Chris R. Rehmann

Importance of interactions between the water column and the sediment for microbial concentrations in streams.

The effect of interactions between the sediment and water column on concentrations of microbes in streams is quantified with a one-dimensional, steady state model. The effects of nine main parameters describing the flow, sediment transport, and microbial growth and decay are encapsulated in two dimensionless parameters: the Damköhler number Da, or the ratio of the time scales of advection and net growth, and the sediment interaction parameter S, or the ratio of the amount of microbes lost or gained in the sediment and the amount of microbes lost or gained in the water column. Applications of the model illustrate the importance of the sediment and identify parameters that require further study. The model predicts the field measurements of Jamieson et al. (2005b) within a factor of 2 in two of three cases, while concentrations predicted by ignoring the sediment exceed the measured values. In general, the effects of ignoring interactions with the sediment depend on Da and S. The loading predicted to meet water quality standards when the sediment is considered can be either greater than or less than the loading predicted when it is not considered. The applications of the model and an analysis of uncertainty suggest that further work on the settling velocity, attached fraction, resuspension rate, and net growth rate in the sediment would help to improve predictions of the fate and transport of microbes.

A model for predicting resuspension of Escherichia coli from streambed sediments.

To improve the modeling of water quality in watersheds, a model is developed to predict resuspension of Escherichia coli from sediment beds in streams. The resuspension rate is expressed as the product of the concentration of E. coli attached to sediment particles and an erosion rate adapted from work on sediment transport. The model uses parameter values mostly taken from previous work, and it accounts for properties of the flow through the bottom shear stress and properties of the sediment through the critical shear stresses for cohesive and non-cohesive sediment. Predictions were compared to resuspension rates inferred from a steady mass balance applied to measurements at sixteen locations in a watershed. The models predictions matched the inferred rates well, especially when the diameter of particles to which E. coli attach was allowed to depend on the bottom shear stress. The models sensitivity to the parameters depends on the contributions of particle packing and binding effects of clay to the critical shear stress. For the current data set, the uncertainty in the predictions is controlled by the concentration of E. coli attached to sediment particles and the slope used to estimate the bottom shear stress.

Diapycnal Diffusivity Inferred from Scalar Microstructure Measurements near the New England Shelf/Slope Front*

Abstract Conductivity microstructure was used to estimate the diapycnal thermal eddy diffusivity KT near the New England shelf/slope front in early August 1997. Two datasets were collected with a towed vehicle. One involved several horizontal tows in and above a warm, salty layer near the seafloor, and the other was from a tow-yo transect that sampled most of the water column. In the bottom layer, KT derived from microstructure is a factor of about 5 smaller than estimates derived from tracer dispersion at the same density level, and the diffusivity decreases sharply as the buoyancy frequency N increases: KT ∝ N−3.1. With several assumptions, this behavior is consistent with laboratory results for shear-driven entrainment across a density interface. The bottom layer cools as it moves up the shelf mainly due to diapycnal mixing, and a simplified temperature budget of the layer yields a diffusivity of 3 × 10−6 m2 s−1, which is between the values derived from microstructure and tracer dispersion. In the tow-...

Laboratory Measurements of Differential Diffusion in a Diffusively Stable, Turbulent Flow

Laboratory experiments were performed to determine the conditions under which differential diffusion occurs and to evaluate its effect on the mixing efficiency. Diffusively stable profiles of temperature and salinity were stirred steadily by horizontally oscillating vertical rods. The two-component stratification ensures that both scalars experience the same stratification and forcing, or Richardson and Reynolds numbers. The eddy diffusivities KT and KS, for temperature and salinity, were estimated by fitting theoretical solutions of diffusion equations to measured profiles, and the mixing efficiency was computed as the ratio of the potential energy change during a stirring interval to the work done in that interval. Differential diffusion occurred for «a/nN 2 , 300‐500, where «a is an average dissipation rate computed from an integrated energy budget. The diffusivity ratio d 5 KS/KT varied between 0.5 and 1 in the range 50 ,« a/nN 2 , 500. The experiments also show that differential diffusion can significantly affect the mixing efficiency. An important dimensionless parameter is the density ratio Rr, which is the ratio of the density change due to temperature to that due to salinity. Measurements in cases with low density ratio (Rr 0.25) and high density ratio (Rr 5) showed that the mixing efficiencies agreed well for weak stratification, or small Richardson number. For larger Richardson number, the efficiency for the highdensity-ratio case exceeded that for the low-density-ratio case by as much as a factor of 1.5.

Measurement of Turbulence with Acoustic Doppler Current Profilers - Sources of Error and Laboratory Results

Acoustic Doppler current profilers (ADCPs) provide a promising method for measuring surface-water turbulence because they can provide data from a large spatial range in a relatively short time with relative ease. Some potential sources of errors in turbulence measurements made with ADCPs include inaccuracy of Doppler-shift measurements, poor temporal and spatial measurement resolution, and inaccuracy of multi-dimensional velocities resolved from one-dimensional velocities measured at separate locations. Results from laboratory measurements of mean velocity and turbulence statistics made with two pulse-coherent ADCPs in 0.87 meters of water are used to illustrate several of inherent sources of error in ADCP turbulence measurements. Results show that processing algorithms and beam configurations have important effects on turbulence measurements. ADCPs can provide reasonable estimates of many turbulence parameters; however, the accuracy of turbulence measurements made with commercially available ADCPs is often poor in comparison to standard measurement techniques.

Small-Scale Structure of Strongly Stratified Turbulence

The small-scale structure of turbulence subjected to strong stratification is analyzed with rapid distortion theory to evaluate the performance of formulas for predicting dissipation of turbulent kinetic energy and dissipation of scalar variance. The approach is restricted to weak turbulence in strong stratification, like that in the thermocline or the abyssal ocean. Flows with and without mean shear are considered. For unsheared turbulence, the small scales are axisymmetric about the vertical axis, as others have previously assumed. The calculations here complement and extend previous work because they can be used to compute errors in dissipation estimates, develop simpler formulas, and examine the effects of shear and other parameters. For example, effects of the initial conditions can be significant. For sheared turbulence, the small-scale velocity and buoyancy fields are neither isotropic nor axisymmetric about the vertical axis. Although dissipation formulas based on isotropy work relatively well for unsheared turbulence, some can be incorrect by more than a factor of 3 for sheared turbulence. However, if the mean flow direction can be identified, then a simple and useful dissipation formula can be proposed.

Kinematic Effects of Differential Transport on Mixing Efficiency in a Diffusively Stable, Turbulent Flow

If temperature and salinity are mixed at different rates, the mixing efficiencies in flows with the same stratification and forcing can vary if the contributions of temperature and salinity to the density differ. Two models are used to examine the effect of differential transport of salt and heat on the mixing efficiency. The first model assumes constant eddy diffusivities for heat and salt and examines the effect of the density ratio Rr 5 aDT/ bDS and the diffusivity ratio d 5 KS/KT on the mixing efficiency. The model predicts that the effect of differential transport can be as large as that due to stratification and the type of process generating the turbulence. The second model incorporates the effect of stratification on the mixing by using results from laboratory experiments on entrainment across a sharp density interface. The model predicts that the mixing efficiency depends on the density ratio and a Richardson number Ri0 based on the density jump and velocity and length scales of the turbulence near the interface. Because the laboratory measurements show that salt and heat are entrained at equal rates for Richardson numbers less than a transition value Ri c, the mixing efficiency initially increases with increasing Ri 0 for all density ratios. However, for Ri 0 . Ric, the efficiency decreases (past a peak at Ric) for low density ratio and increases monotonically for high density ratio. These results suggest that the generation of fine structure in diffusively stable regions of the ocean can depend on the density ratio.

Layering in a Flow with Diffusively Stable Temperature and Salinity Stratification

Abstract Laboratory experiments were conducted to study the formation of layers and interfaces in a fluid stratified with two scalars. Fluid with initially linear, diffusively stable temperature and salinity profiles was stirred using an arrangement of horizontally oscillating, vertical rods. Layers occurred when the density ratio, or the ratio of the contributions of temperature and salinity to the density gradient, was small, but they did not form in similar conditions of turbulence intensity and stratification strength when the density ratio was large. The difference in behavior is ascribed to differential diffusion, or the preferential transport of temperature, which occurred in all of the experiments. Eddy diffusivities were linearly proportional to ea/νN 2, where ea is an averaged rate of dissipation of turbulent kinetic energy. The mixing efficiency, computed as the ratio of potential energy change to work input to the system, increased with the density ratio. As previous researchers have found, th...

Buoyancy generated turbulence in stably stratified flow with shear

The energy evolution in buoyancy-generated turbulence subjected to shear depends on the gradient Richardson number Ri and the stratification number St, which is a ratio of the time scale of the initial buoyancy fluctuations to the time scale of the mean stratification. During an initial period, the flow state evolves as in the unsheared case. After this period, shear generates fluctuating velocity components for St=0.25, but it depletes the fluctuating vertical velocity component and temperature variance faster than in the unsheared case for St=4. Weak shear causes the kinetic and total energy to decrease faster than in the unsheared case, whereas strong shear adds more energy in comparison with the unsheared case. Energy increased with time in only one case considered (St=0.1 and Ri=0.04). When St>1, the nonlinearity of the flow does not become significant even when Ri is small. Thus, results from rapid distortion theory and direct numerical simulation compare well. In particular, the theory reproduces t...

An agent-based platform for the study of watersheds as coupled natural and human systems

Abstract This study describes the architecture and capabilities of an open source agent-based Java platform that permits the systematic study of interactions among hydrology, climate, and strategic human decision-making in a watershed over time. To demonstrate the platforms use and capabilities, an application is presented in accordance with ODD protocol requirements that captures, in simplified form, the structural attributes of the Squaw Creek watershed in central Iowa. Illustrative findings are reported for the sensitivity of farmer and city social welfare outcomes to changes in three key treatment factors: farmer land-allocation decision method, farmer targeted savings, and levee quality effectiveness for the mitigation of city flood damage.