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## Abstract

The Osborn-Cox model is a simplified tracer variance budget that is a basis for direct estimates of the diapycnal *K _{v}
*. diffusivity When used to interpret temperature variance dissipation measurements, it indicates

*K*to be O(10−5 m

_{v}^{2}s

^{−1}) in the thermocline–much smaller than the diffusivities found by matching large-scale observations to models or budgets. It is argued that, if the Osborn-Cox model is to describe fluxes in the general circulation, it must describe the variance budget of all fluctuations around the long-term average used to define the general circulation. Within this framework, the simplifications leading to the Osborn-Cox model are re-examined to find if they still hold and which is most likely to cause

*K*errors. Factors examined (and the importance found) are approximations in the Fourier and Ficks diffusion laws (unimportant), accumulation and advection of tracer variance (unimportant except in regions of strong upwelling), variance production by lateral fluxes (dominant at higher latitudes), sampling errors in estimating the mean tracer gradient (unimportant), and turbulent fluxes of variance 〈

_{v}**u**′θ′

^{2}〉. Variance production by lateral fluxes is most common where stratification is weak and causes the Osborn–Cox model to overestimate

*K*. The triple product, or turbulent flux of variance, represents potential exchanges of variance between the small turbulent scales and larger variability scales. It cannot be dismissed by scale analysis, and relying on the analogy or a hypothesis of scale isolation to neglect this effect makes the Osborn-Cox model a theory to be verified rather than a deduction.

_{v}## Abstract

The Osborn-Cox model is a simplified tracer variance budget that is a basis for direct estimates of the diapycnal *K _{v}
*. diffusivity When used to interpret temperature variance dissipation measurements, it indicates

*K*to be O(10−5 m

_{v}^{2}s

^{−1}) in the thermocline–much smaller than the diffusivities found by matching large-scale observations to models or budgets. It is argued that, if the Osborn-Cox model is to describe fluxes in the general circulation, it must describe the variance budget of all fluctuations around the long-term average used to define the general circulation. Within this framework, the simplifications leading to the Osborn-Cox model are re-examined to find if they still hold and which is most likely to cause

*K*errors. Factors examined (and the importance found) are approximations in the Fourier and Ficks diffusion laws (unimportant), accumulation and advection of tracer variance (unimportant except in regions of strong upwelling), variance production by lateral fluxes (dominant at higher latitudes), sampling errors in estimating the mean tracer gradient (unimportant), and turbulent fluxes of variance 〈

_{v}**u**′θ′

^{2}〉. Variance production by lateral fluxes is most common where stratification is weak and causes the Osborn–Cox model to overestimate

*K*. The triple product, or turbulent flux of variance, represents potential exchanges of variance between the small turbulent scales and larger variability scales. It cannot be dismissed by scale analysis, and relying on the analogy or a hypothesis of scale isolation to neglect this effect makes the Osborn-Cox model a theory to be verified rather than a deduction.

_{v}## Abstract

The Osborn–Cox model is the basis for the most direct estimates of the diapycnal diffusivity *K _{v}
* for tracers. When used to interpret temperature variance dissipation measurements, it leads to

*K*of O (10

_{v}^{−5}m

^{2}s

^{−1}) or less in the main thermocline. Large-scale diagnostic models typically match observations best using

*K*of O (10

_{v}^{−4}m

^{2}s

^{−1}). The framework for describing diapycnal fluxes of tracers like temperature or density from large-scale property distributions is reexamined in an attempt to discover possible causes for this disagreement. Starting from basic thermodynamics principles, suitable tracer conservation equations are developed and the simplifications leading to conventional mean-field and variance balances are examined. It is argued that separation of mean and eddy fields is best based on long but finite time averages rather than the usual space-scale separation. Because this separation leads to a more vigorous eddy field than the usual procedure it is necessary to reexamine all conventional simplifications. The usual approximate descriptions of molecular transport are found adequate. Direct effects of molecular fluxes are important only in the density equation where they lead to a density source that cannot be expressed as a flux divergence. Observed large-scale time changes of temperature and salinity are so large that inferring diapycnal diffusivities of O (10

^{−5}m

^{2}s

^{−1}) is difficult even from multilayer averages. On horizontal scales of hundreds of kilometers, lateral eddy fluxes of heat and salt are so large that it is nearly impossible to accurately determine a

*K*of O (10

_{v}^{−5}m

^{2}s

^{−1}) from local potential temperature or salt budgets. The density source is comparable to the divergence of turbulent density fluxes and confuses inference of

*K*from potential density budgets. This source also causes the velocity field to be slightly divergent, confusing inference of vertical velocity from observations of horizontal flow.

_{v}## Abstract

The Osborn–Cox model is the basis for the most direct estimates of the diapycnal diffusivity *K _{v}
* for tracers. When used to interpret temperature variance dissipation measurements, it leads to

*K*of O (10

_{v}^{−5}m

^{2}s

^{−1}) or less in the main thermocline. Large-scale diagnostic models typically match observations best using

*K*of O (10

_{v}^{−4}m

^{2}s

^{−1}). The framework for describing diapycnal fluxes of tracers like temperature or density from large-scale property distributions is reexamined in an attempt to discover possible causes for this disagreement. Starting from basic thermodynamics principles, suitable tracer conservation equations are developed and the simplifications leading to conventional mean-field and variance balances are examined. It is argued that separation of mean and eddy fields is best based on long but finite time averages rather than the usual space-scale separation. Because this separation leads to a more vigorous eddy field than the usual procedure it is necessary to reexamine all conventional simplifications. The usual approximate descriptions of molecular transport are found adequate. Direct effects of molecular fluxes are important only in the density equation where they lead to a density source that cannot be expressed as a flux divergence. Observed large-scale time changes of temperature and salinity are so large that inferring diapycnal diffusivities of O (10

^{−5}m

^{2}s

^{−1}) is difficult even from multilayer averages. On horizontal scales of hundreds of kilometers, lateral eddy fluxes of heat and salt are so large that it is nearly impossible to accurately determine a

*K*of O (10

_{v}^{−5}m

^{2}s

^{−1}) from local potential temperature or salt budgets. The density source is comparable to the divergence of turbulent density fluxes and confuses inference of

*K*from potential density budgets. This source also causes the velocity field to be slightly divergent, confusing inference of vertical velocity from observations of horizontal flow.

_{v}## Abstract

Recently it has been argued that in many regions of the ocean the Osborn–Cox model accurately determines the total long-term diapycnal flux of a tracer θ if the mean gradient and dissipation in the model are long-time averages. The mean gradient is easily determined, but averaging the scalar dissipation χ = 2κ|∇θ′|^{2} is notoriously difficult because of its highly intermittent distribution. The distribution of χ has long been known to be approximately lognormal, and Baker and Gibson suggest estimating (χ) by fitting observations to a lognormal probability distribution. There are four reasons why this does not apply to the observations needed to find long-term averages of χ. First, the theoretical arguments for the lognormal distribution apply to dissipation under a single set of local macroscopic factors (shear, stability, etc.) and low-frequency modulation of macroscopic factors is likely to cause slow changes of the parameters of the local lognormal distribution, leading to a different distribution for the total variability. Second, it is |∇θ| that is most apt to be lognormal, whereas measurements are usually of a single gradient component θ_{z}0; if |∇θ| is lognormal and isotropic. then |θ_{z}| is not lognormal. Third, correcting for instrumental response often requires that spatial averages of the squared gradient be processed and averages of lognormal variables are not lognormal. Finally, even if |∇θ′| were lognormal, very small errors in the estimated mean gradient would upset the distribution. Examination of these departures from lognormality and their effect on estimating (χ) indicates that methods based on knowing the form of the sampling distribution are dangerous. The procedure of fitting χ observations to a lognormal distribution can give quite erroneous results. For this reason direct arithmetic averaging appears to be the best analysis procedure. Similar considerations apply to sampling kinetic energy dissipation ε = 2ν∇u:∇u although it is more difficult to show that ε should have a lognormal distribution or to relate the distribution of total dissipation to that of shears measured.

## Abstract

Recently it has been argued that in many regions of the ocean the Osborn–Cox model accurately determines the total long-term diapycnal flux of a tracer θ if the mean gradient and dissipation in the model are long-time averages. The mean gradient is easily determined, but averaging the scalar dissipation χ = 2κ|∇θ′|^{2} is notoriously difficult because of its highly intermittent distribution. The distribution of χ has long been known to be approximately lognormal, and Baker and Gibson suggest estimating (χ) by fitting observations to a lognormal probability distribution. There are four reasons why this does not apply to the observations needed to find long-term averages of χ. First, the theoretical arguments for the lognormal distribution apply to dissipation under a single set of local macroscopic factors (shear, stability, etc.) and low-frequency modulation of macroscopic factors is likely to cause slow changes of the parameters of the local lognormal distribution, leading to a different distribution for the total variability. Second, it is |∇θ| that is most apt to be lognormal, whereas measurements are usually of a single gradient component θ_{z}0; if |∇θ| is lognormal and isotropic. then |θ_{z}| is not lognormal. Third, correcting for instrumental response often requires that spatial averages of the squared gradient be processed and averages of lognormal variables are not lognormal. Finally, even if |∇θ′| were lognormal, very small errors in the estimated mean gradient would upset the distribution. Examination of these departures from lognormality and their effect on estimating (χ) indicates that methods based on knowing the form of the sampling distribution are dangerous. The procedure of fitting χ observations to a lognormal distribution can give quite erroneous results. For this reason direct arithmetic averaging appears to be the best analysis procedure. Similar considerations apply to sampling kinetic energy dissipation ε = 2ν∇u:∇u although it is more difficult to show that ε should have a lognormal distribution or to relate the distribution of total dissipation to that of shears measured.

## Abstract

Nonseasonal variability of sea level pressure (SLP) and sea surface temperature (SST) in the mid-latitude North Pacific Ocean is examined. The objective is examination of the basic scales of the variability and determination of possible causal connections which might allow prediction of short-term climatic (time scales between a month and a year) variability.

Using empirical orthogonal function descriptions of the spatial structure, it is found that SLP variability is concentrated in a few large-scale modes but has a nearly white frequency spectrum. SST variability is spatially complex (being spread over many spatial modes, some of which have small-scale changes) but is dominated by low-frequency changes.

The use of linear statistical estimators to examine predictability is discussed and the importance of limiting the number of candidate data used in a correlation starch is underscored. Using linear statistical predictors, it is found that (A) SST anomalies can be predicted from SST observations several months in advance with measurable skill, (B) the anomalous SLP variability can be specified from simultaneous SST data with significant skill, thus showing the fields are related, and (C) future SLP anomalous variability cannot be predicted from SST data although previous SLP can be specified. The fact that previous SLP variability is better specified by SST data than is simultaneous SLP variability, coupled with a complete inability to predict future SLP anomalies, suggests that, in the region studied and on the time scales of a month to a year, the observed connection between SST and SLP variabilities is the result of the atmosphere driving the ocean.

## Abstract

Nonseasonal variability of sea level pressure (SLP) and sea surface temperature (SST) in the mid-latitude North Pacific Ocean is examined. The objective is examination of the basic scales of the variability and determination of possible causal connections which might allow prediction of short-term climatic (time scales between a month and a year) variability.

Using empirical orthogonal function descriptions of the spatial structure, it is found that SLP variability is concentrated in a few large-scale modes but has a nearly white frequency spectrum. SST variability is spatially complex (being spread over many spatial modes, some of which have small-scale changes) but is dominated by low-frequency changes.

The use of linear statistical estimators to examine predictability is discussed and the importance of limiting the number of candidate data used in a correlation starch is underscored. Using linear statistical predictors, it is found that (A) SST anomalies can be predicted from SST observations several months in advance with measurable skill, (B) the anomalous SLP variability can be specified from simultaneous SST data with significant skill, thus showing the fields are related, and (C) future SLP anomalous variability cannot be predicted from SST data although previous SLP can be specified. The fact that previous SLP variability is better specified by SST data than is simultaneous SLP variability, coupled with a complete inability to predict future SLP anomalies, suggests that, in the region studied and on the time scales of a month to a year, the observed connection between SST and SLP variabilities is the result of the atmosphere driving the ocean.

## Abstract

The relationships between sea surface temperature (SST) and sea level pressure (SLP) anomalies over the North Pacific are examined using seasonally stratified statistics. These indicate that autumn and winter SLP anomalies are predictable from prior observations of either SST or SLP. The relationships are a strong function of season and therefore are not detectable in statistics generated by averaging over all seasons. Neither spring nor summer SLP anomalies appear predictable. The patterns of predictable SLP anomalies and the SST and SLP anomalies from which they can be predicted are found as principal estimator patterns. Statistical predictors of autumn and winter SLP anomalies, developed on a 20-year dependent data set, are found to be useful in forecasting a period of 10 other years.

## Abstract

The relationships between sea surface temperature (SST) and sea level pressure (SLP) anomalies over the North Pacific are examined using seasonally stratified statistics. These indicate that autumn and winter SLP anomalies are predictable from prior observations of either SST or SLP. The relationships are a strong function of season and therefore are not detectable in statistics generated by averaging over all seasons. Neither spring nor summer SLP anomalies appear predictable. The patterns of predictable SLP anomalies and the SST and SLP anomalies from which they can be predicted are found as principal estimator patterns. Statistical predictors of autumn and winter SLP anomalies, developed on a 20-year dependent data set, are found to be useful in forecasting a period of 10 other years.

## Abstract

As part of the World Ocean Circulation Experiment, 306 autonomous floats were deployed in the tropical and South Pacific Ocean and 228 were deployed in the Indian Ocean to observe the basinwide circulation near 900-m depth. Mean velocities, seasonal variability, and lateral eddy diffusivity from the resultant 2583 float-years of data are presented. Area averages, local function fits, and a novel application of objective mapping are used to estimate the mean circulation. Patterns of mean circulation resemble those at the surface in both basins. Well-developed subtropical gyres, twice as strong in the Indian Ocean as in the Pacific, feed western boundary currents. Tropical gyres are separated by eastward flow along the equator in both hemispheres of both basins, although the Indian subcontinent splits the north Indian tropical gyre. The Antarctic Circumpolar Current (ACC) and west wind drifts are prominent in both basins, generally tending slightly southward but deviating to the north behind the Del Cano, Kerguelen, and Campbell Plateaus and, of course, South America. Remarkably, the eastern boundaries of the southern subtropical gyres in all three basins apparently occur in the ocean interior, away from land. The Indian Ocean’s subtropical gyre, and perhaps part of the South Atlantic’s, reaches east to a retroflection just upstream of the Campbell Plateau south of New Zealand. Seasonal variability at 900 m is focused around the equator with weaker variability found near certain bathymetric features. There is a remarkable agreement between the observed seasonable variability and that predicted by the Jet Propulsion Laboratory (JPL)–Estimating the Circulation and Climate of the Ocean (ECCO) data-assimilating numerical model. Aside from seasonal effects, eddy variability is greatest along the equator, in tropical and subtropical western basins, and along the ACC. Integrals of velocity across regional passages (Tasman Sea, Mozambique Channel) provide useful reference for hydrographic analyses of transport. Across whole ocean basins, however, the uncertainty associated with the appropriate continuity relation for horizontal flow (e.g., geostrophy vs nondivergence) is comparable to the mean flow.

## Abstract

As part of the World Ocean Circulation Experiment, 306 autonomous floats were deployed in the tropical and South Pacific Ocean and 228 were deployed in the Indian Ocean to observe the basinwide circulation near 900-m depth. Mean velocities, seasonal variability, and lateral eddy diffusivity from the resultant 2583 float-years of data are presented. Area averages, local function fits, and a novel application of objective mapping are used to estimate the mean circulation. Patterns of mean circulation resemble those at the surface in both basins. Well-developed subtropical gyres, twice as strong in the Indian Ocean as in the Pacific, feed western boundary currents. Tropical gyres are separated by eastward flow along the equator in both hemispheres of both basins, although the Indian subcontinent splits the north Indian tropical gyre. The Antarctic Circumpolar Current (ACC) and west wind drifts are prominent in both basins, generally tending slightly southward but deviating to the north behind the Del Cano, Kerguelen, and Campbell Plateaus and, of course, South America. Remarkably, the eastern boundaries of the southern subtropical gyres in all three basins apparently occur in the ocean interior, away from land. The Indian Ocean’s subtropical gyre, and perhaps part of the South Atlantic’s, reaches east to a retroflection just upstream of the Campbell Plateau south of New Zealand. Seasonal variability at 900 m is focused around the equator with weaker variability found near certain bathymetric features. There is a remarkable agreement between the observed seasonable variability and that predicted by the Jet Propulsion Laboratory (JPL)–Estimating the Circulation and Climate of the Ocean (ECCO) data-assimilating numerical model. Aside from seasonal effects, eddy variability is greatest along the equator, in tropical and subtropical western basins, and along the ACC. Integrals of velocity across regional passages (Tasman Sea, Mozambique Channel) provide useful reference for hydrographic analyses of transport. Across whole ocean basins, however, the uncertainty associated with the appropriate continuity relation for horizontal flow (e.g., geostrophy vs nondivergence) is comparable to the mean flow.

## Abstract

Neutral-buoyancy vehicles demand high-density energy sources and lithium is light with high oxidation energy. PolyPlus Battery Company has developed a prototype lithium-seawater battery that is attractive for powering long-duration autonomous oceanographic vehicles (floats and underwater gliders). These batteries were tested in the laboratory and at sea.

PolyPlus batteries use “Protected Lithium Electrodes” with proprietary “windows” protecting the volatile lithium anode from water while passing lithium ions. The cathode reduces oxygen dissolved in seawater, or hydrolyzes seawater to produce hydrogen. Not requiring additional electrolyte, fuel, or pressure cases, these cells have impressive weight advantages. Good electrode–seawater mass transfer is required but can increase drag and be impeded by biofouling.

Tests assessing robustness of the PolyPlus batteries in oceanographic use, evaluating mass transfer issues, and observing biofouling impacts are reported. In sea trials, two cells were tested for 69 days mounted on a Spray glider. Findings are as follows: 1) the cells were robust over 900 dives, most to 400 m; 2) without antifouling measures, the cells became substantially biofouled, but their performance was undiminished; and 3) performance was complex, depending on current density, oxygen concentration, and flow conditions. For dissolved oxygen concentration above 1 mL L^{−1}, the cells delivered 9 W m^{−2} of electrode surface at 3 V. For low oxygen, the cell shifted to hydrolysis near 2.3 V, but mass transfer was less critical so current density could be increased and observed power reached 5 W m^{−2}. This could be increased using a lower resistance load.

## Abstract

Neutral-buoyancy vehicles demand high-density energy sources and lithium is light with high oxidation energy. PolyPlus Battery Company has developed a prototype lithium-seawater battery that is attractive for powering long-duration autonomous oceanographic vehicles (floats and underwater gliders). These batteries were tested in the laboratory and at sea.

PolyPlus batteries use “Protected Lithium Electrodes” with proprietary “windows” protecting the volatile lithium anode from water while passing lithium ions. The cathode reduces oxygen dissolved in seawater, or hydrolyzes seawater to produce hydrogen. Not requiring additional electrolyte, fuel, or pressure cases, these cells have impressive weight advantages. Good electrode–seawater mass transfer is required but can increase drag and be impeded by biofouling.

Tests assessing robustness of the PolyPlus batteries in oceanographic use, evaluating mass transfer issues, and observing biofouling impacts are reported. In sea trials, two cells were tested for 69 days mounted on a Spray glider. Findings are as follows: 1) the cells were robust over 900 dives, most to 400 m; 2) without antifouling measures, the cells became substantially biofouled, but their performance was undiminished; and 3) performance was complex, depending on current density, oxygen concentration, and flow conditions. For dissolved oxygen concentration above 1 mL L^{−1}, the cells delivered 9 W m^{−2} of electrode surface at 3 V. For low oxygen, the cell shifted to hydrolysis near 2.3 V, but mass transfer was less critical so current density could be increased and observed power reached 5 W m^{−2}. This could be increased using a lower resistance load.

## Abstract

Linear statistical estimators are used to examine 29 years of nonseasonal, monthly-mean, tide-gauge sea-level data along the west coast of North America. The objective is exploration of the structure, and causes of nearshore ocean variability over time scales of months to years at 20 stations from Alaska to Mexico. North of San Francisco, 50–60% of the sea-level variability reflects a simple inverse barometric response to local atmospheric pressure. These inverted barometer effects account for only 10–15% of the variance at stations to the south.

The dominant signal of inverse-barometer-corrected sea level represents a nearly uniform rise or fall of sea level everywhere along the eastern rim of the North Pacific. The interannual aspects of this large-scale sea-level variability are closely related to El Niño occurrences in the eastern tropical Pacific which appear to propagate poloward with phase speeds of ∼40 cm s^{−1}. Higher frequency aspects of this large-scale sea-level variability appear to represent quasi-geostrophic currents driven by basin-wide scales of wind forcing over the North Pacific.

The nature of local (individual station) inverse-barometer-corrected sea-level variability is examined through a series of statistical models and the results are compared with existing dynamical models. The longshore component of wind stress generally forces a larger response than the onshore component (except in large semi-enclosed basins) but the important dynamical aspects of the wind field appear to be basin wide rather than local. The response is consistent with that expected from Ekman dynamics. An apparent non-barometric response to local atmospheric pressure is shown to partly represent an influence of sea-level anomalies farther south. Efforts to determine the nature of this indirect coupling between local pressure and sea level at stations to the south are somewhat limited by the ability of statistical estimators to accurately isolate the responses of sea level to a number of correlated inputs. However, evidence is presented indicating that part of the apparent non-barometric response is due to longshore wind-stress forcing at stations to the south. A response 30–50% greater than inverse barometric remains unexplained from Tofino to San Franciso.

## Abstract

Linear statistical estimators are used to examine 29 years of nonseasonal, monthly-mean, tide-gauge sea-level data along the west coast of North America. The objective is exploration of the structure, and causes of nearshore ocean variability over time scales of months to years at 20 stations from Alaska to Mexico. North of San Francisco, 50–60% of the sea-level variability reflects a simple inverse barometric response to local atmospheric pressure. These inverted barometer effects account for only 10–15% of the variance at stations to the south.

The dominant signal of inverse-barometer-corrected sea level represents a nearly uniform rise or fall of sea level everywhere along the eastern rim of the North Pacific. The interannual aspects of this large-scale sea-level variability are closely related to El Niño occurrences in the eastern tropical Pacific which appear to propagate poloward with phase speeds of ∼40 cm s^{−1}. Higher frequency aspects of this large-scale sea-level variability appear to represent quasi-geostrophic currents driven by basin-wide scales of wind forcing over the North Pacific.

The nature of local (individual station) inverse-barometer-corrected sea-level variability is examined through a series of statistical models and the results are compared with existing dynamical models. The longshore component of wind stress generally forces a larger response than the onshore component (except in large semi-enclosed basins) but the important dynamical aspects of the wind field appear to be basin wide rather than local. The response is consistent with that expected from Ekman dynamics. An apparent non-barometric response to local atmospheric pressure is shown to partly represent an influence of sea-level anomalies farther south. Efforts to determine the nature of this indirect coupling between local pressure and sea level at stations to the south are somewhat limited by the ability of statistical estimators to accurately isolate the responses of sea level to a number of correlated inputs. However, evidence is presented indicating that part of the apparent non-barometric response is due to longshore wind-stress forcing at stations to the south. A response 30–50% greater than inverse barometric remains unexplained from Tofino to San Franciso.

## Abstract

A unified theory of frontogenesis in mixed layers is proposed. Analytical solutions of the nonlinear mass and density balances in a mixed layer are found in the Lagrangian frame for a wide class of entrainment parameterizations. These solutions show mixed-layer depth and density to be functions of particle position and separation, where mixing is represented by an integral over time following a particle. Thus, given a knowledge of only the crossfront velocity field, the likelihood of frontal formation can be predicted. Both surface convergence, and divergence in conjunction with vertical mixing can be frontogenetic. Three different types of fronts, distinguished by their associated crossfront velocity fields, are discussed. Large-scale fronts, such as the subtropical front, are described by a convergent surface flow acting upon an initial horizontal density gradient. The powerful divergence caused by an offshore Ekman flow forced to zero at a coast causes upwelling fronts. The divergence associated with a shoaling barotropic flow forms tidal mixing fronts, which may be sharpened by convergence during an outgoing tide.

## Abstract

A unified theory of frontogenesis in mixed layers is proposed. Analytical solutions of the nonlinear mass and density balances in a mixed layer are found in the Lagrangian frame for a wide class of entrainment parameterizations. These solutions show mixed-layer depth and density to be functions of particle position and separation, where mixing is represented by an integral over time following a particle. Thus, given a knowledge of only the crossfront velocity field, the likelihood of frontal formation can be predicted. Both surface convergence, and divergence in conjunction with vertical mixing can be frontogenetic. Three different types of fronts, distinguished by their associated crossfront velocity fields, are discussed. Large-scale fronts, such as the subtropical front, are described by a convergent surface flow acting upon an initial horizontal density gradient. The powerful divergence caused by an offshore Ekman flow forced to zero at a coast causes upwelling fronts. The divergence associated with a shoaling barotropic flow forms tidal mixing fronts, which may be sharpened by convergence during an outgoing tide.

## Abstract

Coarse-resolution numerical models of ocean circulation rely on parameterizations of unresolved mesoscale eddy effects. In order to investigate the role of eddy-flux divergences in the density equation, the GFDL Modular Ocean Model (MOM) has been configured as a simple flat-bottomed channel model with sufficient resolution to represent mesoscale eddies. Eady-type baroclinic instability and a wind-forced channel have been considered. As an analog to the large-scale components addressed by low-resolution models, the influence of eddy fluxes on the zonal-mean density field was evaluated. Results show that eddy-flux divergences are larger than mean-flux divergences. The effect of mesoscale eddies on the mean density field is often hypothesized to take an advective form that conserves mean density so that eddy effects are adiabatic in the zonal mean. However, in both of the examples studied a significant component of the mesoscale eddy effect on the zonal mean is diabatic and makes mean density nonconservative. The associated diapycnal fluxes result from zonally averaging terms representing processes that are locally adiabatic.

Subgrid-scale parameterizations (such as eddy diffusion) represent the unresolved eddy-flux divergence as a function of the resolved density field. The authors computed optimal coefficients for a variety of parameterizations and evaluated their skill. When the model output is time-averaged, quasi-adiabatic parameterizations, such as the one proposed by Gent and McWilliams, are able to explain as much as 43% of the mean-squared eddy-flux divergence. However, for shorter averaging periods or instantaneous snapshots, even for the spatially averaged model fields, parameterization skill drops.

## Abstract

Coarse-resolution numerical models of ocean circulation rely on parameterizations of unresolved mesoscale eddy effects. In order to investigate the role of eddy-flux divergences in the density equation, the GFDL Modular Ocean Model (MOM) has been configured as a simple flat-bottomed channel model with sufficient resolution to represent mesoscale eddies. Eady-type baroclinic instability and a wind-forced channel have been considered. As an analog to the large-scale components addressed by low-resolution models, the influence of eddy fluxes on the zonal-mean density field was evaluated. Results show that eddy-flux divergences are larger than mean-flux divergences. The effect of mesoscale eddies on the mean density field is often hypothesized to take an advective form that conserves mean density so that eddy effects are adiabatic in the zonal mean. However, in both of the examples studied a significant component of the mesoscale eddy effect on the zonal mean is diabatic and makes mean density nonconservative. The associated diapycnal fluxes result from zonally averaging terms representing processes that are locally adiabatic.

Subgrid-scale parameterizations (such as eddy diffusion) represent the unresolved eddy-flux divergence as a function of the resolved density field. The authors computed optimal coefficients for a variety of parameterizations and evaluated their skill. When the model output is time-averaged, quasi-adiabatic parameterizations, such as the one proposed by Gent and McWilliams, are able to explain as much as 43% of the mean-squared eddy-flux divergence. However, for shorter averaging periods or instantaneous snapshots, even for the spatially averaged model fields, parameterization skill drops.