ALBERT

Description: We report on the results of a laboratory investigation using a rotating two-layer annulus experiment, which exhibits both large-scale vortical modes and short-scale divergent modes. A sophisticated visualization method allows us to observe the flow at very high spatial and temporal resolution. The balanced long-wavelength modes appear only when the Froude number is supercritical (i.e. F 〉 Fcritical ≡ π2/2), and are therefore consistent with generation by a baroclinic instability. The unbalanced short-wavelength modes appear locally in every single baroclinically unstable flow, providing perhaps the first direct experimental evidence that all evolving vortical flows will tend to emit freely propagating inertia-gravity waves. The short-wavelength modes also appear in certain baroclinically stable flows. We infer the generation mechanisms of the short-scale waves, both for the baroclinically unstable case in which they co-exist with a large-scale wave, and for the baroclinically stable case in which they exist alone. The two possible mechanisms considered are spontaneous adjustment of the large-scale flow, and Kelvin-Helmholtz shear instability. Short modes in the baroclinically stable regime are generated only when the Richardson number is subcritical (i.e. Ri 〈 Ricritical ≡ 1), and are therefore consistent with generation by a Kelvin-Helmholtz instability. We calculate five indicators of short-wave generation in the baroclinically unstable regime, using data from a quasi-geostrophic numerical model of the annulus. There is excellent agreement between the spatial locations of short-wave emission observed in the laboratory, and regions in which the model Lighthill/Ford inertia-gravity wave source term is large. We infer that the short waves in the baroclinically unstable fluid are freely propagating inertia-gravity waves generated by spontaneous adjustment of the large-scale flow. © 2005 Cambridge University Press.

Description: This paper describes laboratory observations of inertia–gravity waves emitted from balanced fluid flow. In a rotating two-layer annulus experiment, the wavelength of the inertia–gravity waves is very close to the deformation radius. Their amplitude varies linearly with Rossby number in the range 0.05–0.14, at constant Burger number (or rotational Froude number). This linear scaling challenges the notion, suggested by several dynamical theories, that inertia–gravity waves generated by balanced motion will be exponentially small. It is estimated that the balanced flow leaks roughly 1% of its energy each rotation period into the inertia–gravity waves at the peak of their generation. The findings of this study imply an inevitable emission of inertia–gravity waves at Rossby numbers similar to those of the large-scale atmospheric and oceanic flow. Extrapolation of the results suggests that inertia–gravity waves might make a significant contribution to the energy budgets of the atmosphere and ocean. In particular, emission of inertia–gravity waves from mesoscale eddies may be an important source of energy for deep interior mixing in the ocean.

Description: 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.

Description: 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.