Steady periodic water waves with constant vorticity: regularity and local bifurcation

This paper studies periodic traveling gravity waves at the free surface of water in a flow of constant vorticity over a flat bed. Using conformal mappings the free-boundary problem is transformed into a quasilinear pseudodifferential equation for a periodic function of one variable. The new formulation leads to a regularity result and, by use of bifurcation theory, to the existence of waves of small amplitude even in the presence of stagnation points in the flow.

A linear model for the structure of turbulence beneath surface water waves

The structure of turbulence in the ocean surface layer is investigated using a simplified semi-analytical model based on rapid-distortion theory. In this model, which is linear with respect to the turbulence, the flow comprises a mean Eulerian shear current, the Stokes drift of an irrotational surface wave, which accounts for the irreversible effect of the waves on the turbulence, and the turbulence itself, whose time evolution is calculated. By analysing the equations of motion used in the model, which are linearised versions of the Craik–Leibovich equations containing a ‘vortex force’, it is found that a flow including mean shear and a Stokes drift is formally equivalent to a flow including mean shear and rotation. In particular, Craik and Leibovich’s condition for the linear instability of the first kind of flow is equivalent to Bradshaw’s condition for the linear instability of the second. However, the present study goes beyond linear stability analyses by considering flow disturbances of finite amplitude, which allows calculating turbulence statistics and addressing cases where the linear stability is neutral. Results from the model show that the turbulence displays a structure with a continuous variation of the anisotropy and elongation, ranging from streaky structures, for distortion by shear only, to streamwise vortices resembling Langmuir circulations, for distortion by Stokes drift only. The TKE grows faster for distortion by a shear and a Stokes drift gradient with the same sign (a situation relevant to wind waves), but the turbulence is more isotropic in that case (which is linearly unstable to Langmuir circulations).

Water quality trends in the Windrush catchment: Nitrogen speciation and sediment interactions

For the predominantly agricultural River Windrush catchment, spatial variations in concentrations of nitrogen species and suspended sediment were strongly related to geology and land use. Temporal patterns of NO3- and NO2- concentrations during the three year study were highly correlated with seasonal variations in baseflow. Suspended sediment concentrations were mainly controlled by storm discharge. Variations in total ammonium concentrations reflected both flow controls. Suspended sediment effects total ammonium and organic nitrogen transport to the aquatic system, and in-stream cycling processes. Organic nitrogen did not display consistent seasonal variations, but concentrations occasionally exceeding those of NO3-. Overall, NO3- and organic nitrogen were the most important at 60% and -40%, of total nitrogen load, respectively. Future assessments of agriculture impact on river water quality should consider the total nitrogen load, and not solely that of NO3-.

Contribution of N Species and P Fractions to Stream Water Quality in Agricultural Catchments

The contribution from agricultural catchments to stream nitrogen and phosphorus concentrations was assessed by evaluation of the chemical composition of these nutrients in agricultural runoff for both surface and subsurface flow pathways. A range of land uses (grazed and ungrazed grassland, cereals, roots) in intensive agricultural systems was studied at scales from hillslope plots (0.5m2) to large catchment (>300km2). By fractionating the total nutrient load it was possible to establish that most of the phosphorus was transported in the unreactive (particulate and organic) fraction via surface runoff. This was true regardless of the scale of measurement. The form of the nitrogen load varied with land use and grazing intensity. High loads of dissolved inorganic nitrogen (with >90% transported as NH4-N) were recorded in surface runoff from heavily grazed land. In subsurface flow from small (2km2) subcatchments and in larger (>300 km2) catchments, organic nitrogen was found to be an important secondary constituent of the total nitrogen load, comprising 40% of the total annual load.

Modelling the impact of land use change on water quality in agricultural catchments

Export coefficient modelling was used to model the impact of agriculture on nitrogen and phosphorus loading on the surface waters of two contrasting agricultural catchments. The model was originally developed for the Windrush catchment where the highly reactive Jurassic limestone aquifer underlying the catchment is well connected to the surface drainage network, allowing the system to be modelled using uniform export coefficients for each nutrient source in the catchment, regardless of proximity to the surface drainage network. In the Slapton catchment, the hydrological path-ways are dominated by surface and lateral shallow subsurface flow, requiring modification of the export coefficient model to incorporate a distance-decay component in the export coefficients. The modified model was calibrated against observed total nitrogen and total phosphorus loads delivered to Slapton Ley from inflowing streams in its catchment. Sensitivity analysis was conducted to isolate the key controls on nutrient export in the modified model. The model was validated against long-term records of water quality, and was found to be accurate in its predictions and sensitive to both temporal and spatial changes in agricultural practice in the catchment. The model was then used to forecast the potential reduction in nutrient loading on Slapton Ley associated with a range of catchment management strategies. The best practicable environmental option (BPEO) was found to be spatial redistribution of high nutrient export risk sources to areas of the catchment with the greatest intrinsic nutrient retention capacity.

The role of rainfall intensity and soil in determining rates of flow through cryoturbated chalk

The effects of different water application rates (3, 10, 15 and 30 mm/h) and of topsoil removal on the rate of downward water movement through the cryoturbated chalk zone in southern England were investigated in situ. During and after each application of water, changes in water content and matric potential of the profile were monitored and percolate was collected in troughs. The measured water breakthrough time showed that water moved to 1.2 m depth quickly (in 8.2 h) even with application rate as low as 3 mm/h and that the time was only 3 h when water was applied at a rate of 15 mm/ h. These breakthrough times were about 150 and 422 fold shorter, respectively, than those expected if the water had been conducted by the matrix alone. Percolate was collected in troughs within 3.5 h at 1.2 m depth when water was applied at 30 mm/h and the quantity collected indicated that a significant amount of the surface applied water moved downward through inter-aggregate pores. The small increase in volumetric water content (about 3%) in excess of matrix water content resulted in a large increase in pore water velocities, from 0.20 to 5.3 m/d. The presence of soil layer had effect on the time taken for water to travel through the cryoturbated chalk layer and in the soil layer, water took about 1-2 h to pass thorough, depending on the intensity.

Stirring and mixing in two-dimensional divergent flow

While stirring and mixing properties in the stratosphere are reasonably well understood in the context of balanced (slow) dynamics, as is evidenced in numerous studies of chaotic advection, the strongly enhanced presence of high-frequency gravity waves in the mesosphere gives rise to a significant unbalanced (fast) component to the flow. The present investigation analyses result from two idealized shallow-water numerical simulations representative of stratospheric and mesospheric dynamics on a quasi-horizontal isentropic surface. A generalization of the Hua–Klein Eulerian diagnostic to divergent flow reveals that velocity gradients are strongly influenced by the unbalanced component of the flow. The Lagrangian diagnostic of patchiness nevertheless demonstrates the persistence of coherent features in the zonal component of the flow, in contrast to the destruction of coherent features in the meridional component. Single-particle statistics demonstrate t2 scaling for both the stratospheric and mesospheric regimes in the case of zonal dispersion, and distinctive scaling laws for the two regimes in the case of meridional dispersion. This is in contrast to two-particle statistics, which in the mesospheric (unbalanced) regime demonstrate a more rapid approach to Richardson’s t3 law in the case of zonal dispersion and is evidence of enhanced meridional dispersion.

The interactive responses of water quality and hydrology to changes in multiple stressors, and implications for the long-term effective management of phosphorus

Soluble reactive phosphorus (SRP) plays a key role in eutrophication, a global problem decreasing habitat quality and in-stream biodiversity. Mitigation strategies are required to prevent SRP fluxes from exceeding critical levels, and must be robust in the face of potential changes in climate, land use and a myriad of other influences. To establish the longevity of these strategies it is therefore crucial to consider the sensitivity of catchments to multiple future stressors. This study evaluates how the water quality and hydrology of a major river system in the UK (the River Thames) respond to alterations in climate, land use and water resource allocations, and investigates how these changes impact the relative performance of management strategies over an 80-year period. In the River Thames, the relative contributions of SRP from diffuse and point sources vary seasonally. Diffuse sources of SRP from agriculture dominate during periods of high runoff, and point sources during low flow periods. SRP concentrations rose under any future scenario which either increased a) surface runoff or b) the area of cultivated land. Under these conditions, SRP was sourced from agriculture, and the most effective single mitigation measures were those which addressed diffuse SRP sources. Conversely, where future scenarios reduced flow e.g. during winters of reservoir construction, the significance of point source inputs increased, and mitigation measures addressing these issues became more effective. In catchments with multiple point and diffuse sources of SRP, an all-encompassing effective mitigation approach is difficult to achieve with a single strategy. In order to attain maximum efficiency, multiple strategies might therefore be employed at different times and locations, to target the variable nature of dominant SRP sources and pathways.

Localization of deep water formation: role of atmospheric moisture transport and geometrical constraints on ocean circulation

A series of coupled atmosphere–ocean–ice aquaplanet experiments is described in which topological constraints on ocean circulation are introduced to study the role of ocean circulation on the mean climate of the coupled system. It is imagined that the earth is completely covered by an ocean of uniform depth except for the presence or absence of narrow barriers that extend from the bottom of the ocean to the sea surface. The following four configurations are described: Aqua (no land), Ridge (one barrier extends from pole to pole), Drake (one barrier extends from the North Pole to 35°S), and DDrake (two such barriers are set 90° apart and join at the North Pole, separating the ocean into a large basin and a small basin, connected to the south). On moving from Aqua to Ridge to Drake to DDrake, the energy transports in the equilibrium solutions become increasingly “realistic,” culminating in DDrake, which has an uncanny resemblance to the present climate. Remarkably, the zonal-average climates of Drake and DDrake are strikingly similar, exhibiting almost identical heat and freshwater transports, and meridional overturning circulations. However, Drake and DDrake differ dramatically in their regional climates. The small and large basins of DDrake exhibit distinctive Atlantic-like and Pacific-like characteristics, respectively: the small basin is warmer, saltier, and denser at the surface than the large basin, and is the main site of deep water formation with a deep overturning circulation and strong northward ocean heat transport. A sensitivity experiment with DDrake demonstrates that the salinity contrast between the two basins, and hence the localization of deep convection, results from a deficit of precipitation, rather than an excess of evaporation, over the small basin. It is argued that the width of the small basin relative to the zonal fetch of atmospheric precipitation is the key to understanding this salinity contrast. Finally, it is argued that many gross features of the present climate are consequences of two topological asymmetries that have profound effects on ocean circulation: a meridional asymmetry (circumpolar flow in the Southern Hemisphere; blocked flow in the Northern Hemisphere) and a zonal asymmetry (a small basin and a large basin).

Hydrology and geomorphology of the Upper White Nile lakes and their relevance for water resources management in the Nile basin

Remote sensing data and digital elevation models were utilized to extract the catchment hydrological parameters and to delineate storage areas for the Ugandan Equatorial Lakes region. Available rainfall/discharge data are integrated with these morphometric data to construct a hydrological model that simulates the water balance of the different interconnected basins and enables the impact of potential management options to be examined. The total annual discharges of the basins are generally very low (less than 7% of the total annual rainfall). The basin of the shallow (5 m deep) Lake Kioga makes only a minor hydrological contribution compared with other Equatorial Lakes, because most of the overflow from Lake Victoria basin into Lake Kioga is lost by evaporation and evapotranspiration. The discharge from Lake Kioga could be significantly increased by draining the swamps through dredging and deepening certain channel reaches. Development of hydropower dams on the Equatorial Lakes will have an adverse impact on the annual water discharge downstream, including the occasional reduction of flow required for filling up to designed storage capacities and permanently increasing the surface areas of water that is exposed to evaporation. On the basis of modelling studies, alternative sites are proposed for hydropower development and water storage schemes

The effects of rotation and ice shelf topography on frazil-laden ice shelf water plumes

A model of the dynamics and thermodynamics of a plume of meltwater at the base of an ice shelf is presented. Such ice shelf water plumes may become supercooled and deposit marine ice if they rise (because of the pressure decrease in the in situ freezing temperature), so the model incorporates both melting and freezing at the ice shelf base and a multiple-size-class model of frazil ice dynamics and deposition. The plume is considered in two horizontal dimensions, so the influence of Coriolis forces is incorporated for the first time. It is found that rotation is extremely influential, with simulated plumes flowing in near-geostrophy because of the low friction at a smooth ice shelf base. As a result, an ice shelf water plume will only rise and become supercooled (and thus deposit marine ice) if it is constrained to flow upslope by topography. This result agrees with the observed distribution of marine ice under Filchner–Ronne Ice Shelf, Antarctica. In addition, it is found that the model only produces reasonable marine ice formation rates when an accurate ice shelf draft is used, implying that the characteristics of real ice shelf water plumes can only be captured using models with both rotation and a realistic topography.

Climate impacts on river flow: projections for the Medway catchment UK with UKCP09 and CATCHMOD

The potential impact of climate change on areas of strategic importance for water resources remains a concern. Here, river flow projections for the River Medway, above Teston in southeast England are presented, which is just such an area of strategic importance. The river flow projections use climate inputs from the Hadley Centre Regional Climate Model (HadRM3) for the time period 1960–2080 (a subset of the early release UKCP09 projections). River flow predictions are calculated using CATCHMOD, the main river flow prediction tool of the Environment Agency (EA) of England and Wales. In order to use this tool in the best way for climate change predictions, model setup and performance are analysed using sensitivity and uncertainty analysis. The model's representation of hydrological processes is discussed and the direct percolation and first linear storage constant parameters are found to strongly affect model results in a complex way, with the former more important for low flows and the latter for high flows. The uncertainty in predictions resulting from the hydrological model parameters is demonstrated and the projections of river flow under future climate are analysed. A clear climate change impact signal is evident in the results with a persistent lowering of mean daily river flows for all months and for all projection time slices. Results indicate that a projection of lower flows under future climate is valid even taking into account the uncertainties considered in this modelling chain exercise. The model parameter uncertainty becomes more significant under future climate as the river flows become lower. This has significant implications for those making policy decisions based on such modelling results. Copyright © 2010 John Wiley & Sons, Ltd.

Frazil dynamics and precipitation in a water column with depth-dependent supercooling

A morphological instability of a mushy layer due to a forced flow in the melt is analysed. The instability is caused by flow induced in the mushy layer by Bernoulli suction at the crests of a sinusoidally perturbed mush–melt interface. The flow in the mushy layer advects heat away from crests which promotes solidification. Two linear stability analyses are presented: the fundamental mechanism for instability is elucidated by considering the case of uniform flow of an inviscid melt; a more complete analysis is then presented for the case of a parallel shear flow of a viscous melt. The novel instability mechanism we analyse here is contrasted with that investigated by Gilpin et al. (1980) and is found to be more potent for the case of newly forming sea ice.

Validity of the ice shelf water plume concept beneath Filchner-Ronne Ice Shelf

In winter, brine rejection from sea ice formation and export in the Weddell Sea, offshore of Filchner-Ronne Ice Shelf (FRIS), leads to the formation of High Salinity Shelf Water (HSSW). This dense water mass enters the cavity beneath FRIS by sinking southward down the sloping continental shelf towards the grounding line. Melting occurs when the HSSW encounters the ice shelf, and the meltwater released cools and freshens the HSSW to form a water mass known as Ice Shelf Water (ISW). If this ISW rises, the ‘ice pump’ is initiated (Lewis and Perkin, 1986), whereby the ascending ISW becomes supercooled and deposits marine ice at shallower locations due to the pressure increase in the in-situ freezing temperature. Sandh¨ager et al. (2004) were able to infer the thickness patterns of marine ice deposits at the base of FRIS (figure 1), so the primary aim of this work is to try to understand the ocean flows that determine these patterns. The plume model we use to investigate ISW flow is described fully by Holland and Feltham (accepted) so only a relatively brief outline is presented here. The plume is simulated by combining a parameterisation of ice shelf basal interaction and a multiplesize- class frazil dynamics model with an unsteady, depth-averaged reduced-gravity plume model. In the model an active region of ISW evolves above and within an expanse of stagnant ambient fluid, which is considered to be ice-free and has fixed profiles of temperature and salinity. The two main assumptions of the model are that there is a well-mixed layer underneath the ice shelf and that the ambient fluid outside the plume is stagnant with fixed properties. The topography of the ice shelf that the plume flows beneath is set to the FRIS ice shelf draft calculated by Sandh¨ager et al. (2004) masked with the grounding line from the Antarctic Digital Database (ADD Consortium, 2002). To initiate the plumes, we assume that the intrusion of dense HSSW initially causes melting at the points on the grounding line where the glaciological tributaries feeding FRIS go afloat.

Development of frazil modelling in ice shelf water plumes

Abstract Preliminary results are presented from a modelling study directed at the spatial variation of frazil ice formation and its effects on flow underneath large ice shelves. The chosen plume and frazil models are briefly introduced, and results from two simplified cases are outlined. It is found that growth and melting dominate the frazil model in the short term. Secondary nucleation converts larger crystals into several nuclei due to crystal collisions (microattrition) and fluid shear and therefore governs the ice crystal dynamics after the initial supercooling has been quenched. Frazil formation is found to have a significant depth-dependence in an idealised study of an Ice Shelf Water plume. Finally, plans for more extensive and realistic studies are discussed.