Mark Holzer

Turbulent Mixing of a Passive Scalar

The small scale properties of a passive scalar mixed by a turbulent velocity field show departures from Komogorov theory at least as prominent as for the velocity field1. While one might have imagined that the scalar merely inherits the intermittency of the velocity field itself, a series of recent numerical experiments with a Gaussian but multiscale velocity field argue otherwise.2 A trivial but multiscale velocity produces scalar statistics in some cases quantitatively similar to those obtained in laboratory experiments.3

Transit-Time and Tracer-Age Distributions in Geophysical Flows

Transport in the atmosphere and in the ocean is the result of the complex action of time-dependent and often highly turbulent flow. A useful diagnostic that summarizes the rate at which fluid elements are transported from some region to a point (or the reverse) via a multiplicity of pathways and mechanisms is the probability density function (pdf ) of transit times. The first moment of this pdf, often referred to as ‘‘mean age,’’ has become an important transport diagnostic commonly used by the observational community. This paper explores how to probe the flow with passive tracers to extract transit-time pdf’s. As a foundation, the literal ‘‘tracer age’’ is defined as the elapsed time since tracer was injected into the flow, and the corresponding tracer-age distribution, Z, as the fractional tracer mass in a given interval of tracer age. The distribution, Z, has concrete physical interpretation for arbitrary sources, but is only equivalent to a tracer-independent transit-time pdf of the flow in special cases. The transit-time pdf is a propagator, G9, of boundary conditions (the ‘‘age spectrum’’ of T. M. Hall and R. A. Plumb) applied over a control surface, V. The propagator G9 is shown to be the flux into V resulting from a unit mass injected into the time-reversed flow. Through explicit construction of the transit-time pdf using the concept of tracer age, the special cases for which Z and G9 coincide are established. This allows a direct physical demonstration of G9, and its adjoint G9† , as the pdf’s of transit times since fluid at point r had last contact with V, and until fluid at r will have first contact with V, respectively. In the limit as V is shrunk to a point, point-to-point transit-time pdf’s are well defined, but their mean transit time and higher-order moments become infinite. Several concrete geophysical examples are considered to illustrate under what conditions characteristics of tracer-age and transit-time pdf’s can be inferred from observations in the atmosphere or the ocean.

Recent Changes in the Ventilation of the Southern Oceans

The Change of Winds As the combined effects of Antarctic stratospheric ozone depletion and climate warming have forced the westerly surface winds in the Southern Hemisphere to shift toward the pole, mixing between the upper ocean and deeper waters has also changed. Waugh et al. (p. 568) now show that water originating at the surface at subtropical latitudes is mixing into the deeper ocean at a higher rate than 20 years ago, while the reverse is true for those originating at higher latitudes. The summer westerly winds that blow in the Southern Hemisphere have shifted toward the South Pole over the past several decades, but why? Lee and Feldstein (p. 563) show that greenhouse gas forcing and ozone depletion impart different signatures to wind patterns and conclude that ozone depletion has been responsible for more than half of the observed shift. Changing westerly winds in the Southern Hemisphere have caused coherent changes in the southern ocean ventilation. [Also see News & Analysis] Surface westerly winds in the Southern Hemisphere have intensified over the past few decades, primarily in response to the formation of the Antarctic ozone hole, and there is intense debate on the impact of this on the oceans circulation and uptake and redistribution of atmospheric gases. We used measurements of chlorofluorocarbon-12 (CFC-12) made in the southern oceans in the early 1990s and mid- to late 2000s to examine changes in ocean ventilation. Our analysis of the CFC-12 data reveals a decrease in the age of subtropical subantarctic mode waters and an increase in the age of circumpolar deep waters, suggesting that the formation of the Antarctic ozone hole has caused large-scale coherent changes in the ventilation of the southern oceans.

The Ocean’s Memory of the Atmosphere: Residence-Time and Ventilation-Rate Distributions of Water Masses

A conceptually new approach to diagnosing tracer-independent ventilation rates is developed. Tracer Green functions are exploited to partition ventilation rates according to the ventilated fluid’s residence time in the ocean interior and according to where this fluid enters and exits the interior. In the presence of mixing by mesoscale eddies, which are reasonably represented by diffusion, ventilation rates for overlapping entry and exit regions cannot meaningfully be characterized by a single rate. It is a physical consequence of diffusive transport that fluid elements that spend an infinitesimally short time in the interior cause singularly large ventilation rates for overlapping entry and exit regions. Therefore, ventilation must generally be characterized by a ventilation-rate distribution, , partitioned according to the time that the ventilated fluid spends in the interior between successive surface contacts. An offline forward and adjoint time-averaged OGCM is used to illustrate the rich detail that and the closely related probability density function of residence times R provide on the way the ocean communicates with the surface. These diagnostics quantify the relative importance of various surface regions for ventilating the interior ocean by either exposing old water masses to the atmosphere or by forming newly ventilated ones. The model results suggest that the Southern Ocean plays a dominant role in ventilating the ocean, both as a region where new waters are ventilated into the interior and where old waters are first reexposed to the atmosphere.

Recent increase in oceanic carbon uptake driven by weaker upper-ocean overturning

The ocean is the largest sink for anthropogenic carbon dioxide (CO2), having absorbed roughly 40 per cent of CO2 emissions since the beginning of the industrial era. Recent data show that oceanic CO2 uptake rates have been growing over the past decade, reversing a trend of stagnant or declining carbon uptake during the 1990s. Here we show that ocean circulation variability is the primary driver of these changes in oceanic CO2 uptake over the past several decades. We use a global inverse model to quantify the mean ocean circulation during the 1980s, 1990s and 2000s, and then estimate the impact of decadal circulation changes on the oceanic CO2 sink using a carbon cycling model. We find that during the 1990s an enhanced upper-ocean overturning circulation drove increased outgassing of natural CO2, thus weakening the global CO2 sink. This trend reversed during the 2000s as the overturning circulation weakened. Continued weakening of the upper-ocean overturning is likely to strengthen the CO2 sink in the near future by trapping natural CO2 in the deep ocean, but ultimately may limit oceanic uptake of anthropogenic CO2.

Simulated Changes in Atmospheric Transport Climate

Atmospheric ‘‘transport climate’’ characterizes how trace gases are distributed by and within the atmosphere, on average, as a consequence of the interaction of atmospheric flow with tracer sources and sinks. The change in transport climate under global warming is investigated using passive tracers. Experiments with constant localized surfaces sources, pulsed sources, and pulsed boundary conditions are analyzed using a Green-function approach in conjunction with a climatological budget calculation. Under climate warming, interhemispheric exchange times, mixing times, and mean transit times all increase by about 10%. The main transport pathway between the hemispheres via the ‘‘tracer fountain’’ at the ITCZ is suppressed. Generally less vigorous flow manifests itself in higher tracer burdens in the source hemisphere and in downwind plumes of enhanced mixing ratio close to the sources; these increases are also about 10%. Resolved advection and subgrid transport do not cooperate for all sources in enhancing the near-source mixing ratio. The warmer climate has a reduced cross-tropopause gradient, primarily due to a slightly higher tropopause, which results in a reduction of about 25% in the average tropospheric tracer mixing ratio, and a corresponding enhancement in the stratosphere. A global variance budget shows increased mean and transient tracer variance due to increased generation from strengthened mean gradients near the source and weakened eddy and subgrid transport.

Analysis of Passive Tracer Transport as Modeled by an Atmospheric General Circulation Model

Abstract Tracers without feedback on the atmosphere are used to probe tropospheric transport. Such passive tracers are considered for two important anthropogenic sources, Europe and eastern North America. The linearity of passive tracer continuity allows transport to be formulated in terms of a Green function, G. A coarse-grained Green function is defined that is suitable for numerical investigation with a GCM. An ensemble of independent realizations of the atmosphere is used to obtain the model’s ensemble mean, or “climate” Green function. With increasing time, the individual realizations of G converge to their climate mean and this convergence is quantified in terms of the decay of ensemble fluctuations. Throughout, G is analyzed with the goal of gaining new insight into the tracer climate that results from constant sources. The climate Green function is used to identify transport timescales, pathways, and mechanisms. The Green function is zonally mixed after about 3 months. The time to mix G to within ...

Skewed, exponential pressure distributions from Gaussian velocities

A simple analytical argument is given to show that the distribution function of the pressure and that of its gradient have exponential tails when the velocity is Gaussian. A calculation of moments implies a negative skewness for the pressure. Explicit analytical results are given for the case of the velocity being restricted to a shell in wave number. Numerical pressure distributions are presented for Gaussian velocities with realistic spectra. For real turbulent flows, one expects that the pressure distribution should retain exponential tails while the pressure gradients should develop stretched‐exponential distributions. In the context of the theory, available numerical and laboratory data are examined for the pressure, along with data for the wall shear stress in a boundary layer.

Optimal Spectral Topography and Its Effect on Model Climate

Abstract Gibbs oscillations in the truncated spectral representation of the earths topography are strongly reduced by determining its spectral coefficients as a minimum of a nonuniformly weighted, nonquadratic cost function. The cost function penalizes the difference between spectral and true topography with weights that are explicit functions of the topographic height and its gradient. The sensitivity of the Canadian Climate Centre general circulation models climate to the presence of Gibbs oscillations is determined for T32 and T48 resolutions by comparing the climates with optimal spectral topography to those with standard spectral topography. The main effect of Gibbs oscillations in the standard spectral topography is to induce spurious grid-scale ripples in the surface fluxes, which, for the surface energy balance, can be on the order of several tens of watts per square meter. Ripples in the surface fluxes are nearly absent in the model climate with the optimal spectral topography.

Ventilation Rates Estimated from Tracers in the Presence of Mixing

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, (), defined as the one-way mass flux of water that resides at least time 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 decreases () increases, encompassing progressively more one-way flux. In general, is a rapidly varying function of (it diverges at small ), and there is no single residence time at which can be evaluated to fully summarize the advective–diffusive flux. To reconcile discrepancies between estimates of formation rates in a recent GCM study, () is used. Then chlorofluorocarbon data are used to bound () 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.