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- Author or Editor: Richard E. Thomson x
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Abstract
This paper describes the circulation, water properties and energetics of an observed cyclonic eddy that formed over the continental margin of Vancouver Island between late July and early September, 1980. The eddy was characterized by a depth scale of 1 km, a radius of 50 km and a maximum near-surface geostrophic flow of 50 cm s−1. Within the middepth core of the eddy, isopycnal surfaces were domed upward by 50 m and were comprised of relatively warm, saline and low dissolved oxygen water that appeared to originate with the California Undercurrent.
The eddy is shown to have been generated through dynamic instability of the seasonal mean flow along Vancouver Island. The appearance in late July of the undercurrent over the slope may have been an important factor in the amplification of the mesoscale meander that eventually deformed into the eddy. Calculation of each of the terms in the integrated energy balance reveals that both barotropic and baroclinic instability contributed to the amplification and that 87% of the energy flux from the mean to the perturbed flow occurred within the upper 150 m. The baroclinic source term alone accounted for 82% of the total energy flux within the upper 500 m of the water column. The measured change in the potential energy distribution and, to a lesser degree, the tilt of the perturbation streamlines with depth are consistent with generation of the eddy through the instability process. An estimate of 25 ± 8 days is obtained for the e-folding growth time of the instability.
Abstract
This paper describes the circulation, water properties and energetics of an observed cyclonic eddy that formed over the continental margin of Vancouver Island between late July and early September, 1980. The eddy was characterized by a depth scale of 1 km, a radius of 50 km and a maximum near-surface geostrophic flow of 50 cm s−1. Within the middepth core of the eddy, isopycnal surfaces were domed upward by 50 m and were comprised of relatively warm, saline and low dissolved oxygen water that appeared to originate with the California Undercurrent.
The eddy is shown to have been generated through dynamic instability of the seasonal mean flow along Vancouver Island. The appearance in late July of the undercurrent over the slope may have been an important factor in the amplification of the mesoscale meander that eventually deformed into the eddy. Calculation of each of the terms in the integrated energy balance reveals that both barotropic and baroclinic instability contributed to the amplification and that 87% of the energy flux from the mean to the perturbed flow occurred within the upper 150 m. The baroclinic source term alone accounted for 82% of the total energy flux within the upper 500 m of the water column. The measured change in the potential energy distribution and, to a lesser degree, the tilt of the perturbation streamlines with depth are consistent with generation of the eddy through the instability process. An estimate of 25 ± 8 days is obtained for the e-folding growth time of the instability.
Abstract
The Alaskan Stream boundary current south of the uniformly curving coastline formed by the Alaskan peninsula-Aleutian Island chain is examined analytically via steady, barotropic frictional theory. It is shown that, as a result of the changing zonal orientation of this boundary, there is an alteration in the characteristic vorticity balance in the current as it progresses westward from the Gulf of Alaska. Where the curving coastline becomes approximately zonal, this vorticity distribution is such that, unless the clockwise vorticity generated at the coast by the no-slip condition is balanced by a vorticity source external to the current, instabilities and separation of the Alaskan Stream from the coast will occur.
Abstract
The Alaskan Stream boundary current south of the uniformly curving coastline formed by the Alaskan peninsula-Aleutian Island chain is examined analytically via steady, barotropic frictional theory. It is shown that, as a result of the changing zonal orientation of this boundary, there is an alteration in the characteristic vorticity balance in the current as it progresses westward from the Gulf of Alaska. Where the curving coastline becomes approximately zonal, this vorticity distribution is such that, unless the clockwise vorticity generated at the coast by the no-slip condition is balanced by a vorticity source external to the current, instabilities and separation of the Alaskan Stream from the coast will occur.
Abstract
Cape St. James is an extensive triangular-shaped promontory located in a tidally energetic region at the southern tip of the Queen Charlotte Islands approximately 150 km off the mainland coast or British Columbia. Several years of oceanographic data collected in vicinity of the cape reveal a regional circulation characterized by a strong (0.50 m s−1) coastal current along the western continental margin and respective clockwise and counterclockwise rotating mesoscale baroclinic eddies to the west and south of the cape. The coastal current flows counter to the prevailing winds while the anticyclonic eddy to the west of the cape is a particularly intense feature that appears consistently in AVHRR imagery of the region. The structure of the mean flow, combined with the marked O(0.1 0 m s−1) low-frequency current variability at fortnightly and monthly tidal periods plus significant coherence at fortnightly periods between low-frequency currents and demodulated tidal flow, suggests that rectification of the strong diurnal and semidiurnal tidal currents is the principal cause of the residual circulation in the vicinity of the cape.
Results from an analytical model indicate that generation of the mean residual circulation is due primarily to the M2 tidal current constituent and that maximum countercurrent velocities occur over the inner portion of the continental shelf. The fortnightly modulation of the mean flow is effected by both diurnal and semidiurnal currents but with a tendency for semidiurnal contributions to dominate in regions of greatest counterflow. Generic depth-dependent numerical simulations for nondimensional frictional parameters typical of the region verify that the asymmetry in the observed location and intensity of the eddy field, together with the presence of the strong coastal countercurrent on the west side of the cape and a narrow jet to the south of the cape, are associated with tidal rectification. These models also suggest that residual vertical motion due to topographic lifting and Ekman suction are responsible for the observed tilting of the isopycnals and thereby the development of baroclinicity in the residual horizontal motion.
Abstract
Cape St. James is an extensive triangular-shaped promontory located in a tidally energetic region at the southern tip of the Queen Charlotte Islands approximately 150 km off the mainland coast or British Columbia. Several years of oceanographic data collected in vicinity of the cape reveal a regional circulation characterized by a strong (0.50 m s−1) coastal current along the western continental margin and respective clockwise and counterclockwise rotating mesoscale baroclinic eddies to the west and south of the cape. The coastal current flows counter to the prevailing winds while the anticyclonic eddy to the west of the cape is a particularly intense feature that appears consistently in AVHRR imagery of the region. The structure of the mean flow, combined with the marked O(0.1 0 m s−1) low-frequency current variability at fortnightly and monthly tidal periods plus significant coherence at fortnightly periods between low-frequency currents and demodulated tidal flow, suggests that rectification of the strong diurnal and semidiurnal tidal currents is the principal cause of the residual circulation in the vicinity of the cape.
Results from an analytical model indicate that generation of the mean residual circulation is due primarily to the M2 tidal current constituent and that maximum countercurrent velocities occur over the inner portion of the continental shelf. The fortnightly modulation of the mean flow is effected by both diurnal and semidiurnal currents but with a tendency for semidiurnal contributions to dominate in regions of greatest counterflow. Generic depth-dependent numerical simulations for nondimensional frictional parameters typical of the region verify that the asymmetry in the observed location and intensity of the eddy field, together with the presence of the strong coastal countercurrent on the west side of the cape and a narrow jet to the south of the cape, are associated with tidal rectification. These models also suggest that residual vertical motion due to topographic lifting and Ekman suction are responsible for the observed tilting of the isopycnals and thereby the development of baroclinicity in the residual horizontal motion.
Abstract
Linear analytical solutions for bottom-trapped subinertial oscillatory flow over simple ridge topographies in a stratified (two-layer) rotating fluid are presented. Results are compared to moored current meter observations of bottom-intensified motions over the Endeavour Segment of Juan de Fuca Ridge in the northeast Pacific. The solutions reproduce many of the observed features including preferential amplification of the clockwise rotary component of velocity over the ridge and increased velocity amplification with proximity to the ridge crest. For a given internal deformation radius, the degree of current amplification increases with increased bottom slope, ridge height, and oscillation frequency. Amplification decreases with increased width of the ridge relative to the deformation radius.
Abstract
Linear analytical solutions for bottom-trapped subinertial oscillatory flow over simple ridge topographies in a stratified (two-layer) rotating fluid are presented. Results are compared to moored current meter observations of bottom-intensified motions over the Endeavour Segment of Juan de Fuca Ridge in the northeast Pacific. The solutions reproduce many of the observed features including preferential amplification of the clockwise rotary component of velocity over the ridge and increased velocity amplification with proximity to the ridge crest. For a given internal deformation radius, the degree of current amplification increases with increased bottom slope, ridge height, and oscillation frequency. Amplification decreases with increased width of the ridge relative to the deformation radius.
Abstract
A solution for a concentrated line front translating at speed U is given. It is shown that the frequency is near-inertial if U≫c 1, where c 1 is the long internal wave speed of the first baroclinic mode. Each more has a charactristic frequency ω n associated with it. The spectra contain a near-inertial primary peak, composed of the higher modes, whose blue shift increases with depth. They also contain secondary peaks at higher internal wave frequencies if U is only slightly larger than c 1. The flow field is intermittent, and involves a continuous interchange of energy between the surface layer and the stratified interior. The dominant period of this intermittency is the beating period of the first mode with a purely inertial oscillation. Short periods of apparent subinertial motion are also generated. Several features of the solution are in agreement with observations.
Abstract
A solution for a concentrated line front translating at speed U is given. It is shown that the frequency is near-inertial if U≫c 1, where c 1 is the long internal wave speed of the first baroclinic mode. Each more has a charactristic frequency ω n associated with it. The spectra contain a near-inertial primary peak, composed of the higher modes, whose blue shift increases with depth. They also contain secondary peaks at higher internal wave frequencies if U is only slightly larger than c 1. The flow field is intermittent, and involves a continuous interchange of energy between the surface layer and the stratified interior. The dominant period of this intermittency is the beating period of the first mode with a purely inertial oscillation. Short periods of apparent subinertial motion are also generated. Several features of the solution are in agreement with observations.
Abstract
We derive expressions that predict the variations of Cartesian, rotary and elliptical properties of free and forced barotropic continental shelf waves as functions of alongshore and cross-shore location. Bottom friction is shown to significantly complicate these expressions. Particular attention is given to the spatial variability in the phases of forced waves as functions of the wavenumber of the forcing and the corresponding free wave mode. Consideration of the alongshore and across-shelf structure predicted by the theory indicates that, for a given frequency, the relative merits of Cartesian or rotary Fourier analysis of data depends on the location of the observation stations in the across shelf direction and on the geometry of the continental shelf and slope. The specific case of observed, diurnal period (K1) continental shelf waves off Vancouver Island is used to illustrate how the free and forced shelf wave models lead to different interpretations for the wavelengths of the free wave component. The results demonstrate the nontrivial nature of the forced problem and emphasize the need for accurate resolution of the wavenumber of the driving mechanism.
Abstract
We derive expressions that predict the variations of Cartesian, rotary and elliptical properties of free and forced barotropic continental shelf waves as functions of alongshore and cross-shore location. Bottom friction is shown to significantly complicate these expressions. Particular attention is given to the spatial variability in the phases of forced waves as functions of the wavenumber of the forcing and the corresponding free wave mode. Consideration of the alongshore and across-shelf structure predicted by the theory indicates that, for a given frequency, the relative merits of Cartesian or rotary Fourier analysis of data depends on the location of the observation stations in the across shelf direction and on the geometry of the continental shelf and slope. The specific case of observed, diurnal period (K1) continental shelf waves off Vancouver Island is used to illustrate how the free and forced shelf wave models lead to different interpretations for the wavelengths of the free wave component. The results demonstrate the nontrivial nature of the forced problem and emphasize the need for accurate resolution of the wavenumber of the driving mechanism.
Abstract
In tropical regions, and for applications where the alongshore scale k −1 of the forcing is large, the assumption of constant Coriolis parameters f in Csanady's Arrested Topographic Wave (ATW) model is invalid. Here we generalize the ATW model for study wind-driven coastal circulation by allowing f to vary according to the β-plane approximation f = 0 + βy, and by deriving solutions for finite width shelves. Bottom friction is assumed to be linear in the depth-averaged velocity with coefficient r and the depth h(x) = sx is assumed to increase linearly with distance x offshore. The generalization includes the ATW solutions as a subset; however, theoretical and numerical calculations show that the dimensionless parameter β/f 0 k plays a key role in the flow structure. In particular, for infinitely wide shelves and nonzero values of β/f 0 k, enhanced trapping occurs for coastal circulation off an east cost while trapped solutions cease to exist for circulation off a west coast. For finite width shelves, specification of zero sea level anomaly at the shelf break allows solutions for wind-driven circulation on both eat and west costs. Inclusion of the β effect results in a smaller trapping scale for coastal flows on east coasts (western ocean boundaries) and a larger trapping scale for coastal flows on west coasts. Asymptotic solutions for geographically varying wind stress with oscillatory form are presented as examples.
Abstract
In tropical regions, and for applications where the alongshore scale k −1 of the forcing is large, the assumption of constant Coriolis parameters f in Csanady's Arrested Topographic Wave (ATW) model is invalid. Here we generalize the ATW model for study wind-driven coastal circulation by allowing f to vary according to the β-plane approximation f = 0 + βy, and by deriving solutions for finite width shelves. Bottom friction is assumed to be linear in the depth-averaged velocity with coefficient r and the depth h(x) = sx is assumed to increase linearly with distance x offshore. The generalization includes the ATW solutions as a subset; however, theoretical and numerical calculations show that the dimensionless parameter β/f 0 k plays a key role in the flow structure. In particular, for infinitely wide shelves and nonzero values of β/f 0 k, enhanced trapping occurs for coastal circulation off an east cost while trapped solutions cease to exist for circulation off a west coast. For finite width shelves, specification of zero sea level anomaly at the shelf break allows solutions for wind-driven circulation on both eat and west costs. Inclusion of the β effect results in a smaller trapping scale for coastal flows on east coasts (western ocean boundaries) and a larger trapping scale for coastal flows on west coasts. Asymptotic solutions for geographically varying wind stress with oscillatory form are presented as examples.
Abstract
Current and sea level data from the Coastal Oceanic Dynamics Experiment conducted of Vancouver Island from May 1979 to September 1980 reveal shelf waves of diurnal period whose motions dominate the flow over the continental shelf. In this paper, current meter data from mooring lines off Brooks Peninsula, Estevan Point and Carmanah Point are compared with theoretical solutions for a combination of free shelf waves and barotropic Kelvin waves over uniform alongshore topography. Use of Brink's scheme for baroclinic shelf waves gives close agreement between the modeled and observed K1-period horizontal currents over the continental margin off central Vancouver Island and accurately predicts vertical velocities and sea levels. The shelf waves am shown to be entirely dominated by the first baroclinic mode. Wavelength derived from the model closely approximate wavelenghts computed from the alongshore change in phase of the observed diurnal current ellipses. The baroclinic model successfully predicts the longer wavelength off southern Vancouver Island and the shorter wavelength at K1 compared to O1 periods. The model's principal failure is its inability to account for the seasonal variation in observed wavelengths. Incorporation of a mean alongshore current with cross-shelf shear into a model for barotropic shelf waves suggests that this variation arises through Doppler shifting of the wave frequency.
A comparison with currents off Carmanah Point is less satisfactory presumably because of the proximity of the current meters to shallow banks and a canyon. Similarly, irregular bottom topography near Brooks Peninsula precludes meaningful comparisons.
Abstract
Current and sea level data from the Coastal Oceanic Dynamics Experiment conducted of Vancouver Island from May 1979 to September 1980 reveal shelf waves of diurnal period whose motions dominate the flow over the continental shelf. In this paper, current meter data from mooring lines off Brooks Peninsula, Estevan Point and Carmanah Point are compared with theoretical solutions for a combination of free shelf waves and barotropic Kelvin waves over uniform alongshore topography. Use of Brink's scheme for baroclinic shelf waves gives close agreement between the modeled and observed K1-period horizontal currents over the continental margin off central Vancouver Island and accurately predicts vertical velocities and sea levels. The shelf waves am shown to be entirely dominated by the first baroclinic mode. Wavelength derived from the model closely approximate wavelenghts computed from the alongshore change in phase of the observed diurnal current ellipses. The baroclinic model successfully predicts the longer wavelength off southern Vancouver Island and the shorter wavelength at K1 compared to O1 periods. The model's principal failure is its inability to account for the seasonal variation in observed wavelengths. Incorporation of a mean alongshore current with cross-shelf shear into a model for barotropic shelf waves suggests that this variation arises through Doppler shifting of the wave frequency.
A comparison with currents off Carmanah Point is less satisfactory presumably because of the proximity of the current meters to shallow banks and a canyon. Similarly, irregular bottom topography near Brooks Peninsula precludes meaningful comparisons.
Abstract
Continental shelf waves of diurnal period are shown to be generated by tidally induced Reynolds stresses within a bottom Stokes-scale boundary layer. The theory is applicable to a uniformly rotating, homogeneous ocean of two-dimensional depth variability in which alongshore variations occur over scales large compared to the shelf width. Explicit solutions are derived for the shelf wave velocity components and for the cross-shelf sea surface slope in the case of a traveling Kelvin wave forcing. Numerical values are presented for an exponential depth profile H = H0 exp(−2αx), where x is the coordinate normal to the coast. Results indicate that the amplitude of the shelf wave current can exceed that of the astronomical tidal current and that the alongshore component of the shelf wave current will consistently lead the alongshore component of the tidal current by 180° to 0° over one, wavelength in the direction of phase propagation.
Abstract
Continental shelf waves of diurnal period are shown to be generated by tidally induced Reynolds stresses within a bottom Stokes-scale boundary layer. The theory is applicable to a uniformly rotating, homogeneous ocean of two-dimensional depth variability in which alongshore variations occur over scales large compared to the shelf width. Explicit solutions are derived for the shelf wave velocity components and for the cross-shelf sea surface slope in the case of a traveling Kelvin wave forcing. Numerical values are presented for an exponential depth profile H = H0 exp(−2αx), where x is the coordinate normal to the coast. Results indicate that the amplitude of the shelf wave current can exceed that of the astronomical tidal current and that the alongshore component of the shelf wave current will consistently lead the alongshore component of the tidal current by 180° to 0° over one, wavelength in the direction of phase propagation.
Abstract
Tide, current and water property data collected in the western basin of Johnstone Strait, British Columbia, are compared with analytical models for M2 semidiurnal motions in a stratified, rotating channel of uniform depth. We show that, for a rectangular basin in which there is a depth-independent mean flow, the tidal fluctuations are readily expressible in terms of a landward (eastward) propagating Kelvin wave and exponentially damped, seaward (westward) propagating baroclinic Kelvin waves. The internal M2 tide appears to be generated through interaction of the surface tide with the shallow sill at the eastern end of the basin and is dominated by a first-mode baroclinic wave whose amplitude undergoes attenuation over an e-folding distance of one wavelength (∼26 km). Near the sill the baroclinic current speed may exceed 50% of the barotropic flow speed. The along-channel energy flux (power) of the barotropic tide is comparatively uniform at ∼1.4×109 W throughout the western portion of the Strait but decreases by a factor of 2 across the sill. Less than 0.3% of this power loss is needed to account for the baroclinic energy flux of ∼2×106 W near the sill; dissipation due to bottom friction is the main sink for the barotropic tidal energy. Attenuation of the baroclinic waves appears to result from a combination of turbulent horizontal friction and bottom boundary layer friction. Based on the first mode amplitudes, we find a horizontal eddy viscosity of ∼4×106 cm2 s−1 and a vertical eddy viscosity of ∼103 cm2 s−1. Our analysis further indicates that higher modes may be subject to attenuation by critical-layer absorption in the presence of the mean estuarine circulation in the basin. The M2 tides and currents are shown to possess considerable variability over periods of weeks and to have seasonal trends that, qualitatively at least, are related to changes in the mean density structure.
Abstract
Tide, current and water property data collected in the western basin of Johnstone Strait, British Columbia, are compared with analytical models for M2 semidiurnal motions in a stratified, rotating channel of uniform depth. We show that, for a rectangular basin in which there is a depth-independent mean flow, the tidal fluctuations are readily expressible in terms of a landward (eastward) propagating Kelvin wave and exponentially damped, seaward (westward) propagating baroclinic Kelvin waves. The internal M2 tide appears to be generated through interaction of the surface tide with the shallow sill at the eastern end of the basin and is dominated by a first-mode baroclinic wave whose amplitude undergoes attenuation over an e-folding distance of one wavelength (∼26 km). Near the sill the baroclinic current speed may exceed 50% of the barotropic flow speed. The along-channel energy flux (power) of the barotropic tide is comparatively uniform at ∼1.4×109 W throughout the western portion of the Strait but decreases by a factor of 2 across the sill. Less than 0.3% of this power loss is needed to account for the baroclinic energy flux of ∼2×106 W near the sill; dissipation due to bottom friction is the main sink for the barotropic tidal energy. Attenuation of the baroclinic waves appears to result from a combination of turbulent horizontal friction and bottom boundary layer friction. Based on the first mode amplitudes, we find a horizontal eddy viscosity of ∼4×106 cm2 s−1 and a vertical eddy viscosity of ∼103 cm2 s−1. Our analysis further indicates that higher modes may be subject to attenuation by critical-layer absorption in the presence of the mean estuarine circulation in the basin. The M2 tides and currents are shown to possess considerable variability over periods of weeks and to have seasonal trends that, qualitatively at least, are related to changes in the mean density structure.
