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- Author or Editor: William W. Hsieh x
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Abstract
Given equal amounts of kinetic energy near the coast, different shelf wave modes (at the same frequency) have different magnitudes of sea-level oscillations—the magnitudes decrease with increasing mode number. Hence, an intrinsic bias for the lowest mode is present when using sea-level data for shelf wave detection.
Shelf waves have many modal-dependent structures in their cross-shelf dimension, which can be used to accurately identify the excited modes in the current fluctuations. In addition to rotary spectral analysis, a new technique that involves fitting (at a particular frequency of interest) the theoretical current ellipses of various barotropic shelf wave modes to the observed current ellipses at stations spread across the continental shelf, is introduced. This technique shows how the current energy is distributed among the modes.
These techniques are illustrated using Oregon shelf data from the summer of 1973. The cross-shelf fitting shows that at frequencies below 0.45 cycles day−1, the current fluctuations on the Oregon shelf were completely dominated by the second mode. Furthermore, the observed alongshore phase speed also agreed very closely with the theoretical value for the second mode shelf wave. This is the clearest shelf wave identification achieved to date.
Abstract
Given equal amounts of kinetic energy near the coast, different shelf wave modes (at the same frequency) have different magnitudes of sea-level oscillations—the magnitudes decrease with increasing mode number. Hence, an intrinsic bias for the lowest mode is present when using sea-level data for shelf wave detection.
Shelf waves have many modal-dependent structures in their cross-shelf dimension, which can be used to accurately identify the excited modes in the current fluctuations. In addition to rotary spectral analysis, a new technique that involves fitting (at a particular frequency of interest) the theoretical current ellipses of various barotropic shelf wave modes to the observed current ellipses at stations spread across the continental shelf, is introduced. This technique shows how the current energy is distributed among the modes.
These techniques are illustrated using Oregon shelf data from the summer of 1973. The cross-shelf fitting shows that at frequencies below 0.45 cycles day−1, the current fluctuations on the Oregon shelf were completely dominated by the second mode. Furthermore, the observed alongshore phase speed also agreed very closely with the theoretical value for the second mode shelf wave. This is the clearest shelf wave identification achieved to date.
Abstract
The low-frequency current fluctuations on the Oregon shelf changed dramatically from winter to spring, 1975. A much faster offshore energy decay occurred simultaneously with a sharp decrease in the alongshore propagation speed. Cross-shelf analysis in a frequency band around 0.16 cpd showed the emergence of the third-mode shelf wave, in spring from the predominantly first-mode motion in winter. At frequencies <0.1 cpd, the current fluctuations propagated southward in winter, opposite to the direction of shelf waves.
On the Oregon and Washington shelves during summer (and early fall) 1972, the location of moorings on irregular topography rendered data interpretation difficult. Nevertheless, the general cross-shelf and alongshore properties of the current fluctuations were consistent with the first-mode shelf wave, in contrast to the situation during summer 1973 when the second mode was excited.
The excitation of relatively high modes and the generally sharp concentration of energy in one particular mode are surprising and difficult to explain with the present shelf-wave generation theories. Nonlinear resonance between wind and current is proposed as a possible explanation.
Abstract
The low-frequency current fluctuations on the Oregon shelf changed dramatically from winter to spring, 1975. A much faster offshore energy decay occurred simultaneously with a sharp decrease in the alongshore propagation speed. Cross-shelf analysis in a frequency band around 0.16 cpd showed the emergence of the third-mode shelf wave, in spring from the predominantly first-mode motion in winter. At frequencies <0.1 cpd, the current fluctuations propagated southward in winter, opposite to the direction of shelf waves.
On the Oregon and Washington shelves during summer (and early fall) 1972, the location of moorings on irregular topography rendered data interpretation difficult. Nevertheless, the general cross-shelf and alongshore properties of the current fluctuations were consistent with the first-mode shelf wave, in contrast to the situation during summer 1973 when the second mode was excited.
The excitation of relatively high modes and the generally sharp concentration of energy in one particular mode are surprising and difficult to explain with the present shelf-wave generation theories. Nonlinear resonance between wind and current is proposed as a possible explanation.
Abstract
From vertical normal mode decomposition, sea level and sea surface temperature (SST) are shown to be modally biased—higher modes are suppressed in sea level while lower modes are suppressed in SST data. Having been effectively “low passed” and “high passed” (with respect to mode number) by nature, sea level and SST contain complementary information which can in principle be combined to yield a relatively unbiased picture. The full potential of the sea level-SST pair is not appreciated in present remote sensing studies, where the two are used separately. A proposed “stereoscopic” method may in the future produce unbiased three-dimensional pictures from satellite-sensed two-dimensional pictures of sea level and SST. Modal bias in coastal trapped waves is studied in the Appendix.
Abstract
From vertical normal mode decomposition, sea level and sea surface temperature (SST) are shown to be modally biased—higher modes are suppressed in sea level while lower modes are suppressed in SST data. Having been effectively “low passed” and “high passed” (with respect to mode number) by nature, sea level and SST contain complementary information which can in principle be combined to yield a relatively unbiased picture. The full potential of the sea level-SST pair is not appreciated in present remote sensing studies, where the two are used separately. A proposed “stereoscopic” method may in the future produce unbiased three-dimensional pictures from satellite-sensed two-dimensional pictures of sea level and SST. Modal bias in coastal trapped waves is studied in the Appendix.
Abstract
No abstract available.
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No abstract available.
Abstract
The release of freshwater from a midlatitude estuary to the continental shelf is modeled numerically as a Rossby adjustment problem using a primitive equation model. As the initial salinity front is relaxed, a first baroclinic-mode Kelvin wave propagates into the estuary, while along the continental shelf, the disturbance travels in the direction of coastally trapped waves but with a relatively slow propagation speed.
When a submarine canyon extends offshore from the estuary, the joint effect of baroclinicity and bottom relief provides forcing for barotropic flow. The disturbance now propagates along the shelf at the first coastally trapped wave-mode phase speed, and the shelf circulation is significantly more energetic and barotropic than in the case without the canyon.
For both the experiments with and without a canyon an anticyclonic circulation, generated by the surface outflow and deeper inflow over changing bottom topography, is formed off the mouth of the estuary. As the deeper inflow encounters shallower depth, the column of fluid is vertically compressed, thereby spinning up anticyclonically due to the conservation of potential vorticity. This feature is in qualitative agreement with the Tully eddy observed off Juan de Fuca Strait.
A study of the reverse estuary (where the estuarine water is denser than the oceanic water) shows that this configuration has more potential energy available for conversion to kinetic energy than the normal estuary. Brass Strait may be considered as a possible reverse estuary for generating coastally trapped waves.
The effects of a wider shelf and a wider estuary are examined by two more experiments. For the wider shelf, the resulting baroclinic flow is similar to that of the other runs, although the barotropic flow is weaker. The wide estuary model proves to be the most dynamic of all, with the intensified anticyclonic circulation now extending well into the estuary.
Abstract
The release of freshwater from a midlatitude estuary to the continental shelf is modeled numerically as a Rossby adjustment problem using a primitive equation model. As the initial salinity front is relaxed, a first baroclinic-mode Kelvin wave propagates into the estuary, while along the continental shelf, the disturbance travels in the direction of coastally trapped waves but with a relatively slow propagation speed.
When a submarine canyon extends offshore from the estuary, the joint effect of baroclinicity and bottom relief provides forcing for barotropic flow. The disturbance now propagates along the shelf at the first coastally trapped wave-mode phase speed, and the shelf circulation is significantly more energetic and barotropic than in the case without the canyon.
For both the experiments with and without a canyon an anticyclonic circulation, generated by the surface outflow and deeper inflow over changing bottom topography, is formed off the mouth of the estuary. As the deeper inflow encounters shallower depth, the column of fluid is vertically compressed, thereby spinning up anticyclonically due to the conservation of potential vorticity. This feature is in qualitative agreement with the Tully eddy observed off Juan de Fuca Strait.
A study of the reverse estuary (where the estuarine water is denser than the oceanic water) shows that this configuration has more potential energy available for conversion to kinetic energy than the normal estuary. Brass Strait may be considered as a possible reverse estuary for generating coastally trapped waves.
The effects of a wider shelf and a wider estuary are examined by two more experiments. For the wider shelf, the resulting baroclinic flow is similar to that of the other runs, although the barotropic flow is weaker. The wide estuary model proves to be the most dynamic of all, with the intensified anticyclonic circulation now extending well into the estuary.
Abstract
The scattering of an incident shelf wave by a long thin offshore barrier located parallel to the coast is solved for a general monotonically increasing depth profile, using the unforced, inviscid barotropic shallow water equations under rigid lid and alongshore geostrophy approximation. In particular, simple analytic formulas for the scattering coefficients are derived for the exponential shelf profile. In the channel between the barrier and the coast, much of the incident shelf wave energy is transferred to the zero (or Kelvin) mode. Seaward of the barrier, substantial energy transfer from an incident second-mode shelf wave to the first mode is possible. Downstream from the barrier, the incident mode may vanish, leaving a different mode to dominate.
Abstract
The scattering of an incident shelf wave by a long thin offshore barrier located parallel to the coast is solved for a general monotonically increasing depth profile, using the unforced, inviscid barotropic shallow water equations under rigid lid and alongshore geostrophy approximation. In particular, simple analytic formulas for the scattering coefficients are derived for the exponential shelf profile. In the channel between the barrier and the coast, much of the incident shelf wave energy is transferred to the zero (or Kelvin) mode. Seaward of the barrier, substantial energy transfer from an incident second-mode shelf wave to the first mode is possible. Downstream from the barrier, the incident mode may vanish, leaving a different mode to dominate.
Abstract
Some numerical experiments On geostrophic adjustment in a gratified channel were carried out, partly to test the use of an ocean general circulation model (GCM), and partly to elucidate the dynamical effects of sloping bottom topography on the adjustment at different latitudes. Interesting dynamical effects include the release of potential energy through shelf waves, the nonlinear generation of barotropic flow by a baroclinic Kelvin wave and the nonlinear generation of shelf waves with approximately half the inertial frequency by internal Poincaré waves of near-inertial frequency. Problems that inevitably occur in the use of GCMs were also highlighted.
Abstract
Some numerical experiments On geostrophic adjustment in a gratified channel were carried out, partly to test the use of an ocean general circulation model (GCM), and partly to elucidate the dynamical effects of sloping bottom topography on the adjustment at different latitudes. Interesting dynamical effects include the release of potential energy through shelf waves, the nonlinear generation of barotropic flow by a baroclinic Kelvin wave and the nonlinear generation of shelf waves with approximately half the inertial frequency by internal Poincaré waves of near-inertial frequency. Problems that inevitably occur in the use of GCMs were also highlighted.
Abstract
From the inviscid, unforced, barotropic long-wave equations for a rotating system, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. While the shelf waves typically have periods of several days, the energy transfer has a time scale of order 12 days. Observational evidence of resonant shelf wave interactions on the Oregon shelf is found in the spectral analyses of Cutchin and Smith (1973) and Huyer et al. (1975), where their observed signals agree well with the resonant frequencies deduced from the theory. The good agreement between theory and observation suggests that nonlinear energy transfer may play a much more significant role in shelf wave dynamics than was previously realized.
Abstract
From the inviscid, unforced, barotropic long-wave equations for a rotating system, it is shown that resonant interactions between three continental shelf waves can occur. Evolution equations governing the amplitude and the energy of individual waves in a resonant triad are derived. The nonlinearity in the governing equations allows energy to be transferred between the waves, but with the total energy conserved. While the shelf waves typically have periods of several days, the energy transfer has a time scale of order 12 days. Observational evidence of resonant shelf wave interactions on the Oregon shelf is found in the spectral analyses of Cutchin and Smith (1973) and Huyer et al. (1975), where their observed signals agree well with the resonant frequencies deduced from the theory. The good agreement between theory and observation suggests that nonlinear energy transfer may play a much more significant role in shelf wave dynamics than was previously realized.
Abstract
The effects of viscosity and finite- differencing on free Kelvin waves in numerical models (which employ the Arakawa B- or C-grid difference schemes) are investigated using the f-plane shallow-water equations with offshore finite-difference grids, (assuming alongshore geostrophy). Three nondimensional parameters arise: Δ [=(offshore grid spacing)/(Rossby radius)], ε characterizes the offshore lateral viscous effect and α the combined vertical and alongshore viscous effect. This study is more relevant to baroclinic Kelvin waves which tend to suffer poor offshore resolution because of their small Rossby radii.
For inviscid models (ε = α = 0), as Δ increases (resolution worsens), the alongshore speed increases dramatically in the B-grid, but stays constant at the gravity wave speed in the C-grid. Models with damping only (α > 0, ε = 0) behave similarly. With lateral viscosity (ε > 0, α > 0), increasing ε decreases the speed in both the B- and C-grids—the drop in speed being less severe when the free-slip boundary condition is imposed instead of the no-slip one. As Δ increases, the speed declines in the B-grid, but in the C-grid, worsening resolution cancels the viscous slow-down, with speed rising to that when ε = 0.
Our theory predicts the alongshore phase speed, the temporal decay rate and the offshore structure for B- and C-grid models of given viscosity and grid-spacing and of given boundary conditions (e.g., no-slip or free-slip). The predictions are checked against observations from two- and three-dimensional model—including the Bryan-Cox model—with good agreement.
Abstract
The effects of viscosity and finite- differencing on free Kelvin waves in numerical models (which employ the Arakawa B- or C-grid difference schemes) are investigated using the f-plane shallow-water equations with offshore finite-difference grids, (assuming alongshore geostrophy). Three nondimensional parameters arise: Δ [=(offshore grid spacing)/(Rossby radius)], ε characterizes the offshore lateral viscous effect and α the combined vertical and alongshore viscous effect. This study is more relevant to baroclinic Kelvin waves which tend to suffer poor offshore resolution because of their small Rossby radii.
For inviscid models (ε = α = 0), as Δ increases (resolution worsens), the alongshore speed increases dramatically in the B-grid, but stays constant at the gravity wave speed in the C-grid. Models with damping only (α > 0, ε = 0) behave similarly. With lateral viscosity (ε > 0, α > 0), increasing ε decreases the speed in both the B- and C-grids—the drop in speed being less severe when the free-slip boundary condition is imposed instead of the no-slip one. As Δ increases, the speed declines in the B-grid, but in the C-grid, worsening resolution cancels the viscous slow-down, with speed rising to that when ε = 0.
Our theory predicts the alongshore phase speed, the temporal decay rate and the offshore structure for B- and C-grid models of given viscosity and grid-spacing and of given boundary conditions (e.g., no-slip or free-slip). The predictions are checked against observations from two- and three-dimensional model—including the Bryan-Cox model—with good agreement.
Abstract
Free Kelvin wave solutions of the linear shallow-water equations are described, for an f-plane. Lateral and vertical viscous effects are represented by terms ν∇2u and du, respectively, where (u,v) is the (onshore, longshore) velocity. Both no-slip and free-slip boundary conditions are considered.
When ν = 0 and d = 0, the lognshore phase speed decreases as longshore wavelength increases. Decay time is independent of wavelength, so the shorter waves are more efficient at sending information alongshore. For ν = 0 and d = 0, speed still decreases with increasing wavelength, but ht longer waves decay more slowly, and the longshore decay distance is now largest for long waves. Several examples are given.
The wave properties are much less dependent on ν when free-slip rather than no-slip conditions are used.
The onshore velocity is nonzero when ν > 0. This property is used to estimate ν = 103–104 m102 s−1, from previous observations of free baroclinic coastally-trapped waves off Peru.
Longshore geostrophy is a good approximation unless ν is large and wavelength is small. With longshore geostrophy wave properties can be found in terms of just two nondimensional parameters: ε, related to offshore viscous effects, and α, which combines vertical and alongshore viscous effects. Wave properties for a wide range of values of ε and α are given.
Effects of lateral and vertical diffusion can be added. With longshore geostrophy, the wave properties can be deduced by simply reinterpreting the parameter α.
Abstract
Free Kelvin wave solutions of the linear shallow-water equations are described, for an f-plane. Lateral and vertical viscous effects are represented by terms ν∇2u and du, respectively, where (u,v) is the (onshore, longshore) velocity. Both no-slip and free-slip boundary conditions are considered.
When ν = 0 and d = 0, the lognshore phase speed decreases as longshore wavelength increases. Decay time is independent of wavelength, so the shorter waves are more efficient at sending information alongshore. For ν = 0 and d = 0, speed still decreases with increasing wavelength, but ht longer waves decay more slowly, and the longshore decay distance is now largest for long waves. Several examples are given.
The wave properties are much less dependent on ν when free-slip rather than no-slip conditions are used.
The onshore velocity is nonzero when ν > 0. This property is used to estimate ν = 103–104 m102 s−1, from previous observations of free baroclinic coastally-trapped waves off Peru.
Longshore geostrophy is a good approximation unless ν is large and wavelength is small. With longshore geostrophy wave properties can be found in terms of just two nondimensional parameters: ε, related to offshore viscous effects, and α, which combines vertical and alongshore viscous effects. Wave properties for a wide range of values of ε and α are given.
Effects of lateral and vertical diffusion can be added. With longshore geostrophy, the wave properties can be deduced by simply reinterpreting the parameter α.
