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Russ E. Davis

Abstract

The Osborn–Cox model is the basis for the most direct estimates of the diapycnal diffusivity Kv for tracers. When used to interpret temperature variance dissipation measurements, it leads to Kv of O (10−5 m2 s−1) or less in the main thermocline. Large-scale diagnostic models typically match observations best using Kv of O (10−4 m2 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 m2 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 Kv of O (10−5 m2 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 Kv 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.

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Russ E. Davis

Abstract

The Osborn-Cox model is a simplified tracer variance budget that is a basis for direct estimates of the diapycnal Kv. diffusivity When used to interpret temperature variance dissipation measurements, it indicates Kv to be O(10−5 m2 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 Kv 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 〈u′θ′2〉. Variance production by lateral fluxes is most common where stratification is weak and causes the Osborn–Cox model to overestimate Kv. 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.

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Russ E. Davis

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.

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Russ E. Davis

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.

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Russ E. Davis

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.

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Russ E. Davis

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 θz0; if |∇θ| is lognormal and isotropic. then |θz| 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.

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Kathleen Dohan and Russ E. Davis

Abstract

Upper-ocean dynamics analyzed from mooring-array observations are contrasted between two storms of comparable magnitude. Particular emphasis is put on the role of the transition layer, the strongly stratified layer between the well-mixed upper layer, and the deeper more weakly stratified region. The midlatitude autumn storms occurred within 20 days of each other and were measured at five moorings. In the first storm, the mixed layer follows a classical slab-layer response, with a steady deepening during the course of the storm and little mixing of the thermocline beneath. In the second storm, rather than deepening, the mixed layer shoals while intense near-inertial waves are resonantly excited within the mixed layer. These create a large shear throughout the transition layer, generating turbulence that broadens the transition layer.

Details of the space–time structure of the frequencies in both short waves and near-inertial waves are presented. Small-scale waves are excited within the transition layer. Their frequencies change with time and there are no clear peaks at harmonics of inertial or tidal frequencies. Wavelet transforms of the inertial oscillations show the evolution as a spreading in frequency, a deepening of the core into the transition layer, and a shift off the inertial frequency. A second near-inertial energy core appears below the transition layer at all moorings coincident with a rapid decay of mixed layer currents.

An overall result is that direct wind-generated motions extend to the depth of the transition layer. The transition layer is a location of enhanced wave activity and enhanced shear-driven mixing.

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Russ E. Davis and Jeffrey T. Sherman

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.

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Sarah T. Gille and Russ E. Davis

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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.

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Jeffrey T. Sherman and Russ E. Davis

Abstract

A new autonomous instrument collected 76 profiles of temperature microstructure over a ten-day period in the eastern subtropical North Atlantic as part of the North Atlantic Tracer Release Experiment. The data between 200-m and 350-m depth was used to determine the mean rate of temperature variance dissipation 〈χ〉. The estimated diapycnal diffusivity is Ky = 1.4×10−5 m2 s−1. The distribution of χ is approximately lognormal, suggesting that the 95% confidence limits on 〈χ〉 are ±4%. This uncertainty is less than that caused by the imperfectly known probe response, possible noise spikes on the probes, and variability in the degree of microstructure anisotropy; the latter two effects were estimated from a pair of closely spaced probes. Each of these uncertainties is about ±15%. Statistically significant low-frequency variability of χ is observed with 〈χ〉 decreasing by a factor of 2 between the first and second half of the observation. This low-frequency variability is likely the largest cause of error in estimating a seasonally averaged diapycnal diffusivity.

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