Abstract-Applications of transport time scales are pervasive in biological, hydrologic, and geochemical studies yet these times scales are not consistently defined and applied with rigor in the literature. We compare three transport time scales (flushing time, age, and residence time) commonly used to measure the retention of water or scalar quantities transported with water. We identify the underlying assumptions associated with each time scale, describe procedures for computing these time scales in idealized cases, and identify pitfalls when real-world systems deviate from these idealizations. We then apply the time scale definitions to a shallow 378 ha tidal lake to illustrate how deviations between real water bodies and the idealized examples can result from: (1) non-steady flow; (2) spatial variability in bathymetry, circulation, and transport time scales; and (3) tides that introduce complexities not accounted for in the idealized cases. These examples illustrate that no single transport time scale is valid for all time periods, locations, and constituents, and no one time scale describes all transport processes. We encourage aquatic scientists to rigorously define the transport time scale when it is applied, identify the underlying assumptions in the application of that concept, and ask if those assumptions are valid in the application of that approach for computing transport time scales in real systems.In aquatic systems, most of the living biomass and masses of nutrients, contaminants, dissolved gases, and suspended particles are carried in a fluid medium, so it is essential to understand hydrodynamic processes that transport water and its constituents. A first-order description of transport is expressed as ''residence time'' or ''flushing time,'' which we conceive as measures of water-mass retention within defined boundaries. Aquatic scientists often estimate retention time and compare it to time scales of inputs or biogeochemical processes to calculate mass balances or understand dynamics of populations and chemical properties. Boynton et al. (1995) argue that residence time is such an important attribute that it should be the basis for comparative analyses of ecosystem-scale nutrient budgets.The classical empirical model of lake eutrophication (Vollenweider 1976) describes algal biomass as a function of phosphorus loading rate scaled by the hydraulic residence time. Since Vollenweider's recognition that the biogeochemical processing of phosphorus varies with residence time, variable water retention or flushing has been used to describe variability of lake thermal stratification (Hamilton and Lewis 1987), isotopic composition (Herczeg and Imboden 1988), alkalinity (Eshleman and Hemond 1988), dissolved organic carbon concentration (Christensen et al. 1996), elemental ratios of heavy metals (Hilton et al. 1995) and nutrients (Hecky et al. 1993), mineralization rates of organic matter (den Heyer and Kalff 1998), and primary production (Jassby et al. 1990). The mechanistic explanation of low plankton abun...

[1] Many benthic organisms form very rough surfaces on the seafloor that can be described as submerged canopies. Recent evidence has shown that, compared with a unidirectional current, an oscillatory flow driven by surface waves can significantly enhance biological processes such as nutrient uptake. However, to date, the physical mechanisms responsible for this enhancement have not been established. This paper presents a theoretical model to estimate flow inside a submerged canopy driven by oscillatory flow. To reduce the complexity of natural canopies, an idealized canopy consisting of an array of vertical cylinders is used. The attenuation of the in-canopy oscillatory flow is shown to be governed by three dimensionless parameters defined on the basis of canopy geometry and flow parameters. The model predicts that an oscillatory flow will always generate a higher in-canopy flow when compared to a unidirectional current of the same magnitude, and specifically that the attenuation will monotonically increase as the wave orbital excursion length is increased. A series of laboratory experiments are conducted for a range of different unidirectional and oscillatory flow conditions, and the results confirm that oscillatory flow increases water motion inside a canopy. It is hypothesized that this higher in-canopy flow will enhance rates of mass transfer from the canopy elements, a problem formally investigated in a companion paper (Lowe et al., 2005b).

A 2 week field experiment was conducted to measure surface wave dissipation on a barrier reef at Kaneohe Bay, Oahu, Hawaii. Wave heights and velocities were measured at several locations on the fore reef and the reef flat, which were used to estimate rates of dissipation by wave breaking and bottom friction. Dissipation on the reef flat was found to be dominated by friction at rates that are significantly larger than those typically observed at sandy beach sites. This is attributed to the rough surface generated by the reef organisms, which makes the reef highly efficient at dissipating energy by bottom friction. Results were compared to a spectral wave friction model, which showed that the variation in frictional dissipation among the different frequency components could be described using a single hydraulic roughness length scale. Surveys of the bottom roughness conducted on the reef flat showed that this hydraulic roughness length was comparable to the physical roughness measured at this site. On the fore reef, dissipation was due to the combined effect of frictional dissipation and wave breaking. However, in this region the magnitude of dissipation by bottom friction was comparable to wave breaking, despite the existence of a well‐defined surf zone there. Under typical wave conditions the bulk of the total wave energy incident on Kaneohe Bay is dissipated by bottom friction, not wave breaking, as is often assumed for sandy beach sites and other coral reefs.

The structure of the salinity field in northern San Francisco Bay and how it is affected by freshwater flow are discussed. Two datasets are examined: the first is 23 years of daily salinity data taken by the U.S. Bureau of Reclamation along the axis of northern San Francisco Bay; the second is a set of salinity transects taken by the U.S. Geological Survey between 1988 and 1993. Central to this paper is a measure of salinity intrusion, X,: the distance from the Golden Gate Bridge to where the bottom salinity is 2 psu. Using X , to scale distance, the authors find that for most flow conditions, the mean salinity distribution of the estuary is nearly self-similar with a salinity gradient in the center 70% of the region between the Golden Gate and X , that is proportional to X;'. Analysis of covariability of Q and X , showed a characteristic timescale of adjustment of the salinity field of approximately 2 weeks. The steady-state response deduced from the X 2 time series implies that X , is proportional to riverflow to the 1/7 power. This relation, which differs from the standard 113 power dependence that is deri\ ed theoretically assuming constant exchange coefficients, shows that the upstream salt flux associated with gravitational circulation is more sensitive to the longitudinal salinity gradient than theory supposes. This is attributed to the strengthening of stratification caused by the stronger longitudinal salinity gradient that accompanies larger river flows.

Populations of native and introduced aquatic organisms in the San Francisco Bay/Sacramento-San Joaquin Delta Estuary ("Bay/Delta") have undergone significant declines over the past two decades. Decreased river inflow due to drought and increased freshwater diversion have contributed to the decline of at least some populations. Effective management of the estuary's biologica! resources requires a sensitive indicator of the response to freshwater inflow that has ecologica! significance, can be measured accurately and easily, and could be used as a "policy" variable to set standards for managing freshwater inflow. Positioning of the 2%o (grams of salt per kilogram of seawater) bottom salinity value along the axis of the estuary was examined for this purpose.The 2%o bottom salinity position (denoted by X2) has simple and significant statistica! relationships with annual measures of many estuarine resources, including the supply of phytoplankton and phytoplankton-derived detritus from local production and river loading; benthic macroinvertebrates (molluscs); mysids and shrimp; larval fish survival; and the abundance of planktivorous, piscivorous, and bottom-foraging fish. The actual mechanisms are understood for only a few of these populations.X 2 also satisfies other recognized requirements for a habitat indicator and probably can be measured with greater accuracy and precision than alternative habitat indicators such as net freshwater inflow into the estuary. The 2%o value may not have special ecologica! significance for other estuaries (in the Bay/Delta, it marks the locations of an estuarine turbidity maximum and peaks in the abundance of several estuarine organisms), but the concept of using near-bottom isohaline position as a habitat indicator should be widely applicable.Although X2 is a sensitive index of the estuarine community's response to net freshwater inflow, other hydraulic features of the estuary also determine population abundances and resource levels. In particular, diversion of water for export from or consumption within the estuary can have a direct effect on population abundance independent of its effect on X2• The need to consider diversion, in addition to X2, for managing certain estuarine resources is illustrated using striped bass survival as an example.The striped bass survival data were also used to illustrate a related important point: incorporating additional explanatory variables may decrease the prediction error for a population or process, but it can increase the uncertainty in parameter estimates and management strategies based on these estimates. Even in cases where the uncertainty is currently too large to guide management decisions, an uncertainty analysis can identify the most practica! direction for future data acquisition.

The geometric complexity of coral reefs leads to interesting fluid mechanics problems at scales ranging from those of coral colonies or even branches a few millimeters in diameter up to whole reefs that can be kilometers in horizontal extent. In many cases, both at the colony and reef scale, unsteady flows, usually due to surface waves, behave very differently than do steady flows for which the coral structures may appear to have quite high resistance to any flow through their interior. Allowing for this difference, engineering formulae for mass transfer describe well the uptake of nutrients by corals, although a priori determination of hydrodynamic roughness of corals and coral reefs is not yet possible. Surface wave-driven flows are a common feature of many coral reefs and appear to follow predictions of theories based on radiation stress gradients. However, comparisons to observations have been relatively limited, and there is some question as to the role played by Stokes drift in these flows. Like other near-shore environments, internal waves and flows driven by horizontal buoyancy gradients can also be important.

We examined the role of wave-driven circulation relative to wind and buoyancy forcing in a coral reef-lagoon system. Circulation measurements in Paopao Bay, Moorea, French Polynesia, during austral summer show the importance of waves in driving flows over the reef crest, through the lagoon, and out the reef pass. Tides were comparatively weak, due to proximity to amphidromic points, and exhibited an unusual spring-neap cycle where the major lunar tide modulated the major solar tide, and the overall tidal phase stayed approximately constant. Wind had only a secondary effect compared to surface waves. A simple fluid mass balance indicated rapid flushing of the shallow back reef and export through the reef pass, and a reef capture zone width of ,2.3 km. The reef pass circulation dynamics exhibited two-layer baroclinic exchange flow when waves were small, which was suppressed during large wave events. The unusually weak tidal forcing provided an opportunity to more closely investigate wave-driven circulation dynamics. As expected theoretically, there was a wave-driven setup of the free surface across the shallow lagoon, which drove a highly frictional flow, evident by a large drag coefficient C D < 0.1. Diverging from extant theory, the observed setup varied strongly with significant wave height and period. Overall, the circulation and exchange between this coral reef system and the adjacent open ocean were largely determined by episodic remote-forcing events and differed significantly from periodic tidal-exchange mechanisms.

In this paper, we examine the relation between the turbulence and the mean flow through the calculation of u,, the friction velocity, and Ca, the coefficient of drag. Finally, we calculate quantities of particular interest in turbulence modeling and analysis, the characteristic lengthscales, including a lengthscale which represents the stream-wise scale of the eddies which dominate the Reynolds stresses.