The boundary layer equations for plane, incompressible, and steady flow are 

$$\matrix{ {u{{\partial u} \over {\partial x}} + v{{\partial u} \over {\partial y}} = - {1 \over \varrho }{{\partial p} \over {\partial x}} + v{{{\partial ^2}u} \over {\partial {y^2}}},} \cr {0 = {{\partial p} \over {\partial y}},} \cr {{{\partial u} \over {\partial x}} + {{\partial v} \over {\partial y}} = 0.} \cr }$$

Boundary Layer Theory

Seagrass meadows are some of the most productive ecosystems on Earth. An analysis of organic carbon data from just under one thousand seagrass meadows indicates that, globally, these systems could store between 4.2 and 8.4 Pg carbon.

Seagrass ecosystems as a globally significant carbon stock

Coastal populations and wetlands have been intertwined for centuries, whereby humans both influence and depend on the extensive ecosystem services that wetlands provide. Although coastal wetlands have long been considered vulnerable to sea-level rise, recent work has identified fascinating feedbacks between plant growth and geomorphology that allow wetlands to actively resist the deleterious effects of sea-level rise. Humans alter the strength of these feedbacks by changing the climate, nutrient inputs, sediment delivery and subsidence rates. Whether wetlands continue to survive sea-level rise depends largely on how human impacts interact with rapid sea-level rise, and socio-economic factors that influence transgression into adjacent uplands.

Tidal wetland stability in the face of human impacts and sea-level rise

Renewable fresh water comprises a tiny fraction of the global water pool but is the foundation for life in terrestrial and freshwater ecosystems. The benefits to humans of renewable fresh water include water for drinking, irrigation, and industrial uses, for production of fish and waterfowl, and for such instream uses as recreation, transportation, and waste disposal.

In the coming century, climate change and a growing imbalance among freshwater supply, consumption, and population will alter the water cycle dramatically. Many regions of the world are already limited by the amount and quality of available water. In the next 30 yr alone, accessible runoff is unlikely to increase more than 10%, but the earth's population is projected to rise by approximately one-third. Unless the efficiency of water use rises, this imbalance will reduce freshwater ecosystem services, increase the number of aquatic species facing extinction, and further fragment wetlands, rivers, deltas, and estuaries.

Based on the scientific evidence currently available, we conclude that: (1) over half of accessible freshwater runoff globally is already appropriated for human use; (2) more than 1 × 109 people currently lack access to clean drinking water and almost 3 × 109 people lack basic sanitation services; (3) because the human population will grow faster than increases in the amount of accessible fresh water, per capita availability of fresh water will decrease in the coming century; (4) climate change will cause a general intensification of the earth's hydrological cycle in the next 100 yr, with generally increased precipitation, evapotranspiration, and occurrence of storms, and significant changes in biogeochemical processes influencing water quality; (5) at least 90% of total water discharge from U.S. rivers is strongly affected by channel fragmentation from dams, reservoirs, interbasin diversions, and irrigation; and (6) globally, 20% of freshwater fish species are threatened or extinct, and freshwater species make up 47% of all animals federally endangered in the United States.

The growing demands on freshwater resources create an urgent need to link research with improved water management. Better monitoring, assessment, and forecasting of water resources will help to allocate water more efficiently among competing needs. Currently in the United States, at least six federal departments and 20 agencies share responsibilities for various aspects of the hydrologic cycle. Coordination by a single panel with members drawn from each department, or by a central agency, would acknowledge the diverse pressures on freshwater systems and could lead to the development of a well-coordinated national plan.

https://scholarworks.umt.edu/cgi/viewcontent.cgi?article=1108&context=ntsg_pubs

Water in a changing world

Perturbations in ecosystems consist of a sequence of 2 events: the disturbance, marked by the application of the disturbing forces, and the response shown by the biota to the damage inflicted by the disturbance. The disturbance must be effectively characterized, without confounding it with the response, for progress to be made in the study of the disturbance ecology of streams. A disturbance may take the form of a pulse, a press, or a ramp, and the consequent trajectory of the response may be a pulse, a press, or a ramp.Floods and droughts are the major forms of natural disturbance in flowing waters and, although the effects of floods have been relatively well studied, those of droughts have been largely neglected. Floods accentuate downstream and lateral transport links, often with damaging consequences, whereas droughts fragment the continuity of streams. Both floods and droughts destroy and generate habitat patchiness and patchiness of the biota. During recovery, there are changes in the biotic...

Disturbance, patchiness, and diversity in streams

An expression for the critical shear stress noncohesive sediment is derived from the balance of forces on individual particles at the surface of a bed. The resulting equation, for a given grain size and density, depends on the near-bed drag force, lift force to drag force ratio, and particle angle of repose. Calculated values of the critical shear stress for uniformly sized sediment correspond closely to those determined from Shields' diagram. The initial motion problem for mixed grain sizes additionally depends on the relative protrusion of the grains into the flow and the particle angle of repose. The latter decreases when the diameter of a moving grain, D, is larger than the length scale of the bed roughness, ks (D/ks > 1), and increases when D/ks < 1, producing a corresponding decrease or increase in critical shear stress. Using the Miller and Byrne experimental relationship between D/ks and particle angle of repose, which is consistent with Shields' definition of initial motion, we obtain results that are in good agreement with the available experimental critical shear stress data for heterogeneous beds.

Calculations of the Critical Shear Stress for Motion of Uniform and Heterogeneous Sediments

The physical processes that control mineral sediment deposition on a mesotidal salt marsh surface on the Atlantic Coast of Virginia were characterized through a series of measurements of sediment concentration, flow velocity, turbulence, water surface elevation, marsh topography and particle size distributions of sediment deposited on the marsh surface. The comprehensive nature of the data set allowed assessment of the temporal and spatial variability in marsh surface deposition, the variability in depositional processes among tides of different amplitudes, as well as the specific processes that control deposition on this tidal marsh. Through three different types of measurements, it was found that sediment deposition occurred on the marsh surface during rising tides at tidal elevations ranging from those barely flooding the creek bank to high spring tides, and that sediment was not remobilized by tidal flows after initial deposition. Sediment deposition occurred on this marsh surface largely because fine sediment in suspension formed flocs. Analysis of inorganic grain size distributions of sediment deposited within 8 m of the tidal creek indicated that 70–80% of this sediment was deposited in a flocculated form. The rest (particles larger than 20 μm) were deposited as individual particles. In the marsh interior, 25 m from the tidal creek, single grain settling predominated. Reduction of turbulence levels within the vegetation canopy on the marsh also promoted particle settling. The processes controlling sediment deposition did not vary among tides. However, suspended sediment concentrations near the creek bank increased with increasing tidal amplitude, consequently promoting higher rates of deposition on higher tides.

Flow and Sediment Transport on a Tidal Salt Marsh Surface

The wavelength, height, and steepness of ripples formed under oscillatory flows in flume and field studies are reexamined to construct a simple and accurate method of predicting these ripple properties. Ripples with wavelengths proportional to near-bed wave orbital diameter (orbital ripples), predominant in laboratory experiments, are found to have heights in excess of the thickness of the wave boundary layer. Ripples with wavelengths that are roughly proportional to grain size and nearly independent of orbital diameter (anorbital ripples), which predominate in the field, have heights at least several times smaller than wave boundary layer thickness. Relating wave boundary layer height to the generally more easily estimated wave orbital diameter, a set of expressions are developed for predicting ripple type and geometry based on mean grain size, wave orbital diameter, and estimated anorbital ripple height. This method provides a good characterization of ripple wavelength and steepness for a large set of combined field and flume data.

Ripple geometry in wave-dominated environments

At sites near the Brazos River, Texas, an iridium anomaly and the paleontologic Cretaceous-Tertiary boundary directly overlie a sandstone bed in which coarse-grained sandstone with large clasts of mudstone and reworked carbonate nodules grades upward to wave ripple-laminated, very fine grained sandstone. This bed is the only sandstone bed in a sequence of uppermost Cretaceous to lowermost Paleocene mudstone that records about 1 million years of quiet water deposition in midshelf to outer shelf depths. Conditions for depositing such a sandstone layer at these depths are most consistent with the occurrence of a tsunami about 50 to 100 meters high. The most likely source for such a tsunami at the Cretaceous-Tertiary boundary is a bolidewater impact.

https://science.sciencemag.org/content/sci/241/4865/567.full.pdf

A Tsunami Deposit at the Cretaceous-Tertiary Boundary in Texas

The equations of motion for a sediment grain near a noncohesive bed and those for the local fluid flow are combined to produce a set of differential equations that can be solved numerically to describe the trajectory of a saltating grain as a function of time. The lift coefficient is set based on a reanalysis of data produced by Chepil, and the other parameters of the problem are set using standard fluid mechanical relationships; the initial velocity and position are specified with a separate model. The heights of the resulting trajectories are found to be significantly lower than available measurements would indicate; therefore two extensions of the model are examined: the effect that spin lift and form lift have on a series of trajectories, and the effect of partially elastic collisions between a moving grain and the bed over which it is traveling. A model that includes the second process is less complicated than one that includes the first, and it yields trajectories that agree very well with available experimental measurements when a rebound coefficient that varies around 0.5 and depends on the impact momentum is used. We conclude that the model provides a reasonable representation of saltation in water and that both fluid-solid and solid-solid interactions are required to reproduce the parameters of measured trajectories.

Patricia L. Wiberg

Papers

Calculations of the Critical Shear Stress for Motion of Uniform and Heterogeneous Sediments

Flow and Sediment Transport on a Tidal Salt Marsh Surface

Ripple geometry in wave-dominated environments

A Tsunami Deposit at the Cretaceous-Tertiary Boundary in Texas

A theoretical model for saltating grains in water