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- Author or Editor: Dale,B. Haidvogel x
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Abstract
A sigma coordinate ocean circulation model is employed to study flow trapped to a tall seamount in a periodic f-plane channel. In Part I, errors arising from the pressure gradient formulation in the steep topography/strong stratification limit are examined. To illustrate the error properties, a linearized adiabatic version of the model is considered, both with and without forcing, and starting from a resting state with level isopycnals.
The systematic discretization errors from the horizontal pressure gradient terms are shown analytically to increase with steeper topography (relative to a fixed horizontal grid) and for stronger stratification (as measured by the Burger number). For an initially quiescent unforced ocean, the pressure gradient errors produce a spurious oscillating current that, at the end of 10 days, is approximately 1 cm s−1 in amplitude. The period of the spurious oscillation (about 0.5 days) is shown to be a consequence of the particular form of the pressure gradient terms in the sigma coordinate system.
With the addition of an alongchannel diurnal forcing, resonantly generated seamount-trapped waves are observed to form. Error levels in these solutions are less than those in the unforced cases; spurious time-mean currents are several orders of magnitude less in amplitude than the resonant propagating waves. However, numerical instability is encountered in a wider range of parameter space. The properties of these resonantly generated waves is explored in detail in Part II of this study.
Several new formulations of the pressure gradient terms are tested. Two of the formulations—constructed to have additional conservation properties relative to the traditional form of the pressure gradient terms (conservation of JEBAR and conservation of energy)—are found to have error properties generally similar to those of the traditional formulation. A corrected gradient algorithm, based upon vertical interpolation of the pressure field, has a dramatically reduced error level but a much more restrictive range of stable behavior.
Abstract
A sigma coordinate ocean circulation model is employed to study flow trapped to a tall seamount in a periodic f-plane channel. In Part I, errors arising from the pressure gradient formulation in the steep topography/strong stratification limit are examined. To illustrate the error properties, a linearized adiabatic version of the model is considered, both with and without forcing, and starting from a resting state with level isopycnals.
The systematic discretization errors from the horizontal pressure gradient terms are shown analytically to increase with steeper topography (relative to a fixed horizontal grid) and for stronger stratification (as measured by the Burger number). For an initially quiescent unforced ocean, the pressure gradient errors produce a spurious oscillating current that, at the end of 10 days, is approximately 1 cm s−1 in amplitude. The period of the spurious oscillation (about 0.5 days) is shown to be a consequence of the particular form of the pressure gradient terms in the sigma coordinate system.
With the addition of an alongchannel diurnal forcing, resonantly generated seamount-trapped waves are observed to form. Error levels in these solutions are less than those in the unforced cases; spurious time-mean currents are several orders of magnitude less in amplitude than the resonant propagating waves. However, numerical instability is encountered in a wider range of parameter space. The properties of these resonantly generated waves is explored in detail in Part II of this study.
Several new formulations of the pressure gradient terms are tested. Two of the formulations—constructed to have additional conservation properties relative to the traditional form of the pressure gradient terms (conservation of JEBAR and conservation of energy)—are found to have error properties generally similar to those of the traditional formulation. A corrected gradient algorithm, based upon vertical interpolation of the pressure field, has a dramatically reduced error level but a much more restrictive range of stable behavior.
Abstract
The hypothesis that variations in eddy diffusivity may account for some aspects of the observed distributions of oceanic scalars is examined by generating solutions to the diffusion equation with spatially variable and/or anisotropic eddy diffusivity. In particular, the solutions generated here demonstrate how a purely diffusive field, with variable and anisotropic diffusion, can itself generate tongue-like property distributions. Although tongues of various oceanic properties have often been interpreted as due primarily to advective effects, such interpretations must be viewed with caution when the gradients of eddy diffusivity are comparable to, or greater than, the local velocity field.
Abstract
The hypothesis that variations in eddy diffusivity may account for some aspects of the observed distributions of oceanic scalars is examined by generating solutions to the diffusion equation with spatially variable and/or anisotropic eddy diffusivity. In particular, the solutions generated here demonstrate how a purely diffusive field, with variable and anisotropic diffusion, can itself generate tongue-like property distributions. Although tongues of various oceanic properties have often been interpreted as due primarily to advective effects, such interpretations must be viewed with caution when the gradients of eddy diffusivity are comparable to, or greater than, the local velocity field.
Abstract
A high-resolution primitive equation numerical model is used to generate a poleward flow along a meridionally oriented eastern boundary slope/shelf system by imposing an along-coast density gradient as the forcing mechanism. Wind forcing is applied to the resulting quasi-steady current system, and the subinertial response is analyzed. Parallel experiments with no slope-poleward flow are conducted for comparison. Moderately strong upwelling- and downwelling-favorable, week-to-month-scale wind events modify the poleward flow but do not significantly change the density-driven current structure at the slope. The alongshore transport within the slope region is reduced by 0.2–0.3 Sv (from 1.2 Sv, where Sv ≡ 106 m3 s–1), under the influence of either downwelling or upwelling winds. Independent of the wind direction, the density-driven poleward flow always remains surface intensified. Wind-driven shelf currents develop with a considerable degree of independence from the slope-poleward circulation. On the shelf, the density field is modified by cross-shelf buoyancy advection within the boundary layers and by strong vertical mixing. The presence of the poleward flow over the slope constitutes an important factor in the behavior of the bottom boundary layer at the shelf break and for the patterns of cross-slope circulation.
Abstract
A high-resolution primitive equation numerical model is used to generate a poleward flow along a meridionally oriented eastern boundary slope/shelf system by imposing an along-coast density gradient as the forcing mechanism. Wind forcing is applied to the resulting quasi-steady current system, and the subinertial response is analyzed. Parallel experiments with no slope-poleward flow are conducted for comparison. Moderately strong upwelling- and downwelling-favorable, week-to-month-scale wind events modify the poleward flow but do not significantly change the density-driven current structure at the slope. The alongshore transport within the slope region is reduced by 0.2–0.3 Sv (from 1.2 Sv, where Sv ≡ 106 m3 s–1), under the influence of either downwelling or upwelling winds. Independent of the wind direction, the density-driven poleward flow always remains surface intensified. Wind-driven shelf currents develop with a considerable degree of independence from the slope-poleward circulation. On the shelf, the density field is modified by cross-shelf buoyancy advection within the boundary layers and by strong vertical mixing. The presence of the poleward flow over the slope constitutes an important factor in the behavior of the bottom boundary layer at the shelf break and for the patterns of cross-slope circulation.
Abstract
A three-dimensional lake model driven by wind stress and heat flux fields derived from an atmospheric model is applied to Lake Kinneret, Israel. The summer wind field over the lake has a strong diurnal and large spatial variation due to complex terrain surrounding the lake, the sharp temperature contrast between the arid land and the lake, and due to the penetration of the Mediterranean sea breeze (MSB) into the lake area. The daily mean wind curl field, which is predominantly determined by the penetration of the MSB, is responsible for the generation of three lake gyres. One of them dominates most of the lake and rotates counterclockwise. It is flanked to the north and to the south by two smaller ones that rotate clockwise. During the summer, the diurnal variation of the wind over the lake is repeated daily due to consistent forcing conditions during that season. Numerical tests show that the rectified flow induced by the diurnal winds plays a minor role in the lake circulation. The thermocline oscillation, which was believed to be the free propagation of internal Kelvin waves, mainly responds to the surface elevation set up by the time-dependent winds, and it appears that no systematic counterclockwise propagating waves with large thermocline displacements exist in the lake. The intense MSB over the lake in the late afternoon pushes the heated surface water toward the east, forcing the deep cooler water to be advected westward, and creating strong mixing over the shallow western shore. This results in higher temperature off the eastern shore and lower temperature off the western shore. However, a strong mean flow is constantly eliminating the temperature difference by counterclockwise transfer of the western cooler water eastward. The results are in good agreement with available observations.
Abstract
A three-dimensional lake model driven by wind stress and heat flux fields derived from an atmospheric model is applied to Lake Kinneret, Israel. The summer wind field over the lake has a strong diurnal and large spatial variation due to complex terrain surrounding the lake, the sharp temperature contrast between the arid land and the lake, and due to the penetration of the Mediterranean sea breeze (MSB) into the lake area. The daily mean wind curl field, which is predominantly determined by the penetration of the MSB, is responsible for the generation of three lake gyres. One of them dominates most of the lake and rotates counterclockwise. It is flanked to the north and to the south by two smaller ones that rotate clockwise. During the summer, the diurnal variation of the wind over the lake is repeated daily due to consistent forcing conditions during that season. Numerical tests show that the rectified flow induced by the diurnal winds plays a minor role in the lake circulation. The thermocline oscillation, which was believed to be the free propagation of internal Kelvin waves, mainly responds to the surface elevation set up by the time-dependent winds, and it appears that no systematic counterclockwise propagating waves with large thermocline displacements exist in the lake. The intense MSB over the lake in the late afternoon pushes the heated surface water toward the east, forcing the deep cooler water to be advected westward, and creating strong mixing over the shallow western shore. This results in higher temperature off the eastern shore and lower temperature off the western shore. However, a strong mean flow is constantly eliminating the temperature difference by counterclockwise transfer of the western cooler water eastward. The results are in good agreement with available observations.
Abstract
Numerical simulations of two-dimensional turbulence show that O(κ−1) and O(κ−4) energy spectra—described by Fox and Orszag (1973a) as enstrophy-equipartitioning and strongly dissipating turbulence, respectively—occur independently of the type of dissipation mechanism, and the inclusion of forcing and the β-effect. In both states the modal decorrelation rate η depends strongly upon wavenumber in accordance with the equations of a direct interaction approximation (Kraichnan, 1958), but in conflict with the hypothetical wavenumber independence of η in an enstrophy-caseading inertial similarity range. Implications for geophysical fluid dynamical modeling are discussed.
Abstract
Numerical simulations of two-dimensional turbulence show that O(κ−1) and O(κ−4) energy spectra—described by Fox and Orszag (1973a) as enstrophy-equipartitioning and strongly dissipating turbulence, respectively—occur independently of the type of dissipation mechanism, and the inclusion of forcing and the β-effect. In both states the modal decorrelation rate η depends strongly upon wavenumber in accordance with the equations of a direct interaction approximation (Kraichnan, 1958), but in conflict with the hypothetical wavenumber independence of η in an enstrophy-caseading inertial similarity range. Implications for geophysical fluid dynamical modeling are discussed.
Abstract
The vacillation of baroclinically unstable waves in a two-layer eddy-resolving oceanic circulation model is described. The vacillation cycle is distinguished kinematically by the mutual coexistence at equilibrium of short (60-day) period mesoscale eddies and a well-defined long (480-day) period modulation to the larger scale flow, as well as the long-term mean ocean circulation. Global energy budgets and related linear stability analyses reveal underlying systematic energy transfers between the slowly varying mean and transient fields of motion. The vacillation phenomenon is shown to occur over a rather narrow range of the nondimensional model parameters. Since the vacillation occurs in the presence of β, a highly structured mean flow field and meridional boundaries, this is perhaps the most complicated geophysical flow situation in which a vacillation cycle has been clearly observed.
Abstract
The vacillation of baroclinically unstable waves in a two-layer eddy-resolving oceanic circulation model is described. The vacillation cycle is distinguished kinematically by the mutual coexistence at equilibrium of short (60-day) period mesoscale eddies and a well-defined long (480-day) period modulation to the larger scale flow, as well as the long-term mean ocean circulation. Global energy budgets and related linear stability analyses reveal underlying systematic energy transfers between the slowly varying mean and transient fields of motion. The vacillation phenomenon is shown to occur over a rather narrow range of the nondimensional model parameters. Since the vacillation occurs in the presence of β, a highly structured mean flow field and meridional boundaries, this is perhaps the most complicated geophysical flow situation in which a vacillation cycle has been clearly observed.
Abstract
Statistically steady states consistent with a horizontally uniform time-averaged temperature gradient in a two-layer quasi-geostrophic model on a beta-plane are found by numerically integrating the equations for deviations from this mean state in a doubly periodic domain. Based on the result that the flow statistics are not strongly dependent on the size of the domain, it is suggested that this homogeneous flow is physically realizable. The dependence of the eddy heat and potential vorticity fluxes and eddy energy level on various model parameters (the beta effect, surface drag, small-scale horizontal mixing) is described. Implications for eddy flux parameterization theories am discussed.
Abstract
Statistically steady states consistent with a horizontally uniform time-averaged temperature gradient in a two-layer quasi-geostrophic model on a beta-plane are found by numerically integrating the equations for deviations from this mean state in a doubly periodic domain. Based on the result that the flow statistics are not strongly dependent on the size of the domain, it is suggested that this homogeneous flow is physically realizable. The dependence of the eddy heat and potential vorticity fluxes and eddy energy level on various model parameters (the beta effect, surface drag, small-scale horizontal mixing) is described. Implications for eddy flux parameterization theories am discussed.
Abstract
The low-frequency variability of the oceanic wind-driven circulation is investigated by use of a reduced-gravity, quasigeostrophic model with slight variations on the classic double-gyre wind forcing. Approximately 30 eddy-resolving simulations of 100–1000 years duration are analyzed to determine the types of low-frequency variability and to estimate statistical uncertainties in the results.
For parameters close to those leading to a stable antisymmetric solution, the system appears to have several preferred phenomenological regimes, each with distinct total energy levels. These states include a high-energy quasi-stable state; a low-energy, weakly penetrating state; and a state of intermediate energy and modest eddy/ring generation. The low-frequency variability of the model is strongly linked to the irregular transitions between these dynamical regimes.
For a central set of reference parameters, the behavior of the system is investigated for each period in which the total energy remains in certain ranges. The structure of the time-averaged streamfunction and eddy energy fields are observed to have remarkable repeatability from event to event for each state.
A parameter study documents the ways in which the probability distribution function of the total energy depends on the strength and asymmetry of the wind forcing field. As the parameters shift away from those leading to a steady antisymmetric solution, we find that increasing the asymmetry of the wind field or reducing the viscosity decreases the occurrences of the high-energy, quasi-stable state. The low-energy, weakly penetrating state is more robust and exists whenever there is both instability and a certain minimal asymmetry in the forcing. As the wind asymmetry is increased, the distributions shift smoothly (but rapidly) away from the higher-energy states, until only the low-energy state remains.
Abstract
The low-frequency variability of the oceanic wind-driven circulation is investigated by use of a reduced-gravity, quasigeostrophic model with slight variations on the classic double-gyre wind forcing. Approximately 30 eddy-resolving simulations of 100–1000 years duration are analyzed to determine the types of low-frequency variability and to estimate statistical uncertainties in the results.
For parameters close to those leading to a stable antisymmetric solution, the system appears to have several preferred phenomenological regimes, each with distinct total energy levels. These states include a high-energy quasi-stable state; a low-energy, weakly penetrating state; and a state of intermediate energy and modest eddy/ring generation. The low-frequency variability of the model is strongly linked to the irregular transitions between these dynamical regimes.
For a central set of reference parameters, the behavior of the system is investigated for each period in which the total energy remains in certain ranges. The structure of the time-averaged streamfunction and eddy energy fields are observed to have remarkable repeatability from event to event for each state.
A parameter study documents the ways in which the probability distribution function of the total energy depends on the strength and asymmetry of the wind forcing field. As the parameters shift away from those leading to a steady antisymmetric solution, we find that increasing the asymmetry of the wind field or reducing the viscosity decreases the occurrences of the high-energy, quasi-stable state. The low-energy, weakly penetrating state is more robust and exists whenever there is both instability and a certain minimal asymmetry in the forcing. As the wind asymmetry is increased, the distributions shift smoothly (but rapidly) away from the higher-energy states, until only the low-energy state remains.
Abstract
The stability of currents generated in an oceanic eddy-resolving general circulation model EGCM (Holland, 1978) is investigated by solving the eigenvalue problem associated with the finite-difference quasi-geostrophic vorticity equations which govern the flow. In general, both barotropically and baroclinically unstable waves are shown to exist for instantaneous currents found in the EGCM. Although these simulated flows are not always quasi-steady in the sense required by the theory and are themselves modified by the presence of the finite-amplitude eddies, many characteristics of the eddy field and its interaction with the time-mean circulation can nevertheless be deduced by the linear stability analysis.
In particular, these investigations show that linear stability considerations correctly identify regions of instability in the ocean circulation model and accurately predict the low-order statistical features of the eddy field such as wavelength, period and phase speed. The effects of weakly unstable regions which are masked by global diagnostic techniques can be studied with the local stability model. The linear stability analysis also predicts, with some success, higher order statistics such as the sign and structure of intra-eddy energy fluxes that are important indicators of the dynamics of the unstable regions.
Abstract
The stability of currents generated in an oceanic eddy-resolving general circulation model EGCM (Holland, 1978) is investigated by solving the eigenvalue problem associated with the finite-difference quasi-geostrophic vorticity equations which govern the flow. In general, both barotropically and baroclinically unstable waves are shown to exist for instantaneous currents found in the EGCM. Although these simulated flows are not always quasi-steady in the sense required by the theory and are themselves modified by the presence of the finite-amplitude eddies, many characteristics of the eddy field and its interaction with the time-mean circulation can nevertheless be deduced by the linear stability analysis.
In particular, these investigations show that linear stability considerations correctly identify regions of instability in the ocean circulation model and accurately predict the low-order statistical features of the eddy field such as wavelength, period and phase speed. The effects of weakly unstable regions which are masked by global diagnostic techniques can be studied with the local stability model. The linear stability analysis also predicts, with some success, higher order statistics such as the sign and structure of intra-eddy energy fluxes that are important indicators of the dynamics of the unstable regions.
