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W. Rockwell
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W. Rockwell
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ArticleQuantifying vertical mixing in estuaries(Springer, 2008-10-21) Geyer, W. Rockwell ; Scully, Malcolm E. ; Ralston, David K.Estuarine turbulence is notable in that both the dissipation rate and the buoyancy frequency extend to much higher values than in other natural environments. The high dissipation rates lead to a distinct inertial subrange in the velocity and scalar spectra, which can be exploited for quantifying the turbulence quantities. However, high buoyancy frequencies lead to small Ozmidov scales, which require high sampling rates and small spatial aperture to resolve the turbulent fluxes. A set of observations in a highly stratified estuary demonstrate the effectiveness of a vessel-mounted turbulence array for resolving turbulent processes, and for relating the turbulence to the forcing by the Reynolds-averaged flow. The observations focus on the ebb, when most of the buoyancy flux occurs. Three stages of mixing are observed: (1) intermittent and localized but intense shear instability during the early ebb; (2) continuous and relatively homogeneous shear-induced mixing during the mid-ebb, and weakly stratified, boundary-layer mixing during the late ebb. The mixing efficiency as quantified by the flux Richardson number Rf was frequently observed to be higher than the canonical value of 0.15 from Osborn (J Phys Oceanogr 10:83–89, 1980). The high efficiency may be linked to the temporal–spatial evolution of shear instabilities.
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ArticleTurbulent energy production and entrainment at a highly stratified estuarine front(American Geophysical Union, 2004-05-01) MacDonald, Daniel G. ; Geyer, W. RockwellRates of turbulent kinetic energy (TKE) production and buoyancy flux in the region immediately seaward (~1 km) of a highly stratified estuarine front at the mouth of the Fraser River (British Columbia, Canada) are calculated using a control volume approach. The calculations are based on field data obtained from shipboard instrumentation, specifically velocity data from a ship mounted acoustic Doppler current profiler (ADCP), and salinity data from a towed conductivity-temperature-depth (CTD) unit. The results allow for the calculation of vertical velocities in the water column, and the total vertical transport of salt and momentum. The vertical turbulent transport quantities (inline equation, inline equation) can then be estimated as the difference between the total transport and the advective transport. Estimated production is on the order of 10−3 m2 s−3, yielding a value of ɛ(νN2)−1 on the order of 104. This rate of TKE production is at the upper limit of reported values for ocean and coastal environments. Flux Richardson numbers in this highly energetic system generally range from 0.15 to 0.2, with most mixing occurring at gradient Richardson numbers slightly less than inline equation. These values compare favorably with other values in the literature that are associated with turbulence observations from regimes characterized by scales several orders of magnitude smaller than are present in the Fraser River.
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PreprintObservations and modeling of wave-supported sediment gravity flows on the Po prodelta and comparison to prior observations from the Eel shelf( 2006-11-14) Traykovski, Peter A. ; Wiberg, Patricia L. ; Geyer, W. RockwellA mooring and tripod array was deployed from the fall of 2002 through the spring of 2003 on the Po prodelta to measure sediment transport processes associated with sediment delivered from the Po River. Observations on the prodelta revealed wave-supported gravity flows of high concentration mud suspensions that are dynamically and kinematically similar to those observed on the Eel shelf (Traykovski et al., 2000). Due to the dynamic similarity between the two sites, a simple one-dimensional across-shelf model with the appropriate bottom boundary condition was used to examine fluxes associated with this transport mechanism at both locations. To calculate the sediment concentrations associated with the wave-dominated and wave-current resuspension, a bottom boundary condition using a reference concentration was combined with an “active layer” formulation to limit the amount of sediment in suspension. Whereas the wave-supported gravity flow mechanism dominates the transport on the Eel shelf, on the Po prodelta flux due to this mechanism is equal in magnitude to transport due to wave resuspension and wind-forced mean currents in cross-shore direction. Southward transport due to wave resuspension and wind forced mean currents move an order of magnitude more sediment along-shore than the downslope flux associated wave-supported gravity flows.
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ArticleTidal and spring-neap variations in horizontal dispersion in a partially mixed estuary(American Geophysical Union, 2008-07-18) Geyer, W. Rockwell ; Chant, Robert J. ; Houghton, R.A sequence of dye releases in the Hudson River estuary provide a quantitative assessment of horizontal dispersion in a partially mixed estuary. Dye was released in the bottom boundary layer on 4 separate occasions, with varying tidal phase and spring-neap conditions. The three-dimensional distribution of dye was monitored by two vessels with in situ, profiling fluorometers. The three-dimensional spreading of the dye was estimated by calculating the time derivative of the second moment of the dye in the along-estuary, cross-estuary and vertical directions. The average along-estuary dispersion rate was about 100 m2/s, but maximum rates up to 700 m2/s occurred during ebb tides, and minimum rates occurred during flood. Vertical shear dispersion was the principal mechanism during neap tides, but transverse shear dispersion became more important during springs. Suppression of mixing across the pycnocline limited the vertical extent of the patch in all but the maximum spring-tide conditions, with vertical diffusivities in the pycnocline estimated at 4 × 10−5 m2/s during neaps. The limited vertical extent of the dye patch limited the dispersion of the dye relative to the overall estuarine dispersion rate, which was an order of magnitude greater than that of the dye. This study indicates that the effective dispersion of waterborne material in an estuary depends sensitively on its vertical distribution as well as the phase of the spring-neap cycle.
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ArticleRapid sediment deposition and fine-scale strata formation in the Hudson estuary(American Geophysical Union, 2004-04-21) Traykovski, Peter A. ; Geyer, W. Rockwell ; Sommerfield, Christopher K.A 9 month time series of tripod-mounted optical and acoustic measurements of sediment concentration and bed elevation was used to examine depositional processes in relationship to hydrodynamic variables in the Hudson River estuary. A series of cores was also taken directly under and adjacent to the acoustic measurements to examine the relation between the depositional processes and the resulting fine-scale stratigraphy. The measurements reveal that deposition occurs as a result of sediment flux convergence behind a salinity front and that the accumulation rates are sufficient to deposit up to 25 cm of new high-porosity sediment in a single ebb-tidal phase. Subsequent dewatering and erosion reduces the thickness of the initial deposit to several centimeters. These depositional events were only observed on spring tides. Ten depositional events during two spring tidal cycles produced a seasonal deposit of 18 cm, consistent with estimates of seasonal deposition from cores. A proxy for near-bed suspended grain size variations was estimated from the combined acoustic and optical measurements, implying that the erosional processes resuspend only the finer-grained sediments, thus leaving behind silt and very fine grained sand beds. The thickness of the deposited homogenous clayey silt beds, and the vertical separation between beds interlaminated with silt and very fine sand, are roughly consistent with the acoustic measurements of changes in bed elevations during deposition and erosion. The variability in individual bed thickness is the result of variations of processes over an individual tidal cycle and is not a product of variations over the spring neap fortnightly timescale.
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ArticleFlood dispersal and deposition by near-bed gravitational sediment flows and oceanographic transport : a numerical modeling study of the Eel River shelf, northern California(American Geophysical Union, 2005-09-30) Harris, Courtney K. ; Traykovski, Peter A. ; Geyer, W. RockwellA large flood of the Eel River, northern California, created a thick sediment deposit between water depths of 50 and 70 m in January 1997. The freshwater plume, however, confined sediment delivery to water depths shallower than 30 m. Mechanisms proposed to explain the apparent cross-shelf transport include dispersal by oceanographic currents, resuspension by energetic waves, and gravitationally forced transport of a thin layer of fluidized mud. Field observations indicate that these processes were all active but cannot determine their relative significance or whether these mechanisms alone explain the location, size, and timing of deposition. Approximately 30% of the sediment delivered by the Eel River is accounted for in the midshelf mud bed and inner shelf, but the fate of the remaining 70% is uncertain. A three-dimensional, hydrodynamic model was used to examine potential mechanisms of sediment transport on the Eel River shelf. The model includes suspended sediment transport and was modified to account for a thin, near-bed layer of fluidized mud. It was used to simulate flood dispersal on the Eel River shelf, to compare the relative importance of transport within the near-bed fluid mud layer to suspended sediment transport, and to evaluate sediment budgets for floods. Settling properties of fine-grained sediment, both within the flood plume and the fluid mud layer, critically impact depositional patterns. To a lesser degree, wind-driven ocean currents influence the volume of sediment that escapes the shelf, and wave magnitude affects the cross-shelf location of flood deposits. Though dilute suspension accounts for a large fraction of total flux, cross-shelf transport by gravitational forcing appears necessary to produce a midshelf mud deposit similar in volume, location, and timing to those seen offshore of the Eel River.
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ArticleNumerical modeling of an estuary : a comprehensive skill assessment(American Geophysical Union, 2005-05-04) Warner, John C. ; Geyer, W. Rockwell ; Lerczak, James A.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 timeseries 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-ε, k-ω, and k-kl.
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ArticleAsymmetric tidal mixing due to the horizontal density gradient(American Meteorological Society, 2008-02) Li, Ming ; Trowbridge, John H. ; Geyer, W. RockwellStratification and turbulent mixing exhibit a flood–ebb tidal asymmetry in estuaries and continental shelf regions affected by horizontal density gradients. The authors use a large-eddy simulation (LES) model to investigate the penetration of a tidally driven bottom boundary layer into stratified water in the presence of a horizontal density gradient. Turbulence in the bottom boundary layer is driven by bottom stress during flood tides, with low-gradient (Ri) and flux (Rf) Richardson numbers, but by localized shear during ebb tides, with Ri = ¼ and Rf = 0.2 in the upper half of the boundary layer. If the water column is unstratified initially, the LES model reproduces periodic stratification associated with tidal straining. The model results show that the energetics criterion based on the competition between tidal straining and tidal stirring provides a good prediction for the onset of periodic stratification, but the tidally averaged horizontal Richardson number Rix has a threshold value of about 0.2, which is lower than the 3 suggested in a recent study. Although the tidal straining leads to negative buoyancy flux on flood tides, the authors find that for typical values of the horizontal density gradient and tidal currents in estuaries and shelf regions, buoyancy production is much smaller than shear production in generating turbulent kinetic energy.
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ArticleSubtidal salinity and velocity in the Hudson River estuary : observations and modeling(American Meteorological Society, 2008-04) Ralston, David K. ; Geyer, W. Rockwell ; Lerczak, James A.A tidally and cross-sectionally averaged model based on the temporal evolution of the quasi-steady Hansen and Rattray equations is applied to simulate the salinity distribution and vertical exchange flow along the Hudson River estuary. The model achieves high skill at hindcasting salinity and residual velocity variation during a 110-day period in 2004 covering a wide range of river discharges and tidal forcing. The approach is based on an existing model framework that has been modified to improve model skill relative to observations. The external forcing has been modified to capture meteorological time-scale variability in salinity, stratification, and residual velocity due to sea level fluctuations at the open boundary and along-estuary wind stress. To reflect changes in vertical mixing due to stratification, the vertical mixing coefficients have been modified to use the bottom boundary layer height rather than the water depth as an effective mixing length scale. The boundary layer parameterization depends on the tidal amplitude and the local baroclinic pressure gradient through the longitudinal Richardson number, and improves the model response to spring–neap variability in tidal amplitude during periods of high river discharge. Finally, steady-state model solutions are evaluated for both the Hudson River and northern San Francisco Bay over a range of forcing conditions. Agreement between the model and scaling of equilibrium salinity intrusions lends confidence that the approach is transferable to other estuaries, despite significant differences in bathymetry. Discrepancies between the model results and observations at high river discharge are indicative of limits at which the formulation begins to fail, and where an alternative approach that captures two-layer dynamics would be more appropriate.
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ArticleThe temporal response of the length of a partially stratified estuary to changes in river flow and tidal amplitude(American Meteorological Society, 2009-04) Lerczak, James A. ; Geyer, W. Rockwell ; Ralston, David K.The temporal response of the length of a partially mixed estuary to changes in freshwater discharge Qf and tidal amplitude UT is studied using a 108-day time series collected along the length of the Hudson River estuary in the spring and summer of 2004 and a long-term (13.4 yr) record of Qf, UT, and near-surface salinity. When Qf was moderately high, the tidally averaged length of the estuary L5, here defined as the distance from the mouth to the up-estuary location where the vertically averaged salinity is 5 psu, fluctuated by more than 47 km over the spring–neap cycle, ranging from 28 to >75 km. During low flow periods, L5 varied very little over the spring–neap cycle and approached a steady length. The response is quantified and compared to predictions of a linearized model derived from the global estuarine salt balance. The model is forced by fluctuations in Qf and UT relative to average discharge Qo and tidal amplitude UTo and predicts the linear response time scale τ and the steady-state length Lo for average forcing. Two vertical mixing schemes are considered, in which 1) mixing is proportional to UT and 2) dependence of mixing on stratification is also parameterized. Based on least squares fits between L5 and estuary length predicted by the model, estimated τ varied by an order of magnitude from a period of high average discharge (Qo = 750 m3 s−1, τ = 4.2 days) to a period of low discharge (Qo = 170 m3 s−1, τ = 40.4 days). Over the range of observed discharge, Lo Qo−0.30±0.03, consistent with the theoretical scaling for an estuary whose landward salt flux is driven by vertical estuarine exchange circulation. Estimated τ was proportional to the discharge advection time scale (LoA/Qo, where A is the cross-sectional area of the estuary). However, τ was 3–4 times larger than the theoretical prediction. The model with stratification-dependent mixing predicted variations in L5 with higher skill than the model with mixing proportional to UT. This model provides insight into the time-dependent response of a partially stratified estuary to changes in forcing and explains the strong dependence of the amplitude of the spring–neap response on freshwater discharge. However, the utility of the linear model is limited because it assumes a uniform channel, and because the underlying dynamics are nonlinear, and the forcing Qf and UT can undergo large amplitude variations. River discharge, in particular, can vary by over an order of magnitude over time scales comparable to or shorter than the response time scale of the estuary.
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ArticleHydraulic control of a highly stratified estuarine front(American Meteorological Society, 2005-03) MacDonald, Daniel G. ; Geyer, W. RockwellObservations at the mouth of the Fraser River (British Columbia, Canada) indicate an abrupt frontal transition between unstratified river outflow and a highly stratified river plume with differences in salinity greater than 25 psu across a few meters in the vertical direction and several hundred meters in the horizontal direction. The front roughly follows a natural break in the bathymetry, crossing the channel at an angle of approximately 45°, and is essentially stationary for a period of approximately 3.5 h centered on the low tide following the larger of two daily ebbs. The location of the front is coincident with observations of significantly supercritical internal Froude numbers at the front, based on velocities in the along-flow direction. This observation contradicts the one-dimensional theory, which indicates that the Froude number should be 1. However, because the front is oriented obliquely to the outflow, a coordinate system can be selected that is normal to the front and for which a critical Froude number of 1 is obtained. This indicates that a Froude angle, similar in application to a Mach angle for transonic flows, can be used to determine critical conditions when the front is oblique to the principal flow direction.
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ArticleMechanisms driving the time-dependent salt flux in a partially stratified estuary(American Meteorological Society, 2006-12) Lerczak, James A. ; Geyer, W. RockwellThe subtidal salt balance and the mechanisms driving the downgradient salt flux in the Hudson River estuary are investigated using measurements from a cross-channel mooring array of current meters, temperature and conductivity sensors, and cross-channel and along-estuary shipboard surveys obtained during the spring of 2002. Steady (subtidal) vertical shear dispersion, resulting from the estuarine exchange flow, was the dominant mechanism driving the downgradient salt flux, and varied by over an order of magnitude over the spring–neap cycle, with maximum values during neap tides and minimum values during spring tides. Corresponding longitudinal dispersion rates were as big as 2500 m2 s−1 during neap tides. The salinity intrusion was not in a steady balance during the study period. During spring tides, the oceanward advective salt flux resulting from the net outflow balanced the time rate of change of salt content landward of the study site, and salt was flushed out of the estuary. During neap tides, the landward steady shear dispersion salt flux exceeded the oceanward advective salt flux, and salt entered the estuary. Factor-of-4 variations in the salt content occurred at the spring–neap time scale and at the time scale of variations in the net outflow. On average, the salt flux resulting from tidal correlations between currents and salinity (tidal oscillatory salt flux) was an order of magnitude smaller than that resulting from steady shear dispersion. During neap tides, this flux was minimal (or slightly countergradient) and was due to correlations between tidal currents and vertical excursions of the halocline. During spring tides, the tidal oscillatory salt flux was driven primarily by oscillatory shear dispersion, with an associated longitudinal dispersion rate of about 130 m2 s−1.
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ArticleEstuarine boundary layer mixing processes : insights from dye experiments(American Meteorological Society, 2007-07) Chant, Robert J. ; Geyer, W. Rockwell ; Houghton, Robert ; Hunter, Elias J. ; Lerczak, James A.A series of dye releases in the Hudson River estuary elucidated diapycnal mixing rates and temporal variability over tidal and fortnightly time scales. Dye was injected in the bottom boundary layer for each of four releases during different phases of the tide and of the spring–neap cycle. Diapycnal mixing occurs primarily through entrainment that is driven by shear production in the bottom boundary layer. On flood the dye extended vertically through the bottom mixed layer, and its concentration decreased abruptly near the base of the pycnocline, usually at a height corresponding to a velocity maximum. Boundary layer growth is consistent with a one-dimensional, stress-driven entrainment model. A model was developed for the vertical structure of the vertical eddy viscosity in the flood tide boundary layer that is proportional to u2*/N∞, where u* and N∞ are the bottom friction velocity and buoyancy frequency above the boundary layer. The model also predicts that the buoyancy flux averaged over the bottom boundary layer is equal to 0.06N∞u2* or, based on the structure of the boundary layer equal to 0.1NBLu2*, where NBL is the buoyancy frequency across the flood-tide boundary layer. Estimates of shear production and buoyancy flux indicate that the flux Richardson number in the flood-tide boundary layer is 0.1–0.18, consistent with the model indicating that the flux Richardson number is between 0.1 and 0.14. During ebb, the boundary layer was more stratified, and its vertical extent was not as sharply delineated as in the flood. During neap tide the rate of mixing during ebb was significantly weaker than on flood, owing to reduced bottom stress and stabilization by stratification. As tidal amplitude increased ebb mixing increased and more closely resembled the boundary layer entrainment process observed during the flood. Tidal straining modestly increased the entrainment rate during the flood, and it restratified the boundary layer and inhibited mixing during the ebb.
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ArticleThe influence of lateral advection on the residual estuarine circulation : a numerical modeling study of the Hudson River Estuary(American Meteorological Society, 2009-01) Scully, Malcolm E. ; Geyer, W. Rockwell ; Lerczak, James A.In most estuarine systems it is assumed that the dominant along-channel momentum balance is between the integrated pressure gradient and bed stress. Scaling the amplitude of the estuarine circulation based on this balance has been shown to have predictive skill. However, a number of authors recently highlighted important nonlinear processes that contribute to the subtidal dynamics at leading order. In this study, a previously validated numerical model of the Hudson River estuary is used to examine the forces driving the residual estuarine circulation and to test the predictive skill of two linear scaling relationships. Results demonstrate that the nonlinear advective acceleration terms contribute to the subtidal along-channel momentum balance at leading order. The contribution of these nonlinear terms is driven largely by secondary lateral flows. Under a range of forcing conditions in the model runs, the advective acceleration terms nearly always act in concert with the baroclinic pressure gradient, reinforcing the residual circulation. Despite the strong contribution of the nonlinear advective terms to the subtidal dynamical balance, a linear scaling accurately predicts the strength of the observed residual circulation in the model. However, this result is largely fortuitous, as this scaling does not account for two processes that are fundamental to the estuarine circulation. The skill of this scaling results because of the compensatory relationship between the contribution of the advective acceleration terms and the suppression of turbulence due to density stratification. Both of these processes, neither of which is accounted for in the linear scaling, increase the residual estuarine circulation but have an opposite dependence on tidal amplitude and, consequently, strength of stratification.