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Abstract
Recent altimetric observations of the ocean surface reveal signatures of long planetary waves near the annual frequency band. Comparisons of the observed wave speeds and those predicted by standard linear theory suggest that the latter is inadequate as it yields different westward speeds than those measured; in the extratropical latitudes the predicted speeds are typically slower than the observations. Here the problem of long, baroclinic wave propagation in a forced, stratified ocean is considered theoretically with a view toward explaining these observations of “too fast” planetary waves.
From a quasigeostrophic analysis, it is argued that baroclinic waves in a sheared environment are accelerated to the west via their interactions with both the mean advective field and the mean potential vorticity field. Conditions under which the ratio of actual to linear phase speeds matches the observed ratio are computed and found to be typical of the open ocean. Extensions of these ideas to continuously stratified quasigeostrophic and layered planetary geostrophic systems are discussed.
Abstract
Recent altimetric observations of the ocean surface reveal signatures of long planetary waves near the annual frequency band. Comparisons of the observed wave speeds and those predicted by standard linear theory suggest that the latter is inadequate as it yields different westward speeds than those measured; in the extratropical latitudes the predicted speeds are typically slower than the observations. Here the problem of long, baroclinic wave propagation in a forced, stratified ocean is considered theoretically with a view toward explaining these observations of “too fast” planetary waves.
From a quasigeostrophic analysis, it is argued that baroclinic waves in a sheared environment are accelerated to the west via their interactions with both the mean advective field and the mean potential vorticity field. Conditions under which the ratio of actual to linear phase speeds matches the observed ratio are computed and found to be typical of the open ocean. Extensions of these ideas to continuously stratified quasigeostrophic and layered planetary geostrophic systems are discussed.
Abstract
The migration of nonlinear frontal jets is examined using an inviscid “reduced gravity” model. Two cases are considered in detail. The first involves the drift of deep jets situated above a sloping bottom, and the second addresses the zonal β-induced migration of meridional jets in the upper ocean. Both kinds of jets are shallower on their left-hand side looking downstream (in the Northern Hemisphere). For the first case, exact nonlinear analytical solutions are derived, and for the second, two different methods are used to calculate the approximate migration speed.
It is found that deep oceanic jets migrate along isobaths (with the shallow ocean on their right-hand side) at a speed of g′S/f 0 (where g′ is the reduced gravity, S the slope of the bottom, and f 0 the Coriolis parameter). This speed is universal in the sense that all jets migrate at the same rate regardless of their details. By contrast, upper-ocean meridional jets on a β plane drift westward at a speed that depends on their structure. Specifically, it is shown that this drift is the average of the two long planetary wave speeds on either side of the front: namely, C = −β(R 2 d+ + R 2 d−)/2, where R d+(R d−) is the deformation radius based on the undisturbed depth east (west) of the jet; for frontal jets the above formula gives half the long Rossby wave speed.
Both kinds of drift occur even if the jets in question are slanted; that is, it is not necessary that the deep jets be directly oriented uphill (or downhill) or that the upper-ocean jets be oriented in the north–south direction. For the drifts to exist, it is sufficient that the deep jets have an uphill (or downhill) component and that the β-plane jets have a north–south component. Possible application of this theory to the jet observed during the Local Dynamic Experiment, which has been observed to drift westward, is discussed.
Abstract
The migration of nonlinear frontal jets is examined using an inviscid “reduced gravity” model. Two cases are considered in detail. The first involves the drift of deep jets situated above a sloping bottom, and the second addresses the zonal β-induced migration of meridional jets in the upper ocean. Both kinds of jets are shallower on their left-hand side looking downstream (in the Northern Hemisphere). For the first case, exact nonlinear analytical solutions are derived, and for the second, two different methods are used to calculate the approximate migration speed.
It is found that deep oceanic jets migrate along isobaths (with the shallow ocean on their right-hand side) at a speed of g′S/f 0 (where g′ is the reduced gravity, S the slope of the bottom, and f 0 the Coriolis parameter). This speed is universal in the sense that all jets migrate at the same rate regardless of their details. By contrast, upper-ocean meridional jets on a β plane drift westward at a speed that depends on their structure. Specifically, it is shown that this drift is the average of the two long planetary wave speeds on either side of the front: namely, C = −β(R 2 d+ + R 2 d−)/2, where R d+(R d−) is the deformation radius based on the undisturbed depth east (west) of the jet; for frontal jets the above formula gives half the long Rossby wave speed.
Both kinds of drift occur even if the jets in question are slanted; that is, it is not necessary that the deep jets be directly oriented uphill (or downhill) or that the upper-ocean jets be oriented in the north–south direction. For the drifts to exist, it is sufficient that the deep jets have an uphill (or downhill) component and that the β-plane jets have a north–south component. Possible application of this theory to the jet observed during the Local Dynamic Experiment, which has been observed to drift westward, is discussed.
Abstract
Mode waters are a distinctive baroclinic feature of the World Ocean characterized by relatively weak vertical stratification. They correspond dynamically to low potential vorticity (PV). In the North Atlantic subtropical gyre, the mode waters have become known as Eighteen Degree Water. Their dynamics involves air–sea interaction, diapycnal and isopycnal mixing, and subduction. Understanding mode water dynamics is therefore both challenging and important since it connects several aspects of the ocean circulation. Mass and PV budget of the mode water's core, evaluated in a realistic primitive equation North Atlantic model, are used to characterize mode water maintenance. It is shown that the surface PV flux has very little impact on mode water; the surface buoyancy flux in combination with eddy mass flux is the most important control on mode water structure. A mean PV formalism is used to show that the PV and water-mass formation budgets are intrinsically linked. A decomposition of the budget demonstrates the role of the mean PV field in permitting the eddy mass flux to discharge the net formation to the surrounding fluid.
Abstract
Mode waters are a distinctive baroclinic feature of the World Ocean characterized by relatively weak vertical stratification. They correspond dynamically to low potential vorticity (PV). In the North Atlantic subtropical gyre, the mode waters have become known as Eighteen Degree Water. Their dynamics involves air–sea interaction, diapycnal and isopycnal mixing, and subduction. Understanding mode water dynamics is therefore both challenging and important since it connects several aspects of the ocean circulation. Mass and PV budget of the mode water's core, evaluated in a realistic primitive equation North Atlantic model, are used to characterize mode water maintenance. It is shown that the surface PV flux has very little impact on mode water; the surface buoyancy flux in combination with eddy mass flux is the most important control on mode water structure. A mean PV formalism is used to show that the PV and water-mass formation budgets are intrinsically linked. A decomposition of the budget demonstrates the role of the mean PV field in permitting the eddy mass flux to discharge the net formation to the surrounding fluid.
Abstract
Surface sources and sinks of potential vorticity (PV) have been examined recently in various publications. These are normally identified as the mechanical and buoyant PV fluxes with the former scaled according to wind stress and the latter from buoyancy flux. The authors here examine a PV source that is often overlooked: namely, the diabatically forced source due to wind-driven deepening.
Based on an idealized model of the mixed layer, the rate of deepening of the mixed layer due to wind is translated into PV extraction. The authors propose the first-order scaling law 
Abstract
Surface sources and sinks of potential vorticity (PV) have been examined recently in various publications. These are normally identified as the mechanical and buoyant PV fluxes with the former scaled according to wind stress and the latter from buoyancy flux. The authors here examine a PV source that is often overlooked: namely, the diabatically forced source due to wind-driven deepening.
Based on an idealized model of the mixed layer, the rate of deepening of the mixed layer due to wind is translated into PV extraction. The authors propose the first-order scaling law
Abstract
It has been shown recently that the California Undercurrent (CUC), and possibly poleward eastern boundary currents in general, generate mixing events through centrifugal instability (CI). Conditions favorable for CI are created by the strong horizontal shears developed in turbulent bottom layers of currents flowing in the direction of topographic waves. At points of abrupt topographic change, like promontories and capes, the coastal current separates from the boundary and injects gravitationally stable but dynamically unstable flow into the interior. The resulting finite-amplitude development of the instability involves overturnings and diabatic mixing. The purpose of this study is to examine the energetics of CI in order to characterize it as has been done for other instabilities and develop a framework in which to estimate its regional and global impacts. This study argues that CI is very efficient at mixing and possibly approaches what is thought to be the maximum efficiency for turbulent flows. The authors estimate that 10% of the initial energy in a CUC-like current is lost to either local mixing or the generation of unbalanced flows. The latter probably leads to nonlocal mixing. Thus, centrifugal instability is an effective process by which energy is lost from the balanced flow and spent in mixing neighboring water masses. The mixing is regionally important but of less global significance given its regional specificity.
Abstract
It has been shown recently that the California Undercurrent (CUC), and possibly poleward eastern boundary currents in general, generate mixing events through centrifugal instability (CI). Conditions favorable for CI are created by the strong horizontal shears developed in turbulent bottom layers of currents flowing in the direction of topographic waves. At points of abrupt topographic change, like promontories and capes, the coastal current separates from the boundary and injects gravitationally stable but dynamically unstable flow into the interior. The resulting finite-amplitude development of the instability involves overturnings and diabatic mixing. The purpose of this study is to examine the energetics of CI in order to characterize it as has been done for other instabilities and develop a framework in which to estimate its regional and global impacts. This study argues that CI is very efficient at mixing and possibly approaches what is thought to be the maximum efficiency for turbulent flows. The authors estimate that 10% of the initial energy in a CUC-like current is lost to either local mixing or the generation of unbalanced flows. The latter probably leads to nonlocal mixing. Thus, centrifugal instability is an effective process by which energy is lost from the balanced flow and spent in mixing neighboring water masses. The mixing is regionally important but of less global significance given its regional specificity.
Abstract
A model of the marine atmospheric boundary layer is developed for ocean-only modeling in order to better represent air–sea exchanges. This model computes the evolution of the atmospheric boundary layer temperature and humidity using a prescribed wind field. These quantities react to the underlying ocean through turbulent and radiative fluxes. With two examples, the authors illustrate that this formulation is accurate for regional and global modeling purposes and that turbulent fluxes are well reproduced in test cases when compared to reanalysis products. The model builds upon and is an extension of Seager et al.
Abstract
A model of the marine atmospheric boundary layer is developed for ocean-only modeling in order to better represent air–sea exchanges. This model computes the evolution of the atmospheric boundary layer temperature and humidity using a prescribed wind field. These quantities react to the underlying ocean through turbulent and radiative fluxes. With two examples, the authors illustrate that this formulation is accurate for regional and global modeling purposes and that turbulent fluxes are well reproduced in test cases when compared to reanalysis products. The model builds upon and is an extension of Seager et al.
Abstract
This paper focuses on potential vorticity (PV) budgets in the North Atlantic with an emphasis on the wind-driven subtropical gyre. Since PV is the key dynamical variable of the wind-driven circulation, these budgets are important to understand. PV is a conservative quantity on isopycnals and can only enter or exit through the boundaries, like the lateral topography or the surface. The latter fluxes are diagnosed and tested against the evolution of the PV content in an isopycnal layer. The former are computed using the Bernoulli function. The essential result is found for all the tested isopycnals, and the dominant feature of PV is recirculation, with very little added at the surface or the boundaries. Density coordinates are well suited to understanding PV circulation. A novel technique for computing the Bernoulli function is proposed. The Bernoulli function is governed by a simple elliptic equation and the solutions demonstrate the dominant contribution of PV advection.
Abstract
This paper focuses on potential vorticity (PV) budgets in the North Atlantic with an emphasis on the wind-driven subtropical gyre. Since PV is the key dynamical variable of the wind-driven circulation, these budgets are important to understand. PV is a conservative quantity on isopycnals and can only enter or exit through the boundaries, like the lateral topography or the surface. The latter fluxes are diagnosed and tested against the evolution of the PV content in an isopycnal layer. The former are computed using the Bernoulli function. The essential result is found for all the tested isopycnals, and the dominant feature of PV is recirculation, with very little added at the surface or the boundaries. Density coordinates are well suited to understanding PV circulation. A novel technique for computing the Bernoulli function is proposed. The Bernoulli function is governed by a simple elliptic equation and the solutions demonstrate the dominant contribution of PV advection.
Abstract
An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model. In ventilated thermocline theory, the western pool is a region bounded on the east by subsurface streamlines that outcrop at the western edge of the interior, and in which additional dynamical assumptions are necessary to complete the solution. Solutions for the western pool were originally obtained under the assumption that the potential vorticity of the subsurface layer was homogenized. In the present theory, it is instead assumed that all of the water in the pool region is ventilated and, therefore, that all the Sverdrup transport is carried in the uppermost, outcropping layer. The result is the formation of a deep, vertically homogeneous, fluid layer in the northwest corner of the subtropical gyre that extends from the surface to the base of the ventilated thermocline. This ventilated pool is an analog of the observed subtropical mode waters. The pool also has the interesting properties that it determines its own boundaries and affects the global potential vorticity–pressure relationship. When there are multiple outcropping layers, ventilated pool fluid is subducted to form a set of nested annuli in ventilated, subsurface layers, which are the deepest subducted layers in the ventilated thermocline.
Abstract
An analytical model of subtropical mode water is presented, based on ventilated thermocline theory and on numerical solutions of a planetary geostrophic basin model. In ventilated thermocline theory, the western pool is a region bounded on the east by subsurface streamlines that outcrop at the western edge of the interior, and in which additional dynamical assumptions are necessary to complete the solution. Solutions for the western pool were originally obtained under the assumption that the potential vorticity of the subsurface layer was homogenized. In the present theory, it is instead assumed that all of the water in the pool region is ventilated and, therefore, that all the Sverdrup transport is carried in the uppermost, outcropping layer. The result is the formation of a deep, vertically homogeneous, fluid layer in the northwest corner of the subtropical gyre that extends from the surface to the base of the ventilated thermocline. This ventilated pool is an analog of the observed subtropical mode waters. The pool also has the interesting properties that it determines its own boundaries and affects the global potential vorticity–pressure relationship. When there are multiple outcropping layers, ventilated pool fluid is subducted to form a set of nested annuli in ventilated, subsurface layers, which are the deepest subducted layers in the ventilated thermocline.
Abstract
A regional numerical study of the California Current System near Monterey Bay, California, is conducted using both hydrostatic and nonhydrostatic models. Frequent sighting of strong anticyclones (Cuddies) have occurred in the area, and previous studies have identified Monterey Bay as an apparent region of strong unbalanced flow generation. Here, by means of a downscaling exercise, a domain just downstream of Point Sur is analyzed and argued to be a preferred site of diapycnal mixing. The scenario suggested by the simulations involves the generation of negative relative vorticity in a bottom boundary layer of the California Undercurrent on the continental shelf break. At Point Sur, the current separates from the coast and moves into deep waters where it rapidly develops finite-amplitude instabilities. These manifest as isopycnal overturnings, but in contrast to the normal Kelvin–Helmholtz paradigm for mixing, this study argues that the instability is primarily centrifugal. The evidence for this comes from comparisons of the model with linear results for ageostrophic instabilities. Mixing increases background potential energy. The authors argue the regional potential energy generation near Point Sur in the upper few hundred meters is comparable to that found in open-ocean regions of strong diapycnal mixing, either by abyssal tides and lee waves near topography. This study computes diapycnal fluxes and estimates turbulent diffusivities to argue mixing by centrifugal instability is characterized by diffusivities O(10−4) m2 s−1, although the potential for contamination by explicit diffusivities exists.
Abstract
A regional numerical study of the California Current System near Monterey Bay, California, is conducted using both hydrostatic and nonhydrostatic models. Frequent sighting of strong anticyclones (Cuddies) have occurred in the area, and previous studies have identified Monterey Bay as an apparent region of strong unbalanced flow generation. Here, by means of a downscaling exercise, a domain just downstream of Point Sur is analyzed and argued to be a preferred site of diapycnal mixing. The scenario suggested by the simulations involves the generation of negative relative vorticity in a bottom boundary layer of the California Undercurrent on the continental shelf break. At Point Sur, the current separates from the coast and moves into deep waters where it rapidly develops finite-amplitude instabilities. These manifest as isopycnal overturnings, but in contrast to the normal Kelvin–Helmholtz paradigm for mixing, this study argues that the instability is primarily centrifugal. The evidence for this comes from comparisons of the model with linear results for ageostrophic instabilities. Mixing increases background potential energy. The authors argue the regional potential energy generation near Point Sur in the upper few hundred meters is comparable to that found in open-ocean regions of strong diapycnal mixing, either by abyssal tides and lee waves near topography. This study computes diapycnal fluxes and estimates turbulent diffusivities to argue mixing by centrifugal instability is characterized by diffusivities O(10−4) m2 s−1, although the potential for contamination by explicit diffusivities exists.
Abstract
The equations of motion are reexamined with the objective of improving upon the Boussinesq approximation. The authors derive new equations that conserve energy, filter out sound waves, are more accurate than the Boussinesq set, and are computationally competitive with them. The new equations are partly enabled by exploiting a reversible exchange between internal and gravitational potential fluid energy. To improve upon these equations appears to require the inclusion of acoustics, at which point one should use full Navier–Stokes. This study recommends the new sets for testing in general circulation modeling.
Abstract
The equations of motion are reexamined with the objective of improving upon the Boussinesq approximation. The authors derive new equations that conserve energy, filter out sound waves, are more accurate than the Boussinesq set, and are computationally competitive with them. The new equations are partly enabled by exploiting a reversible exchange between internal and gravitational potential fluid energy. To improve upon these equations appears to require the inclusion of acoustics, at which point one should use full Navier–Stokes. This study recommends the new sets for testing in general circulation modeling.
