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  • Author or Editor: Darryn W. Waugh x
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Darryn W. Waugh and Timothy M. Hall

Abstract

The propagation of a range of tracer signals in a simple model of the deep western boundary current is examined. Analytical expressions are derived in certain limits for the transit-time distributions and the propagation times (tracer ages) of tracers with exponentially growing or periodic concentration histories at the boundary current’s origin. If mixing between the boundary current and the surrounding ocean is either very slow or very rapid, then all tracer signals propagate at the same rate. In contrast, for intermediate mixing rates tracer ages generally depend on the history of the tracer variations at the origin and range from the advective time along the current to the much larger mean age. Close agreement of the model with chlorofluorocarbon (CFC) and tritium observations in the North Atlantic deep western boundary current (DWBC) is obtained when the model is in the intermediate mixing regime, with current speed around 5 cm s−1 and mixing time scale around 1 yr. In this regime anomalies in temperature and salinity of decadal or shorter period will propagate downstream at roughly the current speed, which is much faster than the spreading rate inferred from CFC or tritium–helium ages (approximately 5 cm s−1 as compared with 2 cm s−1). This rapid propagation of anomalies is consistent with observations in the subpolar DWBC, but is at odds with inferences from measurements in the tropical DWBC. This suggests that observed tropical temperature and salinity anomalies are not simply propagated signals from the north. The sensitivity of the tracer spreading rates to tracer and mixing time scales in the model suggests that tight constraints on the flow and transport in real DWBCs may be obtained from simultaneous measurements of several different tracers—in particular, hydrographic anomalies and steadily increasing transient tracers.

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Hong Zhang, Thomas W. N. Haine, and Darryn W. Waugh

Abstract

The relationships between different tracer ages and between tracer age and potential vorticity are examined by simulating barotropic double-gyre circulations. The unsteady model flow crudely represents aspects of the midlatitude, middepth ocean circulation including inhomogeneous and anisotropic variability. Temporal variations range in scale from weeks to years, although the statistics are stationary. These variations have a large impact on the time-averaged tracer age fields. Transport properties of the tracer age fields that have been proved for steady flow are shown to also apply to unsteady flow and are illustrated in this circulation. Variability of tracer ages from ideal age tracer, linear, and exponential transient tracers is highly coordinated in phase and amplitude and is explained using simple theory. These relationships between different tracer ages are of practical benefit to the problem of interpreting tracer ages from the real ocean or from general circulation models. There is also a close link between temporal anomalies of tracer age and potential vorticity throughout a significant fraction of the domain. There are highly significant anticorrelations between ideal age and potential vorticity in the subtropical gyre and midbasin jet region, but correlation in the central subpolar gyre and eastern part of the domain is not significant. The existence of the relationship is insensitive to the character of the flow, the tracer sources, and the potential vorticity dynamics. Its structure may be understood by considering the different time-mean states of the tracer age and potential vorticity, the different tracer sources and sinks, and the effect of variability in the flow. Prediction of the correlation without knowledge of the time-mean fields is a harder problem, however. Detecting the correlation between potential vorticity and tracer age in the real ocean will be difficult with typical synoptic oceanographic transect data that are well-sampled in space, but sparse in time. Nevertheless, it is reasonable to suppose the correlation exists in some places.

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Darryn W. Waugh, Shane R. Keating, and Mei-Lin Chen

Abstract

The relationship between two commonly used diagnostics of stirring in ocean and atmospheric flows, the finite-time Lyapunov exponents λ and relative dispersion R 2, is examined for a simple uniform strain flow and ocean flow inferred from altimetry. Although both diagnostics are based on the separation of initially close particles, the two diagnostics measure different aspects of the flow and, in general, there is not a one-to-one relationship between the diagnostics. For a two-dimensional flow with time-independent uniform strain, there is a single time-independent λ, but there is a wide range of values of R 2 for individual particle pairs. However, it is shown that the upper and lower limits of R 2 for individual pairs, the mean value over a large ensemble of pairs, and the probability distribution function (PDF) of R 2 have simple relationships with λ. Furthermore, these analytical expressions provide a reasonable approximation for the R 2λ relationship in the surface ocean flow based on geostrophic velocities derived from satellite altimeter measurements. In particular, the bimodal distribution, upper and lower bounds, and mean values from the ocean flow are similar to the analytical expressions for a uniform strain flow. How well, as well as over what integration time scale, this holds depends on the spatial and temporal variations within the ocean region being considered.

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Darryn W. Waugh, Edward R. Abraham, and Melissa M. Bowen

Abstract

Stirring in the Tasman Sea is examined using surface geostrophic currents derived from satellite altimeter measurements. Calculations of the distribution of finite-time Lyapunov exponents (FTLEs) indicate that the stirring in this region is not uniform and stretching rates over 15 days vary from less than 0.02 day−1 to over 0.3 day−1. These variations occur at both small (∼10 km) and large (∼1000 km) scales and in both cases are linked to dynamical features of the flow. The small-scale variations are related to the characteristics of coherent vortex structures, and there are low FTLEs inside vortices and filaments of high FTLEs in strain-dominated regions surrounding these vortices. Regional variations in the stirring are closely related to variations in mesoscale activity and eddy kinetic energy (EKE). High values of mean FTLE occur in regions of high EKE (highest mean values of around 0.2 day−1 occur in the East Australia Current separation region) whereas small values occur in regions with low EKE (mean values around 0.03 day−1 in the east Tasman Sea). There is a compact relationship between the mean FTLEs and EKE, raising the possibility of using the easily calculated EKE to estimate the stirring. This possibility is even more intriguing because the FTLE distributions can be approximated, for the time scales considered here, by Weibull distributions with shape parameter equal to 1.6, which can be defined from the mean value alone.

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Timothy M. Hall, Thomas W. N. Haine, Darryn W. Waugh, Mark Holzer, Francesca Terenzi, and Deborah A. LeBel

Abstract

The intimate relationship among ventilation, transit-time distributions, and transient tracer budgets is analyzed. To characterize the advective–diffusive transport from the mixed layer to the interior ocean in terms of flux we employ a cumulative ventilation-rate distribution, Φ(τ), defined as the one-way mass flux of water that resides at least time τ in the interior before returning. A one-way (or gross) flux contrasts with the net advective flux, often called the subduction rate, which does not accommodate the effects of mixing, and it contrasts with the formation rate, which depends only on the net effects of advection and diffusive mixing. As τ decreases Φ(τ) increases, encompassing progressively more one-way flux. In general, Φ is a rapidly varying function of τ (it diverges at small τ), and there is no single residence time at which Φ can be evaluated to fully summarize the advective–diffusive flux. To reconcile discrepancies between estimates of formation rates in a recent GCM study, Φ(τ) is used. Then chlorofluorocarbon data are used to bound Φ(τ) for Subtropical Mode Water and Labrador Sea Water in the North Atlantic Ocean. The authors show that the neglect of diffusive mixing leads to spurious behavior, such as apparent time dependence in the formation, even when transport is steady.

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