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- Author or Editor: K. J. Richards x
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Abstract
The effect of a depth-limited bottom boundary layer on the stability of a baroclinic zonal current is investigated. The model is of a two-layer quasi-geostrophic flow. Limiting the height of the boundary layer introduces a shear between the advection velocities within the boundary layer and the geostrophic flow above. This can induce a new type of instability, the unstable mode being a barotropic Rossby wave, a baroclinic Rossby wave or a bottom wave, or a mixture of all three. The system can be unstable outside the regions predicted by conventional inviscid baroclinic instability theory, in particular when there is zero shear in the mean zonal flow. The energy source for the growth of the disturbance is the kinetic energy of the mean zonal flow of the lower layer and this acts as a type of topographic drag on the mean flow. When applied to the ocean the theory gives an e-folding time of 3 months for this unstable mode.
Abstract
The effect of a depth-limited bottom boundary layer on the stability of a baroclinic zonal current is investigated. The model is of a two-layer quasi-geostrophic flow. Limiting the height of the boundary layer introduces a shear between the advection velocities within the boundary layer and the geostrophic flow above. This can induce a new type of instability, the unstable mode being a barotropic Rossby wave, a baroclinic Rossby wave or a bottom wave, or a mixture of all three. The system can be unstable outside the regions predicted by conventional inviscid baroclinic instability theory, in particular when there is zero shear in the mean zonal flow. The energy source for the growth of the disturbance is the kinetic energy of the mean zonal flow of the lower layer and this acts as a type of topographic drag on the mean flow. When applied to the ocean the theory gives an e-folding time of 3 months for this unstable mode.
Abstract
A second-order turbulence closure model is used to study the development of the benthic boundary layer. Results are presented on the effects of a time-dependent oscillatory forcing flow and an initially stably stratified density gradient. Using typical values for the deep ocean, the model suggests a development time for the layer of ∼10 days.
The results of the model show that for a neutrally stratified layer, although the flow is oscillating, the turbulence is essentially in local equilibrium and that an eddy viscosity approach is appropriate to determine the equilibrium boundary-layer height. The time development of the two models was however different. For an initially stratified case, although local shear production of turbulence is suppressed nest the top of the layer, diffusive effects enable the boundary layer to continue growing past a height set by a critical value of the Richardson number based on shear flow stability arguments.
Attempts to relate the growth rate of the boundary layer to the integral properties of the flow have not been totally successful and highlight the difficulties in doing so. They are, however, consistent with experimental results.
Abstract
A second-order turbulence closure model is used to study the development of the benthic boundary layer. Results are presented on the effects of a time-dependent oscillatory forcing flow and an initially stably stratified density gradient. Using typical values for the deep ocean, the model suggests a development time for the layer of ∼10 days.
The results of the model show that for a neutrally stratified layer, although the flow is oscillating, the turbulence is essentially in local equilibrium and that an eddy viscosity approach is appropriate to determine the equilibrium boundary-layer height. The time development of the two models was however different. For an initially stratified case, although local shear production of turbulence is suppressed nest the top of the layer, diffusive effects enable the boundary layer to continue growing past a height set by a critical value of the Richardson number based on shear flow stability arguments.
Attempts to relate the growth rate of the boundary layer to the integral properties of the flow have not been totally successful and highlight the difficulties in doing so. They are, however, consistent with experimental results.
Abstract
The interaction between a bottom mixed layer and a mesoscale eddy field is studied using a numerical model of a two-layer quasi-geostrophic fluid above a mixed layer. The height of the mixed layer is assumed to be restricted by stratification. A shear exists between the advection velocities within the mixed layer and the geostrophic flow above. The linear stability of such a system has been investigated by Richards. The present paper investigates nonlinear effects. The development of the instability discovered by Richards caused by the presence of the mixed layer, is found to be limited after 20 days by the overturning of the wave on the mixed layer-interior interface. For some nonlinear flows, however, there is a strong interaction between the mixed layer and the internal motions of the fluid. The differential advection of the structures on the mixed layer-interior interface can produce a negative topographic drag and transfer energy from the eddying motions into a mean flow. This enhances the β-effect and can drive zonal flows. Allowing mixing to take place between the mixed layer and interior fluid reduces this effect
The horizontal structure of the mixed layer is studied for various velocity and length scales of the mesoscale motions. Horizontal advection is found to play a dominant role in the dynamics of the bottom mixed layer making the use of one-dimensional models for the layer inappropriate unless an allowance for advection is made. A comparison of the model with observations made by Armi and D'Assaro of the horizontal structure of the bottom mixed layer suggests that some of the features they observe way be accounted for by forcing due to mesoscale eddies.
Abstract
The interaction between a bottom mixed layer and a mesoscale eddy field is studied using a numerical model of a two-layer quasi-geostrophic fluid above a mixed layer. The height of the mixed layer is assumed to be restricted by stratification. A shear exists between the advection velocities within the mixed layer and the geostrophic flow above. The linear stability of such a system has been investigated by Richards. The present paper investigates nonlinear effects. The development of the instability discovered by Richards caused by the presence of the mixed layer, is found to be limited after 20 days by the overturning of the wave on the mixed layer-interior interface. For some nonlinear flows, however, there is a strong interaction between the mixed layer and the internal motions of the fluid. The differential advection of the structures on the mixed layer-interior interface can produce a negative topographic drag and transfer energy from the eddying motions into a mean flow. This enhances the β-effect and can drive zonal flows. Allowing mixing to take place between the mixed layer and interior fluid reduces this effect
The horizontal structure of the mixed layer is studied for various velocity and length scales of the mesoscale motions. Horizontal advection is found to play a dominant role in the dynamics of the bottom mixed layer making the use of one-dimensional models for the layer inappropriate unless an allowance for advection is made. A comparison of the model with observations made by Armi and D'Assaro of the horizontal structure of the bottom mixed layer suggests that some of the features they observe way be accounted for by forcing due to mesoscale eddies.
Abstract
A theory for the observed interleaving of water masses at the equator is presented. Unlike layers at midlatitudes, individual layers are observed to be coherent over horizontal scales of hundreds of kilometers. To allow for the large horizontal scales, the theory extends previous linear stability analyses for double-diffusive interleaving to an equatorial β-plane. The poleward increase in the Coriolis parameter is found to limit the latitudinal extent of the layers. The latitudinal length scale [O(10 m)] together with the vertical scale [O(10 m)] given by the theory compare well with that observed.
Abstract
A theory for the observed interleaving of water masses at the equator is presented. Unlike layers at midlatitudes, individual layers are observed to be coherent over horizontal scales of hundreds of kilometers. To allow for the large horizontal scales, the theory extends previous linear stability analyses for double-diffusive interleaving to an equatorial β-plane. The poleward increase in the Coriolis parameter is found to limit the latitudinal extent of the layers. The latitudinal length scale [O(10 m)] together with the vertical scale [O(10 m)] given by the theory compare well with that observed.
Abstract
The jet structure of the Antarctic Circumpolar Current (ACC) simulated by two general circulation models (GCMs), FRAM (Fine Resolution Antarctic Model) and POP (Parallel Ocean Program), is examined in relation to the bottom topography field. Despite differences in configuration both GCMs display similar behavior: the model ACC consists of a number of distinct current cores superimposed on broader-scale flow. The jets display temporal and spatial (including vertical) coherence with maximum velocities occurring at the surface. It is shown that multiple jets can arise in wind-forced baroclinic quasigeostrophic flow. The main factors influencing the number and spacing of jets are found to be the bottom topography and the proximity of lateral boundaries. The meridional spacing of jets on a flat-bottomed β plane is consistent with the Rhines scaling criterion for barotropic β-plane turbulence with a small modification due to baroclinicity and the presence of meridional boundaries. When a zonally oriented ridge is present, the meridional spacing decreases. This is explained by postulating that the β effect is augmented by a factor related to the topographic slope. Smaller-scale roughness alters the magnitude of the mean flow and mass transport but does not necessarily alter the meridional scaling. The number and meridional spacing of multiple jets in FRAM are also found to be broadly consistent with this hypothesis, although other effects such as topographic steering may also be important. The POP model generally exhibits shorter length scales than would be expected from the topographically modified Rhines scaling alone, and it is likely that other factors are present.
Abstract
The jet structure of the Antarctic Circumpolar Current (ACC) simulated by two general circulation models (GCMs), FRAM (Fine Resolution Antarctic Model) and POP (Parallel Ocean Program), is examined in relation to the bottom topography field. Despite differences in configuration both GCMs display similar behavior: the model ACC consists of a number of distinct current cores superimposed on broader-scale flow. The jets display temporal and spatial (including vertical) coherence with maximum velocities occurring at the surface. It is shown that multiple jets can arise in wind-forced baroclinic quasigeostrophic flow. The main factors influencing the number and spacing of jets are found to be the bottom topography and the proximity of lateral boundaries. The meridional spacing of jets on a flat-bottomed β plane is consistent with the Rhines scaling criterion for barotropic β-plane turbulence with a small modification due to baroclinicity and the presence of meridional boundaries. When a zonally oriented ridge is present, the meridional spacing decreases. This is explained by postulating that the β effect is augmented by a factor related to the topographic slope. Smaller-scale roughness alters the magnitude of the mean flow and mass transport but does not necessarily alter the meridional scaling. The number and meridional spacing of multiple jets in FRAM are also found to be broadly consistent with this hypothesis, although other effects such as topographic steering may also be important. The POP model generally exhibits shorter length scales than would be expected from the topographically modified Rhines scaling alone, and it is likely that other factors are present.
Abstract
The dispersion of a tracer by a two-dimensional gyre circulation is studied using simple numerical models. Two approaches are taken: a random walk model formulated in a streamline coordinate system and the numerical solution of the advection-diffusion equation. A number of different gyres are considered. Attention is focused on the characteristics of the gyre that determine the spreading and mixing time of the tracer. The authors find that the dispersion by a given gyre can be characterized in terms of a bulk Péclet number and the three length scales: L the horizontal width of the gyre, l the width of the boundary current, and L the length of the boundary current. By taking into account the length of the boundary layer, gyre dispersion is found to conform moderately well with previous analytic models, in particular the partitioning between weak and strong diffusive regimes, even though the shear characteristics may be quite variable across the gyre. The analytic models become less valid as the length of the boundary layer increases. Simple expressions are given for the cross-streamline diffusion coefficient and mixing time in terms of the characteristics of the gyre. An important conclusion coming from the present study is the importance of the structure of the recirculation region in determining the shape of the tracer distribution. The results highlight the need for care in comparing model tracer fields with observed tracer distributions.
Abstract
The dispersion of a tracer by a two-dimensional gyre circulation is studied using simple numerical models. Two approaches are taken: a random walk model formulated in a streamline coordinate system and the numerical solution of the advection-diffusion equation. A number of different gyres are considered. Attention is focused on the characteristics of the gyre that determine the spreading and mixing time of the tracer. The authors find that the dispersion by a given gyre can be characterized in terms of a bulk Péclet number and the three length scales: L the horizontal width of the gyre, l the width of the boundary current, and L the length of the boundary current. By taking into account the length of the boundary layer, gyre dispersion is found to conform moderately well with previous analytic models, in particular the partitioning between weak and strong diffusive regimes, even though the shear characteristics may be quite variable across the gyre. The analytic models become less valid as the length of the boundary layer increases. Simple expressions are given for the cross-streamline diffusion coefficient and mixing time in terms of the characteristics of the gyre. An important conclusion coming from the present study is the importance of the structure of the recirculation region in determining the shape of the tracer distribution. The results highlight the need for care in comparing model tracer fields with observed tracer distributions.
Abstract
The dynamics of the Southern Ocean have been studied using two high-resolution models, namely the Fine Resolution Antarctic Model (FRAM) and the Parallel Ocean Program (POP) model. Analysis of these models includes zonal averaging at Drake Passage latitudes, averaging along streamlines (or contours of constant sea surface height), and examining particular subregions of the flow in some detail. The subregions considered in the local analysis capture different flow regimes in the vicinity of the Crozet Plateau, the Macquarie–Ridge Complex, and Drake Passage.
Many aspects of the model results are similar, for example, the magnitude of eddy kinetic energy (EKE) in the “eddy rich” regions associated with the large-scale topography. An important difference between the two models is that away from the strong topographic features the level of EKE in POP is 2–4 times greater than in FRAM, giving values close to those observed in altimeter studies.
In both FRAM and POP instability analysis performed over ACC jets showed that baroclinic instability is likely to be the main mechanism responsible for generating EKE. In the case of FRAM this view is confirmed by regional energy budgets made within the ACC. In contrast to quasigeostrophic numerical experiments upgradient transfer of momentum was not found in the whole ACC, or over large subregions of the Southern Ocean. The only place it occurred was in localized tight jets (e.g., the flow northeast of Drake Passage) where the transients are found to transfer kinetic energy into energy of the mean flow. The transient eddies result in a net deceleration of the ACC for the streamwise averaging.
Abstract
The dynamics of the Southern Ocean have been studied using two high-resolution models, namely the Fine Resolution Antarctic Model (FRAM) and the Parallel Ocean Program (POP) model. Analysis of these models includes zonal averaging at Drake Passage latitudes, averaging along streamlines (or contours of constant sea surface height), and examining particular subregions of the flow in some detail. The subregions considered in the local analysis capture different flow regimes in the vicinity of the Crozet Plateau, the Macquarie–Ridge Complex, and Drake Passage.
Many aspects of the model results are similar, for example, the magnitude of eddy kinetic energy (EKE) in the “eddy rich” regions associated with the large-scale topography. An important difference between the two models is that away from the strong topographic features the level of EKE in POP is 2–4 times greater than in FRAM, giving values close to those observed in altimeter studies.
In both FRAM and POP instability analysis performed over ACC jets showed that baroclinic instability is likely to be the main mechanism responsible for generating EKE. In the case of FRAM this view is confirmed by regional energy budgets made within the ACC. In contrast to quasigeostrophic numerical experiments upgradient transfer of momentum was not found in the whole ACC, or over large subregions of the Southern Ocean. The only place it occurred was in localized tight jets (e.g., the flow northeast of Drake Passage) where the transients are found to transfer kinetic energy into energy of the mean flow. The transient eddies result in a net deceleration of the ACC for the streamwise averaging.
Abstract
Along-stream variations in the dynamics of the Antarctic Circumpolar Current (ACC) impact heat and tracer transport, regulate interbasin exchange, and influence closure of the overturning circulation. Topography is primarily responsible for generating deviations from zonal-mean properties, mainly through standing meanders associated with regions of high eddy kinetic energy. Here, an idealized channel model is used to explore the spatial distribution of energy exchange and its relationship to eddy geometry, as characterized by both eddy momentum and eddy buoyancy fluxes. Variations in energy exchange properties occur not only between standing meander and quasi-zonal jet regions, but throughout the meander itself. Both barotropic and baroclinic stability properties, as well as the magnitude of energy exchange terms, undergo abrupt changes along the path of the ACC. These transitions are captured by diagnosing eddy fluxes of energy and by adopting the eddy geometry framework. The latter, typically applied to barotropic stability properties, is applied here in the depth–along-stream plane to include information about both barotropic and baroclinic stability properties of the flow. These simulations reveal that eddy momentum fluxes, and thus barotropic instability, play a leading role in the energy budget within a standing meander. This result suggests that baroclinic instability alone cannot capture the dynamics of ACC standing meanders, a challenge for models where eddy fluxes are parameterized.
Abstract
Along-stream variations in the dynamics of the Antarctic Circumpolar Current (ACC) impact heat and tracer transport, regulate interbasin exchange, and influence closure of the overturning circulation. Topography is primarily responsible for generating deviations from zonal-mean properties, mainly through standing meanders associated with regions of high eddy kinetic energy. Here, an idealized channel model is used to explore the spatial distribution of energy exchange and its relationship to eddy geometry, as characterized by both eddy momentum and eddy buoyancy fluxes. Variations in energy exchange properties occur not only between standing meander and quasi-zonal jet regions, but throughout the meander itself. Both barotropic and baroclinic stability properties, as well as the magnitude of energy exchange terms, undergo abrupt changes along the path of the ACC. These transitions are captured by diagnosing eddy fluxes of energy and by adopting the eddy geometry framework. The latter, typically applied to barotropic stability properties, is applied here in the depth–along-stream plane to include information about both barotropic and baroclinic stability properties of the flow. These simulations reveal that eddy momentum fluxes, and thus barotropic instability, play a leading role in the energy budget within a standing meander. This result suggests that baroclinic instability alone cannot capture the dynamics of ACC standing meanders, a challenge for models where eddy fluxes are parameterized.
Abstract
High levels of diapycnal mixing and geothermal heating near midocean ridges contribute to the buoyancy fluxes that are required to close the global circulation. In topographically confined areas, such as the deep median valleys of slow-spreading ridges, these fluxes strongly influence the local hydrography and dynamics. Data from a segment-scale hydrographic survey of the rift valley of the Mid-Atlantic Ridge and from an array of current meters deployed there during an entire year are analyzed in order to characterize the dominant hydrographic patterns and dynamical processes. Comparison with historic hydrographic data indicates that the temporal variability during the last few decades has been small compared to the observed segment-scale gradients. The rift valley circulation is characterized by inflow from the eastern ridge flank and persistent unidirectional along-segment flow into a cul-de-sac. Therefore, most of the water flowing along the rift valley upwells within the segment with a mean vertical velocity >10−5 m s−1. The observed streamwise hydrographic gradients indicate that diapycnal mixing dominates the rift valley buoyancy fluxes by more than an order of magnitude, in spite of the presence of a large hydrothermal vent field supplying several gigawatts of heat to the water column. Hydrographic budgets in the rift valley yield diffusivity values of order 5 × 10−3 m2 s−1, consistent with estimates derived from statically unstable overturns, the largest of which were observed downstream of topographic obstacles in the path of the along-segment flow. This suggests vertical shear associated with cross-sill flows as the dominant contributor to the mechanical mixing in the rift valley.
Abstract
High levels of diapycnal mixing and geothermal heating near midocean ridges contribute to the buoyancy fluxes that are required to close the global circulation. In topographically confined areas, such as the deep median valleys of slow-spreading ridges, these fluxes strongly influence the local hydrography and dynamics. Data from a segment-scale hydrographic survey of the rift valley of the Mid-Atlantic Ridge and from an array of current meters deployed there during an entire year are analyzed in order to characterize the dominant hydrographic patterns and dynamical processes. Comparison with historic hydrographic data indicates that the temporal variability during the last few decades has been small compared to the observed segment-scale gradients. The rift valley circulation is characterized by inflow from the eastern ridge flank and persistent unidirectional along-segment flow into a cul-de-sac. Therefore, most of the water flowing along the rift valley upwells within the segment with a mean vertical velocity >10−5 m s−1. The observed streamwise hydrographic gradients indicate that diapycnal mixing dominates the rift valley buoyancy fluxes by more than an order of magnitude, in spite of the presence of a large hydrothermal vent field supplying several gigawatts of heat to the water column. Hydrographic budgets in the rift valley yield diffusivity values of order 5 × 10−3 m2 s−1, consistent with estimates derived from statically unstable overturns, the largest of which were observed downstream of topographic obstacles in the path of the along-segment flow. This suggests vertical shear associated with cross-sill flows as the dominant contributor to the mechanical mixing in the rift valley.
