W. Rockwell Geyer

Numerical modeling of an estuary : a comprehensive skill assessment

[i] Numerical simulations of the Hudson River estuary using a terrain-following, three-dimensional model (Regional Ocean Modeling System (ROMS)) are compared with an extensive set of time series and spatially resolved measurements over a 43 day period with large variations in tidal forcing and river discharge. The model is particularly effective at reproducing the observed temporal variations in both the salinity and current structure, including tidal, spring neap, and river discharge-induced variability. Large observed variations in stratification between neap and spring tides are captured qualitatively and quantitatively by the model. The observed structure and variations of the longitudinal salinity gradient are also well reproduced. The most notable discrepancy between the model and the data is in the vertical salinity structure. While the surface-to-bottom salinity difference is well reproduced, the stratification in the model tends to extend all the way to the water surface, whereas the observations indicate a distinct pycnocline and a surface mixed layer. Because the southern boundary condition is located near the mouth the estuary, the salinity within the domain is particularly sensitive to the specification of salinity at the boundary. A boundary condition for the horizontal salinity gradient, based on the local value of salinity, is developed to incorporate physical processes beyond the open boundary not resolved by the model. Model results are sensitive to the specification of the bottom roughness length and vertical stability functions, insofar as they influence the intensity of vertical mixing. The results only varied slightly between different turbulence closure methods of k-e, k-ω, and k-kl.

Response of a river plume during an upwelling favorable wind event

The response of a surface-trapped river plume to an upwelling favorable wind is studied using a three-dimensional model in a simple, rectangular domain. Model simulations demonstrate that the plume thins and is advected offshore by the cross-shore Ekman transport. The thinned plume is susceptible to significant mixing because of the vertically sheared horizontal currents. The Ekman dynamics and shear-induced mixing cause the plume to evolve to a quasi-steady uniform thickness, which can be estimated by a critical Richardson number criterion. Although the mixing rate decreases slowly in time, mixing continues under a sustained upwelling wind until the plume is destroyed. Mixing persists at the seaward plume front because of an Ekman straining mechanism in which there is a balance between the advection of cross-shore salinity gradients and vertical mixing. The plume mixing rate observed is similar to the mixing law obtained by previous studies of one-dimensional mixing, although the river plume mixing is essentially two-dimensional.

Transient eddy formation around headlands

Eddies with length scales of 1–10 km are commonly observed in coastal waters and play an important role in the dispersion of water-borne materials. The generation and evolution of these eddies by oscillatory tidal flow around coastal headlands is investigated with analytical and numerical models. Using shallow water depth-averaged vorticity dynamics, eddies are shown to form when flow separation occurs near the tip of the headland, causing intense vorticity generated along the headland to be injected into the interior. An analytic boundary layer model demonstrates that flow separation occurs when the pressure gradient along the boundary switches from favoring (accelerating) to adverse (decelerating), and its occurrence depends principally on three parameters: the aspect ratio [b/a], where b and a are characteristic width and length scales of the headland; [H/CDa], where H is the water depth, CD is the depth-averaged drag coefficient; and [Uo/σa], where Uo and σ are the magnitude and frequency of the far-field tidal flow. Simulations with a depth-averaged numerical model show a wide range of responses to changes in these parameters, including cases where no separation occurs, cases where only one eddy exists at a given time, and cases where bottom friction is weak enough that eddies produced during successive tidal cycles coexist, interacting strongly with each other. These simulations also demonstrate that in unsteady flow, a strong start-up vortex forms after the flow separates, leading to a much more intense patch of vorticity and stronger recirculation than found in steady flow.

The importance of suppression of turbulence by stratification on the estuarine turbidity maximum

A simple numerical model demonstrates that the reduction in turbulence due to stratification greatly enhances the trapping of suspended sediment that occurs at the estuarine turbidity maximum. In moderately and highly stratified estuaries the turbulent diffusivity decreases markedly between the region upstream of the salinity intrusion, where the turbulence is uninhibited by salt stratification, and the stratified regime within the salinity intrusion, where turbulence is reduced by the inhibitory influence of salt stratification. This reduction in turbulent diffusion results in a reduction in the quantity of sediment that can be carried by the flow, causing sediment to be trapped near the landward limit of the salinity intrusion. This trapping process occurs at the same location as that due to the estuarine convergence, but it appears to be many times more effective at trapping silt-size particles. A model is formulated that is similar to Festa and Hansens (1978) model of the estuarine turbidity maximum, with the addition of a stratification-dependent eddy diffusivity. For silt-size sediment particles, the model indicates as much as a 20-fold increase in the trapping rate with inclusion of the stratification effect. it is likely that this mechanism is important in many partially mixed and highly stratified estuaries.

Three-dimensional tidal flow around headlands

Field measurements of tidal flow around a headland indicate secondary circulation induced by flow curvature. The secondary flow, defined to be the flow in the plane normal to the direction of the vertically averaged current, is directed toward the headland near the bottom and seaward near the surface, consistent with theoretical predictions. The strength of the secondary flow varies from 5 to 15% of the streamwise flow. It is strongest when the water column is stratified because of both the enhanced shear of the streamwise flow and the reduced frictional damping of the secondary flow. The transverse exchange accomplished by the secondary flow significantly influences the structure of the streamwise flow, causing a broadening of the transverse shear and changing the horizontal and vertical distributions of momentum. It may also have a significant influence on horizontal dispersion in the vicinity of headlands.

Controls on effective settling velocity of suspended sediment in the Eel River flood plume

Abstract Bulk effective settling velocities required to explain sinking losses from the Eel River flood plume off the coast of northern California are of order 0.1 mm s −1 for five different helicopter-based sampling surveys conducted in January and February 1998. These effective settling velocities exceed those expected for single-grain sinking and implicate flocculation as an important mechanism for speeding the removal of sediment from the Eel River plume. The relative constancy of effective settling velocities despite widely varying winds, waves, and currents is consistent with photographs in the plume that show little variability in floc size with total suspended sediment mass concentration, turbulent-kinetic-energy dissipation rate, elapsed time since sediment within flocs left the river mouth, or depth. These observations of floc size contrast with those made in winter 1997 during the exceptionally large New Years flood. During that event, increases of floc size with depth are evident. In 1997, higher sediment concentrations associated with the significantly larger discharge likely allowed flocs to grow substantially as they sank through the plume, whereas in 1998 low concentrations precluded significant increases in floc size with depth. These observations do not support the hypothesis that concentration controls maximal floc size; rather they indicate that the growth rate of flocs is a function of concentration. Using a published relationship between floc size and settling velocity for the Eel shelf suggests that approximately three fourths of the sediment in the plume was packaged as flocs during the 1998 floods.

Physical oceanography of the Amazon shelf

Abstract The Amazon shelf is subject to energetic forcing from a number of different sources, including near-resonant semi-diurnal tides, large buoyancy flux from the Amazon River discharge, wind stress from the northeasterly tradewinds and strong along-shelf flow associated with the North Brazil Current. Although the large volume of river discharge produces a pronounced salinity anomaly, the water motions on the shelf are dominated by the other forcing factors. Tidal velocities of up to 200 cm s−1 are generally oriented in the cross-shelf direction. Tide-induced mixing influences the position and structure of the bottom salinity front that separates the well-mixed nearshore region from the stratified plume. High concentrations of suspended sediment trapped along the frontal zone increase the stability of the tidal boundary layer and thus reduce the bottom stress. At subtidal frequencies, motion is primarily along-shelf toward the northwest, both in the plume and in the ambient, high-salinity water of the outer-shelf. The plume is generally 5–10 m thick, with a salinity of 20–30 psu. The along-shelf velocity within the plume varies as a function of the along-shelf wind stress. This variability results in large temporal variations in plume structure and freshwater content on the shelf. The net northwestward motion of the Amazon plume and of the ambient shelf water appears to be the result of a large-scale pressure gradient associated with the North Brazil Current system.

Modeling the lateral circulation in straight, stratified estuaries

Abstract The dynamics of lateral circulation in an idealized, straight estuary under varying stratification conditions is investigated using a three-dimensional, hydrostatic, primitive equation model in order to determine the importance of lateral circulation to the momentum budget within the estuary. For all model runs, lateral circulation is about 4 times as strong during flood tides as during ebbs. This flood–ebb asymmetry is due to a feedback between the lateral circulation and the along-channel tidal currents, as well as to time-varying stratification over a tidal cycle. As the stratification is increased, the lateral circulation is significantly reduced because of the adverse pressure gradient set up by isopycnals being tilted by the lateral flow itself. When rotation is included, a time-dependent, cross-channel Ekman circulation is driven, and the tidally averaged, bottom lateral circulation is enhanced toward the right bank (when looking toward the ocean in the Northern Hemisphere). This asymmetry...

Sediment Transport and Trapping in the Hudson River Estuary

The Hudson River estuary has a pronounced turbidity maximum zone, in which rapid, short-term deposition of sediment occurs during and following the spring freshet. Water-column measurements of currents and suspended sediment were performed during the spring of 1999 to determine the rate and mechanisms of sediment transport and trapping in the estuary. The net convergence of sediment in the lower estuary was approximately 300,000 tons, consistent with an estimate based on sediment cores. The major input of sediment from the watershed occurred during the spring freshet, as expected. Unexpected, however, was that an even larger quantity of sediment was transported landward into the estuary during the 3-mo observation period. The landward movement was largely accomplished by tidal pumping (i.e., the correlation between concentration and velocity at tidal frequencies) during spring tides, when the concentrations were 5 to 10 times higher than during neap tides. The landward flux is not consistent with the long-term sediment budget, which requires a seaward flux at the mouth to account for the excess input from the watershed relative to net accumulation. The anomalous, landward transport in 1999 occurred in part because the freshet was relatively weak, and the freshet occurred during neapetides when sediment resuspension was minimal. An extreme freshet occurred during 1998, which may have provided a repository of sediment just seaward of the mouth that re-entered the estuary in 1999. The amplitude of the spring freshet and its timing with respect to the spring-neap cycle cause large interannual variations in estuarine sediment flux. These variations can result in the remobilization of previously deposited sediment, the mass of which may exceed the annual inputs from the watershed.

Shear Instability in a Highly Stratified Estuary

Abstract Shear instability is found to be the principal mechanism of vertical exchange within the pycnocline of a salt wedge estuary. A field program involving high-resolution velocity and density measurements, as well as high-frequency acoustic imagery, allowed direct comparison of instantaneous Richardson number distributions to the occurrence of shear instability. The theoretical stability threshold of 0.25 is consistent with the measurements, based on estimates of gradients that contain the mean as well as fluctuations due to internal waves. An effective stability threshold based on mean gradients is found to be approximately one-third, reflecting a significant contribution of internal wave shear. The integral effect of the mixing process is to homogenize the gradients of velocity and density, producing linear profiles of these quantities across the pycnocline. A turbulent Prandtl number of unity is suggested by the vertical distributions of velocity and density during periods of active vertical mixin...