Numerical Methods for Scientists and Engineers

Fifty years of hyporheic zone research have shown the important role played by the hyporheic zone as an interface between groundwater and surface waters. However, it is only in the last two decades that what began as an empirical science has become a mechanistic science devoted to modeling studies of the complex fluid dynamical and biogeochemical mechanisms occurring in the hyporheic zone. These efforts have led to the picture of surface-subsurface water interactions as regulators of the form and function of fluvial ecosystems. Rather than being isolated systems, surface water bodies continuously interact with the subsurface. Exploration of hyporheic zone processes has led to a new appreciation of their wide reaching consequences for water quality and stream ecology. Modern research aims toward a unified approach, in which processes occurring in the hyporheic zone are key elements for the appreciation, management, and restoration of the whole river environment. In this unifying context, this review summarizes results from modeling studies and field observations about flow and transport processes in the hyporheic zone and describes the theories proposed in hydrology and fluid dynamics developed to quantitatively model and predict the hyporheic transport of water, heat, and dissolved and suspended compounds from sediment grain scale up to the watershed scale. The implications of these processes for stream biogeochemistry and ecology are also discussed.

Hyporheic flow and transport processes: Mechanisms, models, and biogeochemical implications

Attention is given to the properties of sediment beds over the full range of conditions (silts to gravel), in particular the effect of fine silt on the bed composition and on initiation of motion (critical conditions) is discussed. High-quality bed-load transport data sets are identified and analyzed, showing that the bed-load transport in the sand range is related to velocity to power 2.5. The bed-load transport is not much affected by particle size. The prediction of bed roughness is addressed and the prediction of bed-load transport in steady river flow is extended to coastal flow applying an intrawave approach. Simplified bed-load transport formulas are presented, which can be used to obtain a quick estimate of bed-load transport in river and coastal flows. It is shown that the sediment transport of fine silts to coarse sand can be described in a unified model framework using fairly simple expressions. The proposed model is fully predictive in the sense that only the basic hydrodynamic parameters (dep...

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Unified view of sediment transport by currents and waves. I: Initiation of motion, bed roughness, and bed-load transport

https://coast.nd.edu/reports_papers/2010_CE_v068.pdf

Modeling hurricane waves and storm surge using integrally-coupled, scalable computations

http://www.vliz.be/imisdocs/publications/ocrd/267179.pdf

Erosion of mud/sand mixtures

Data from a three-year long field study of fine sediment dynamics in Cleveland Bay show that wave-induced liquefaction of the fine sediment bed on the seafloor in shallow water was the main process causing bed erosion under small waves during tradewinds, and that shear-induced erosion prevailed during cyclonic conditions. These data were used to verify a model of fine sediment dynamics that calculates sediment resuspension by both excess shear stress and wave-induced liquefaction of the bed. For present land-use conditions, the amount of riverine sediments settling on the bay may exceed by 50–75% the amount of sediment exported from the bay. Sediment is thus accumulating in the bay on an annual basis, which in turn may degrade the fringing coral reefs. For those years when a tropical cyclone impacted the bay there may be a net sediment outflow from the bay. During the dry, tradewind season, fine sediment was progressively winnowed out of the shallow, reefal waters.

Importance of wave-induced bed liquefaction in the fine sediment budget of Cleveland Bay, Great Barrier Reef

Measurements of wave and suspended sediment concentration (SSC) were conducted near the 5-m isobath on the muddy inner shelf fronting Atchafalaya Bay, Louisiana, during Hurricane Claudette. The data show that wave and current activity resuspended large quantities of sediment, with SSC R 0.5 kg/m 3 throughout the water column. In the waning phase of the storm, settling generated a suspension layer, with concentrations over 1.7 kg/m 3 measured as high as 1 m above the bottom. Numerical simulations of post-storm sediment settling showed that observations are consistent with a high-density fluid mud layer (SSC between 10 and 20 kg/m 3 ), and separated from the upper water column by a lutocline located at about 1 m above the bottom. The formation of the fluid-mud layer is correlated with strong, broad-spectrum wave dissipation, consistent with the hypothesis that surface–interface wave interaction plays an important part in the energy transfer from the surface to the soft bottom. 2004 Elsevier Ltd. All rights reserved.

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Wave–sediment interaction on a muddy inner shelf during Hurricane Claudette

The threshold condition for the incipient transport of sediment linking cohesionless to cohesive size ranges is revisited using known concepts. The functional dependence of the threshold or critical shear stress on the principal parameters characterizing the sediment bed is examined, while recognizing that the actual relationships among these parameters remain largely unknown. For marine muds, until further experimental evidence is obtained, it is argued that erosion shear stress formulations for cohesionless sediment transport should be restricted to sediments containing grains larger than about 20 um, and empirical erosion shear strength formulations be applied to sediments smaller than this size. Given this limit, the classical definition of silt size range (2 um to 62um) based on the plastic properties of soil does not appear to be very useful in delineating the domains of cohesion-dominated and cchesionless sediment transport.

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Problems in Linking the Threshold Condition for the Transport of Cohesionless and Cohesive Sediment Grain

The compaction rate of suspended mud depends not only on the sediment concentration but also on the turbulent intensity. This effect appears to be due to the turbulence plugging micro-channels used in the dewatering process. The compaction rate decreases by a factor of up to 10 with increasing stirring or turbulence in the inhibited settling (fluid mud) range. Our findings are based on the results of laboratory experiments where this effect was measured directly, and on observations of the suspended sediment stratification cycle at tidal frequency in the Normanby River estuary, Australia.

The Role of Turbulence in the Settling of Mud Flocs

Tidal entrances constitute an important boundary condition for the coastal ocean regime. Based on data from 67 sandy entrances in Florida, morphodynamic relationships between tidal prism, entrance throat area, and ebb and flood delta volumes are revisited. The main source of sand in these deltas is the littoral zone as opposed to the river. It is found that, as a rule of thumb, the volume of a mature ebb delta is equal to one fifth of the prism at the spring range of tide. Data for the coasts of Florida taken together indicate that the volume of mature flood delta varies with one third power of the prism. The Atlantic Coast flood delta volumes by themselves do not show any correlation with the prism, presumably because entrance depths have been altered by dredging. A case study of the closure of a land barrier breach at Matanzas Inlet illustrates the application of the derived morphodynamic relationships between prism, throat area, and ebb delta volume. These relationships are useful for prediction of changes in the throat area and the ebb delta volume when morphologic changes occur over time scales consistent with the reestablishment of equilibrium.

Ashish J. Mehta

Papers

Importance of wave-induced bed liquefaction in the fine sediment budget of Cleveland Bay, Great Barrier Reef

Wave–sediment interaction on a muddy inner shelf during Hurricane Claudette

Problems in Linking the Threshold Condition for the Transport of Cohesionless and Cohesive Sediment Grain

The Role of Turbulence in the Settling of Mud Flocs

Morphodynamic relationships for ebb and flood delta volumes at Florida’s tidal entrances