than that contained in the full primitive equations yet more complete than in the quasi-geostrophic equations, and are capable of representing subinertial flows over O(1) bottom topographic variations and/or with O(1) isopycnal slopes. In addition, intermediate models dynamically filter out high-frequency gravity- inertial motions leading, potentially, to higher computational efficiency and well-posed limited area forecast/hindcast models. Initial studies focus on single layer flows on an f-plane with a free surface, governed by the shallow-water equations. In Part I, various intermediate models are formulated and their accuracy assessed by comparing some exact nonlinear analytical solutions that exist for the shallow-water equations with corresponding analytical solutions of the intermediate models. Here in Part II, an extensive set of numerical finite-difference solutions to initial-value problems in doubly periodic domains (to isolate model differences from the influence of boundary condition implementation on solid walls) is used to determine the accuracy of various intermediate models by comparing their predictions with those of a shallow-water equation model that uses a potential enstrophy and energy conserving numerical scheme (SWE). Intermediate model results are also contrasted with those from a quasi-geostrophic (QG) model. The intermediate models considered are based on the geostrophic momentum (GM) approximation, the derivation of Salmon utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, a combination of the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), and on Lynch's slow equations in their original form (SE) and in a modified form (MSE). In addition, a semi-implicit version (SEMI) of the shallow-water equations, which numerically filters high-frequency motions, is included in the study. The basic initial-value problem used to test the various intermediate models involves sinusoidal flow over a symmetric Gaussian-shaped bottom topographic feature. Comparisons are made for a range of the relevant dimensionless model parameters including the strength of the flow (as measured by the Rossby number), the square of the ratio of a characteristic horizontal length scale to the Rossby radius of deformation, and the height of the topographic feature. A second initial-value problem involves the evolution of a rotating elliptical vortex over both flat and variable bottom topography. Results show that in cases with low local Rossby number flow, but with large topographic height, most of the intermediate models are substantially more accurate than QG. Even for flows with O(1) local Rossby numbers, some of the intermediate models continue to give excellent results. Specifically, BE, BEM and SEMI consistently do the best in the comparisons. Although the relative ordering of the remaining models is somewhat parameter-dependent, in general the next most accurate models are MSE and LQBE followed by HP and NBE. These are followed in quality by GV and GM while the remaining models, HBE, IM and LBE, perform least accurately for the range of parameters studied. Generally, intermediate models that have an integral invariant corresponding to conservation of potential enstrophy do better than those without, with the best results coming from models which have this property and a nonlinear balance equation. Title: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part II: Comparison of Numerical Model Solutions in Doubly Periodic Domains Author: Newberger, P. A., Allen, J. S., Barth, J. A. As part of a program to improve understanding of the dynamics of the complicated, vigorous eddy and jet flow fields recently observed over the continental shelf and slope, we investigate the potential of intermediate models for use in both process and data assimilation studies of these flows. Intermediate models incorporate physics simpler than that contained in the full primitive equations yet more complete than in the quasi-geostrophic equations, and are capable of representing subinertial flows over O(1) bottom topographic variations and/or with O(1) isopycnal slopes. In addition, intermediate models dynamically filter out high-frequency gravity- inertial motions leading, potentially, to higher computational efficiency and well-posed limited area forecast/hindcast models. Initial studies focus on single layer flows on an f-plane with a free surface, governed by the shallow-water equations. In Part I, various intermediate models are formulated and their accuracy assessed by comparing some exact nonlinear analytical solutions that exist for the shallow-water equations with corresponding analytical solutions of the intermediate models. Here in Part II, an extensive set of numerical finite-difference solutions to initial-value problems in doubly periodic domains (to isolate model differences from the influence of boundary condition implementation on solid walls) is used to determine the accuracy of various intermediate models by comparing their predictions with those of a shallow-water equation model that uses a potential enstrophy and energy conserving numerical scheme (SWE). Intermediate model results are also contrasted with those from a quasi-geostrophic (QG) model. The intermediate models considered are based on the geostrophic momentum (GM) approximation, the derivation of Salmon utilizing Hamilton's principle (HP), a geostrophic vorticity (GV) approximation, a combination of the quasi-geostrophic momentum and full continuity equations (IM), the linear balance equations (LBE), the balance equations (BE), the related balance-type (HBE, BEM, NBE) and modified linear balance equations (LQBE), and on Lynch's slow equations in their original form (SE) and in a modified form (MSE). In addition, a semi-implicit version (SEMI) of the shallow-water equations, which numerically filters high-frequency motions, is included in the study. The basic initial-value problem used to test the various intermediate models involves sinusoidal flow over a symmetric Gaussian-shaped bottom topographic feature. Comparisons are made for a range of the relevant dimensionless model parameters including the strength of the flow (as measured by the Rossby number), the square of the ratio of a characteristic horizontal length scale to the Rossby radius of deformation, and the height of the topographic feature. A second initial-value problem involves the evolution of a rotating elliptical vortex over both flat and variable bottom topography. Results show that in cases with low local Rossby number flow, but with large topographic height, most of the intermediate models are substantially more accurate than QG. Even for flows with O(1) local Rossby numbers, some of the intermediate models continue to give excellent results. Specifically, BE, BEM and SEMI consistently do the best in the comparisons. Although the relative ordering of the remaining models is somewhat parameter-dependent, in general the next most accurate models are MSE and LQBE followed by HP and NBE. These are followed in quality by GV and GM while the remaining models, HBE, IM and LBE, perform least accurately for the range of parameters studied. Generally, intermediate models that have an integral invariant corresponding to conservation of potential enstrophy do better than those without, with the best results coming from models which have this property and a nonlinear balance equation. Close

• 4. [Article] Upwelling Circulation on the Oregon Continental Shelf. Part I: Response to Idealized Forcing

  Time-dependent upwelling on the Oregon continental shelf is studied with a two-dimensional approximation, that is, spatial variations across-shelf and with depth, using the Blumberg–Mellor, finite-difference, ...

  Citation × Citation Citation Abstract Copy Title: Upwelling Circulation on the Oregon Continental Shelf. Part I: Response to Idealized Forcing Author: Newberger, P. A., Federiuk, J., Allen, J. S. Time-dependent upwelling on the Oregon continental shelf is studied with a two-dimensional approximation, that is, spatial variations across-shelf and with depth, using the Blumberg–Mellor, finite-difference, stratified, primitive equation model. The time-dependent response of a coastal ocean at rest to constant, upwelling favorable, wind stress is examined. Topography and stratification representative of the Oregon continental shelf are used for the basic case experiment. The wind stress forces offshore flow in a turbulent surface boundary layer. The compensating onshore flow below the surface layer accelerates an alongshore current in the form of a vertically and horizontally sheared coastal jet. Dense water is advected onshore and upward into the surface layer. An upwelling front characterized by relatively large horizontal gradients in density and alongshore velocity v is formed near the surface at the inshore edge of the coastal jet. Large vertical gradients in v and large values of turbulent kinetic energy are also found in the frontal region. Additional experiments show the dependence of the response flow field on the initial stratification and the shelf topography. Experiments with the vertical turbulent kinematic viscosity and diffusivity parameterized as constants or as functions of a local Richardson number show substantial dependence of the response flow field on the choice of turbulence submodel. Title: Upwelling Circulation on the Oregon Continental Shelf. Part I: Response to Idealized Forcing Author: Newberger, P. A., Federiuk, J., Allen, J. S. Time-dependent upwelling on the Oregon continental shelf is studied with a two-dimensional approximation, that is, spatial variations across-shelf and with depth, using the Blumberg–Mellor, finite-difference, stratified, primitive equation model. The time-dependent response of a coastal ocean at rest to constant, upwelling favorable, wind stress is examined. Topography and stratification representative of the Oregon continental shelf are used for the basic case experiment. The wind stress forces offshore flow in a turbulent surface boundary layer. The compensating onshore flow below the surface layer accelerates an alongshore current in the form of a vertically and horizontally sheared coastal jet. Dense water is advected onshore and upward into the surface layer. An upwelling front characterized by relatively large horizontal gradients in density and alongshore velocity v is formed near the surface at the inshore edge of the coastal jet. Large vertical gradients in v and large values of turbulent kinetic energy are also found in the frontal region. Additional experiments show the dependence of the response flow field on the initial stratification and the shelf topography. Experiments with the vertical turbulent kinematic viscosity and diffusivity parameterized as constants or as functions of a local Richardson number show substantial dependence of the response flow field on the choice of turbulence submodel. Close

• 5. [Article] Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part II: Modeling Flow over the Heceta Bank Complex on the Oregon Coast

  This study investigates wind-driven circulation in the vicinity of the Heceta Bank complex along the Oregon shelf. Numerical experiments forced with steady winds (0.1 Pa) are conducted; upwelling and downwelling ...

  Citation × Citation Citation Abstract Copy Title: Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part II: Modeling Flow over the Heceta Bank Complex on the Oregon Coast Author: Whitney, Michael M., Allen, J. S. This study investigates wind-driven circulation in the vicinity of the Heceta Bank complex along the Oregon shelf. Numerical experiments forced with steady winds (0.1 Pa) are conducted; upwelling and downwelling cases are compared. The asymmetric bank bathymetry is the only configurational difference from the symmetric bank runs analyzed in Part I (Whitney and Allen). Upwelling-favorable winds generate an upwelling front and southward baroclinic jet. Model results indicate the upwelling jet is centered on the 100-m isobath along the straight shelf. The jet follows this isobath offshore around the northern part of the bank but separates from sharply turning isobaths in the southern half and flows over deeper waters. The jet turns back toward the coast farther downstream. Inshore of the main jet, currents reverse and flow back onto the bank. These reversed currents turn southward again (at the bank center) and join a secondary southward coastal upwelling jet. This secondary coastal jet converges with the stronger main jet farther downstream. Upwelling is intense at the northern bank edge near the coast, where a dense water tongue is advected over the bank. Upwelling also is strong on the southern bank half where the flow turns and reverses. Other areas of the bank have reduced upwelling or even downwelling during upwelling-favorable winds. Downwelling-favorable winds drive a near-bottom density front and a northward jet. The slower downwelling jet flows along the 130-m isobath over the straight shelf. The jet departs from isobaths over the southern bank half and follows a straighter path over shallower waters. There are no reversed currents over the bank. The bank is an area of reduced downwelling. Some of the differences in the evolution of the current and density fields are linked to fundamental differences between the upwelling and downwelling regimes; these are anticipated by the symmetric bank results of Part I. Other differences arise because of the bank asymmetry and opposite flow directions over the bank. The lowest-order depth-averaged across-stream momentum balance remains geostrophic over the bank. Advection, ageostrophic pressure gradients, wind stress, and bottom stress all are important in the depth-averaged alongstream momentum balance over the Heceta Bank complex. Both across-shelf and alongshelf density advection are important. Barotropic potential vorticity is not conserved over the bank, but the tendency for relative vorticity changes and depth changes to partially counter each other influences the different paths of the upwelling and downwelling jets. There are several regions of active upwelling and downwelling over the bank. In these areas, vertical velocities at the top of the bottom boundary layer are linked to topographic upwelling and downwelling and Ekman pumping. There is considerable spatial variability in the currents, densities, and dynamics over the Heceta Bank complex. Title: Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part II: Modeling Flow over the Heceta Bank Complex on the Oregon Coast Author: Whitney, Michael M., Allen, J. S. This study investigates wind-driven circulation in the vicinity of the Heceta Bank complex along the Oregon shelf. Numerical experiments forced with steady winds (0.1 Pa) are conducted; upwelling and downwelling cases are compared. The asymmetric bank bathymetry is the only configurational difference from the symmetric bank runs analyzed in Part I (Whitney and Allen). Upwelling-favorable winds generate an upwelling front and southward baroclinic jet. Model results indicate the upwelling jet is centered on the 100-m isobath along the straight shelf. The jet follows this isobath offshore around the northern part of the bank but separates from sharply turning isobaths in the southern half and flows over deeper waters. The jet turns back toward the coast farther downstream. Inshore of the main jet, currents reverse and flow back onto the bank. These reversed currents turn southward again (at the bank center) and join a secondary southward coastal upwelling jet. This secondary coastal jet converges with the stronger main jet farther downstream. Upwelling is intense at the northern bank edge near the coast, where a dense water tongue is advected over the bank. Upwelling also is strong on the southern bank half where the flow turns and reverses. Other areas of the bank have reduced upwelling or even downwelling during upwelling-favorable winds. Downwelling-favorable winds drive a near-bottom density front and a northward jet. The slower downwelling jet flows along the 130-m isobath over the straight shelf. The jet departs from isobaths over the southern bank half and follows a straighter path over shallower waters. There are no reversed currents over the bank. The bank is an area of reduced downwelling. Some of the differences in the evolution of the current and density fields are linked to fundamental differences between the upwelling and downwelling regimes; these are anticipated by the symmetric bank results of Part I. Other differences arise because of the bank asymmetry and opposite flow directions over the bank. The lowest-order depth-averaged across-stream momentum balance remains geostrophic over the bank. Advection, ageostrophic pressure gradients, wind stress, and bottom stress all are important in the depth-averaged alongstream momentum balance over the Heceta Bank complex. Both across-shelf and alongshelf density advection are important. Barotropic potential vorticity is not conserved over the bank, but the tendency for relative vorticity changes and depth changes to partially counter each other influences the different paths of the upwelling and downwelling jets. There are several regions of active upwelling and downwelling over the bank. In these areas, vertical velocities at the top of the bottom boundary layer are linked to topographic upwelling and downwelling and Ekman pumping. There is considerable spatial variability in the currents, densities, and dynamics over the Heceta Bank complex. Close

• 6. [Article] Nonlinear shear instabilities of alongshore currents over barred beaches

  copyrighted by American Geophysical Union

  Citation × Citation Citation Abstract Copy Title: Nonlinear shear instabilities of alongshore currents over barred beaches Author: Newberger, P. A., Slinn, Donald N., Holman, Robert A., Allen, J. S. copyrighted by American Geophysical Union Title: Nonlinear shear instabilities of alongshore currents over barred beaches Author: Newberger, P. A., Slinn, Donald N., Holman, Robert A., Allen, J. S. copyrighted by American Geophysical Union Close

• 7. [Article] Alongshore current over variable beach topography

  copyrighted by American Geophysical Union

  Citation × Citation Citation Abstract Copy Title: Alongshore current over variable beach topography Author: Slinn, Donald N., Holman, Robert A., Allen, J. S. copyrighted by American Geophysical Union Title: Alongshore current over variable beach topography Author: Slinn, Donald N., Holman, Robert A., Allen, J. S. copyrighted by American Geophysical Union Close

• 8. [Article] On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part III: Comparison of Numerical Model Solutions in Periodic Channels

  The study of intermediate models for barotropic continental shelf and slope flow fields initiated in Parts I and II is continued. The objective is to investigate the possible use of intermediate models ...

  Citation × Citation Citation Abstract Copy Title: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part III: Comparison of Numerical Model Solutions in Periodic Channels Author: Newberger, P. A., Barth, J. A., Allen, J. S. The study of intermediate models for barotropic continental shelf and slope flow fields initiated in Parts I and II is continued. The objective is to investigate the possible use of intermediate models for process and data assimilation studies of nonlinear mesoscale eddy and jet current fields over the continental shelf and slope. Intermediate models contain physics between that in the primitive equations and that in the quasi-geostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope while filtering out high-frequency gravity–inertial waves. We concentrate on the application of intermediate models to the f-plane shallow-water equations. The accuracy of several intermediate models is evaluated here by a comparison of numerical finite-difference solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG) for flow in a periodic channel. The intermediate models that we consider are based on the balance equations (BE), the balance equations derived from momentum equations (BEM), the potential vorticity conserving linear balance equations (LQBE), the hybrid balance equations (HBE), the near balance equation (NBE), a geostrophic vorticity (GV) approximation, the geostrophic momentum (GM) approximation, and the quasi-geostrophic momentum and full continuity equations (IM). The periodic channel provides a basic geometry for the study of physical flow processes over the continental shelf and slope. Wall boundary conditions are formulated for the intermediate models and implemented in the numerical finite-difference approximations. The ability of intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, is verified by numerical experiments. The results of numerical solution intercomparisons for initial-value problems involving O(1) topographic variations are as follows. For flow at small local Rossby number |ϵ[subscript]L| < 0.2, where ϵ[subscript]L is given by the magnitude of the vorticity divided by f, all of the intermediate models do well, while the QG model does poorly. For flows with larger values of |ϵ[subscript]L|, e.g., |ϵ[subscript]L| ≈ 0.5, the performance of the different intermediate models varies. BEM and BE consistently give extremely accurate solutions while the solutions from LQBE are almost as good. The other models are substantially less accurate with errors generally increasing in the order NBE, HBE, GV, GM, IM. The QG solution always has the largest errors. Consistent with the results from the studies in Part II in a doubly periodic domain, the balance equations BE and BEM, followed closely by LQBE, appear to be the most accurate intermediate model Title: On Intermediate Models for Barotropic Continental Shelf and Slope Flow Fields. Part III: Comparison of Numerical Model Solutions in Periodic Channels Author: Newberger, P. A., Barth, J. A., Allen, J. S. The study of intermediate models for barotropic continental shelf and slope flow fields initiated in Parts I and II is continued. The objective is to investigate the possible use of intermediate models for process and data assimilation studies of nonlinear mesoscale eddy and jet current fields over the continental shelf and slope. Intermediate models contain physics between that in the primitive equations and that in the quasi-geostrophic equations and are capable of representing subinertial frequency motion over the O(1) topographic variations typical of the continental slope while filtering out high-frequency gravity–inertial waves. We concentrate on the application of intermediate models to the f-plane shallow-water equations. The accuracy of several intermediate models is evaluated here by a comparison of numerical finite-difference solutions with those of the primitive shallow-water equations (SWE) and with those of the quasi-geostrophic equations (QG) for flow in a periodic channel. The intermediate models that we consider are based on the balance equations (BE), the balance equations derived from momentum equations (BEM), the potential vorticity conserving linear balance equations (LQBE), the hybrid balance equations (HBE), the near balance equation (NBE), a geostrophic vorticity (GV) approximation, the geostrophic momentum (GM) approximation, and the quasi-geostrophic momentum and full continuity equations (IM). The periodic channel provides a basic geometry for the study of physical flow processes over the continental shelf and slope. Wall boundary conditions are formulated for the intermediate models and implemented in the numerical finite-difference approximations. The ability of intermediate models to represent linear ageostrophic coastally trapped waves, i.e., Kelvin and continental shelf waves, is verified by numerical experiments. The results of numerical solution intercomparisons for initial-value problems involving O(1) topographic variations are as follows. For flow at small local Rossby number |ϵ[subscript]L| < 0.2, where ϵ[subscript]L is given by the magnitude of the vorticity divided by f, all of the intermediate models do well, while the QG model does poorly. For flows with larger values of |ϵ[subscript]L|, e.g., |ϵ[subscript]L| ≈ 0.5, the performance of the different intermediate models varies. BEM and BE consistently give extremely accurate solutions while the solutions from LQBE are almost as good. The other models are substantially less accurate with errors generally increasing in the order NBE, HBE, GV, GM, IM. The QG solution always has the largest errors. Consistent with the results from the studies in Part II in a doubly periodic domain, the balance equations BE and BEM, followed closely by LQBE, appear to be the most accurate intermediate model Close

• 9. [Article] Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part I: Modeling Flow over Idealized Symmetric Banks

  This study examines how coastal banks influence wind-driven circulation along stratified continental shelves. Numerical experiments are conducted for idealized symmetric banks; the standard bank (200 km ...

  Citation × Citation Citation Abstract Copy Title: Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part I: Modeling Flow over Idealized Symmetric Banks Author: Whitney, Michael M., Allen, J. S. This study examines how coastal banks influence wind-driven circulation along stratified continental shelves. Numerical experiments are conducted for idealized symmetric banks; the standard bank (200 km long and 50 km wide) has dimensions similar to the Heceta Bank complex along the Oregon shelf. Model runs are forced with 10 days of steady winds (0.1 Pa); upwelling and downwelling cases are compared. The bank introduces significant alongshelf variability in the currents and density fields. Upwelling-favorable winds create an upwelling front and a baroclinic jet (flowing opposite coastal-trapped wave propagation) that bend around the standard bank, approximately centered on the 90-m isobath. The upwelling jet is strongest over the upstream bank half, where it advects a tongue of dense water over the bank. There is a current reversal shoreward of the main jet at the bank center. Upwelling is most intense over the upstream part of the bank, while there is reduced upwelling and even downwelling over other bank sections. Downwelling-favorable winds create a near-bottom density front and a baroclinic jet (flowing in the direction of coastal-trapped wave propagation) that bend around the standard bank; the jet core moves from the 150-m isobath to the 100-m isobath and back over the bank. The downwelling jet is slowest and widest over the bank; there are no current reversals. Results over the bank are more similar to 2D results (that preclude alongshelf variability) than in the upwelling case. Downwelling is weakened over the bank. The density field evolution over the bank is fundamentally different from the upwelling case. Most model results for banks with different dimensions are qualitatively similar to the standard run. The exceptions are banks having a radius of curvature smaller than the inertial radius; the main jet remains detached from the coast far downstream from these banks. The lowest-order across-stream momentum balance indicates that the depth-averaged flow is geostrophic. Advection, ageostrophic pressure gradients, wind stress, and bottom stress are all important in the depth-averaged alongstream momentum balance over the bank. There is considerable variability in alongstream momentum balances over different bank sections. Across-shelf and alongshelf advection both change the density field over the bank. Barotropic potential vorticity is not conserved, but the tendency for relative vorticity changes and depth changes to partially counter each other results in differences between the upwelling and downwelling jet paths over the bank. Only certain areas of the bank have significant vertical velocities. In these areas of active upwelling and downwelling, vertical velocities at the top of the bottom boundary layer are due to either the jet crossing isobaths or bottom Ekman pumping Title: Coastal Wind-Driven Circulation in the Vicinity of a Bank. Part I: Modeling Flow over Idealized Symmetric Banks Author: Whitney, Michael M., Allen, J. S. This study examines how coastal banks influence wind-driven circulation along stratified continental shelves. Numerical experiments are conducted for idealized symmetric banks; the standard bank (200 km long and 50 km wide) has dimensions similar to the Heceta Bank complex along the Oregon shelf. Model runs are forced with 10 days of steady winds (0.1 Pa); upwelling and downwelling cases are compared. The bank introduces significant alongshelf variability in the currents and density fields. Upwelling-favorable winds create an upwelling front and a baroclinic jet (flowing opposite coastal-trapped wave propagation) that bend around the standard bank, approximately centered on the 90-m isobath. The upwelling jet is strongest over the upstream bank half, where it advects a tongue of dense water over the bank. There is a current reversal shoreward of the main jet at the bank center. Upwelling is most intense over the upstream part of the bank, while there is reduced upwelling and even downwelling over other bank sections. Downwelling-favorable winds create a near-bottom density front and a baroclinic jet (flowing in the direction of coastal-trapped wave propagation) that bend around the standard bank; the jet core moves from the 150-m isobath to the 100-m isobath and back over the bank. The downwelling jet is slowest and widest over the bank; there are no current reversals. Results over the bank are more similar to 2D results (that preclude alongshelf variability) than in the upwelling case. Downwelling is weakened over the bank. The density field evolution over the bank is fundamentally different from the upwelling case. Most model results for banks with different dimensions are qualitatively similar to the standard run. The exceptions are banks having a radius of curvature smaller than the inertial radius; the main jet remains detached from the coast far downstream from these banks. The lowest-order across-stream momentum balance indicates that the depth-averaged flow is geostrophic. Advection, ageostrophic pressure gradients, wind stress, and bottom stress are all important in the depth-averaged alongstream momentum balance over the bank. There is considerable variability in alongstream momentum balances over different bank sections. Across-shelf and alongshelf advection both change the density field over the bank. Barotropic potential vorticity is not conserved, but the tendency for relative vorticity changes and depth changes to partially counter each other results in differences between the upwelling and downwelling jet paths over the bank. Only certain areas of the bank have significant vertical velocities. In these areas of active upwelling and downwelling, vertical velocities at the top of the bottom boundary layer are due to either the jet crossing isobaths or bottom Ekman pumping Close

• 10. [Article] Combined Effects of Wind-Driven Upwelling and Internal Tide on the Continental Shelf

  Internal tides on the continental shelf can be intermittent as a result of changing hydrographic conditions associated with wind-driven upwelling. In turn, the internal tide can affect transports associated ...

  Citation × Citation Citation Abstract Copy Title: Combined Effects of Wind-Driven Upwelling and Internal Tide on the Continental Shelf Author: Allen, J. S., Egbert, G. D., Kurapov, A. L. Internal tides on the continental shelf can be intermittent as a result of changing hydrographic conditions associated with wind-driven upwelling. In turn, the internal tide can affect transports associated with upwelling. To study these processes, simulations in an idealized, alongshore uniform setup are performed utilizing the hydrostatic Regional Ocean Modeling System (ROMS) with conditions corresponding, as closely as possible, to the central Oregon shelf. ‘‘Wind only’’ (WO), ‘‘tide only’’ (TO), and ‘‘tide and wind’’ (TW) solutions are compared, utilizing cases with constant upwelling-favorable wind stress as well as with timevariable observed stress. The tide is forced by applying cross-shore barotropic flow at the offshore boundary with intensity sufficient to generate an internal tide with horizontal velocity amplitudes near 0.15 m s21, corresponding to observed levels. The internal tide affects the subinertial circulation, mostly through the changes in the bottom boundary layer variability, resulting in a larger bottom stress and a weaker depthaveraged alongshore current in the TW case compared to WO. The spatial variability of the cross-shore and vertical volume transport is also affected. Divergence in the Reynolds stress associated with the baroclinic tidal flow contributes to the tidally averaged cross-shore momentum balance. Internal waves cause highfrequency variability in the turbulent kinetic energy in both the bottom and surface boundary layers, causing periodic restratification of the inner shelf in the area of the upwelling front. Increased vertical shear in the horizontal velocity resulting from the superposition of the upwelling jet and the internal tide results in intermittent patches of intensified turbulence in the mid–water column. Variability in stratification associated with upwelling can affect not only the propagation of the internal tide on the shelf, but also the barotropic-tobaroclinic energy conversion on the continental slope, in this case changing the classification of the slope from nearly critical to supercritical such that less barotropic tidal energy is converted to baroclinic and a larger fraction of the baroclinic energy is radiated into the open ocean. Title: Combined Effects of Wind-Driven Upwelling and Internal Tide on the Continental Shelf Author: Allen, J. S., Egbert, G. D., Kurapov, A. L. Internal tides on the continental shelf can be intermittent as a result of changing hydrographic conditions associated with wind-driven upwelling. In turn, the internal tide can affect transports associated with upwelling. To study these processes, simulations in an idealized, alongshore uniform setup are performed utilizing the hydrostatic Regional Ocean Modeling System (ROMS) with conditions corresponding, as closely as possible, to the central Oregon shelf. ‘‘Wind only’’ (WO), ‘‘tide only’’ (TO), and ‘‘tide and wind’’ (TW) solutions are compared, utilizing cases with constant upwelling-favorable wind stress as well as with timevariable observed stress. The tide is forced by applying cross-shore barotropic flow at the offshore boundary with intensity sufficient to generate an internal tide with horizontal velocity amplitudes near 0.15 m s21, corresponding to observed levels. The internal tide affects the subinertial circulation, mostly through the changes in the bottom boundary layer variability, resulting in a larger bottom stress and a weaker depthaveraged alongshore current in the TW case compared to WO. The spatial variability of the cross-shore and vertical volume transport is also affected. Divergence in the Reynolds stress associated with the baroclinic tidal flow contributes to the tidally averaged cross-shore momentum balance. Internal waves cause highfrequency variability in the turbulent kinetic energy in both the bottom and surface boundary layers, causing periodic restratification of the inner shelf in the area of the upwelling front. Increased vertical shear in the horizontal velocity resulting from the superposition of the upwelling jet and the internal tide results in intermittent patches of intensified turbulence in the mid–water column. Variability in stratification associated with upwelling can affect not only the propagation of the internal tide on the shelf, but also the barotropic-tobaroclinic energy conversion on the continental slope, in this case changing the classification of the slope from nearly critical to supercritical such that less barotropic tidal energy is converted to baroclinic and a larger fraction of the baroclinic energy is radiated into the open ocean. Close