On the well-posedness of a mathematical model describing water-mud interaction

In this paper we consider a mathematical model describing the two-phase interaction between water and mud in a water canal when the width of the canal is small compared to its depth. The mud is treated as a non-Netwonian fluid and the interface between the mud and fluid is allowed to move under the influence of gravity and surface tension. We reduce the mathematical formulation, for small boundary and initial data, to a fully nonlocal and nonlinear problem and prove its local well-posedness by using abstract parabolic theory.Comment: 16 page

Effects of tidal-forcing variations on tidal properties along a narrow convergent estuary

A 1D analytical framework is implemented in a narrow convergent estuary that is 78 km in length (the Guadiana, Southern Iberia) to evaluate the tidal dynamics along the channel, including the effects of neap-spring amplitude variations at the mouth. The close match between the observations (damping from the mouth to ∼ 30 km, shoaling upstream) and outputs from semi-closed channel solutions indicates that the M2 tide is reflected at the estuary head. The model is used to determine the contribution of reflection to the dynamics of the propagating wave. This contribution is mainly confined to the upper one third of the estuary. The relatively constant mean wave height along the channel (< 10% variations) partly results from reflection effects that also modify significantly the wave celerity and the phase difference between tidal velocity and elevation (contradicting the definition of an “ideal” estuary). Furthermore, from the mouth to ∼ 50 km, the variable friction experienced by the incident wave at neap and spring tides produces wave shoaling and damping, respectively. As a result, the wave celerity is largest at neap tide along this lower reach, although the mean water level is highest in spring. Overall, the presented analytical framework is useful for describing the main tidal properties along estuaries considering various forcings (amplitude, period) at the estuary mouth and the proposed method could be applicable to other estuaries with small tidal amplitude to depth ratio and negligible river discharge.info:eu-repo/semantics/publishedVersio

Quantifying measures to limit wind driven resuspension of sediments for improvement of the ecological quality in some shallow Dutch lakes

Although phosphorus loadings are considered the main pressure for most shallow lakes, wind-driven resuspension can cause additional problems for these aquatic ecosystems. We quantified the potential effectiveness of measures to reduce the contribution of resuspended sediments, resulting from wind action, to the overall light attenuation for three comparable shallow peat lakes with poor ecological status in the Netherlands: Loosdrecht, Nieuwkoop, and Reeuwijk (1.8–2.7 m depth, 1.6–2.5 km fetch). These measures are: 1. wave reducing barriers, 2. water level fluctuations, 3. capping of the sediment with sand, and 4. combinations of above. Critical shear stress of the sediments for resuspension (Vcrit), size distribution, and optical properties of the suspended material were quantified in the field (June 2009) and laboratory. Water quality monitoring data (2002–2009) showed that light attenuation by organic suspended matter in all lakes is high. Spatial modeling of the impact of these measures showed that in Lake Loosdrecht limiting wave action can have significant effects (reductions from 6% exceedance to 2% exceedance of Vcrit), whereas in Lake Nieuwkoop and Lake Reeuwijk this is less effective. The depth distribution and shape of Lake Nieuwkoop and Lake Reeuwijk limit the role of wind-driven resuspension in the total suspended matter concentration. Although the lakes are similar in general appearance (origin, size, and depth range) measures suitable to improve their ecological status differ. This calls for care when defining the programme of measures to improve the ecological status of a specific lake based on experience from other lakes.

The area-to-mass ratio and fractal dimension of marine flocs

publisher: Elsevier articletitle: The area-to-mass ratio and fractal dimension of marine flocs journaltitle: Estuarine, Coastal and Shelf Science articlelink: http://dx.doi.org/10.1016/j.ecss.2017.03.026 content_type: article copyright: © 2017 The Authors. Published by Elsevier Ltd

Erosion characteristics and horizontal variability for small erosion depths in the Sacramento-San Joaquin River Delta, California, USA

Erodibility of cohesive sediment in the Sacramento-San Joaquin River Delta (Delta) was investigated with an erosion microcosm. Erosion depths in the Delta and in the microcosm were estimated to be about one floc diameter over a range of shear stresses and times comparable to half of a typical tidal cycle. Using the conventional assumption of horizontally homogeneous bed sediment, data from 27 of 34 microcosm experiments indicate that the erosion rate coefficient increased as eroded mass increased, contrary to theory. We believe that small erosion depths, erosion rate coefficient deviation from theory, and visual observation of horizontally varying biota and texture at the sediment surface indicate that erosion cannot solely be a function of depth but must also vary horizontally. We test this hypothesis by developing a simple numerical model that includes horizontal heterogeneity, use it to develop an artificial time series of suspended-sediment concentration (SSC) in an erosion microcosm, then analyze that time series assuming horizontal homogeneity. A shear vane was used to estimate that the horizontal standard deviation of critical shear stress was about 30% of the mean value at a site in the Delta. The numerical model of the erosion microcosm included a normal distribution of initial critical shear stress, a linear increase in critical shear stress with eroded mass, an exponential decrease of erosion rate coefficient with eroded mass, and a stepped increase in applied shear stress. The maximum SSC for each step increased gradually, thus confounding identification of a single well-defined critical shear stress as encountered with the empirical data. Analysis of the artificial SSC time series with the assumption of a homogeneous bed reproduced the original profile of critical shear stress, but the erosion rate coefficient increased with eroded mass, similar to the empirical data. Thus, the numerical experiment confirms the small-depth erosion hypothesis. A linear model of critical shear stress and eroded mass is proposed to simulate small-depth erosion, assuming that the applied and critical shear stresses quickly reach equilibrium

Bedform migration in a mixed sand and cohesive clay intertidal environment and implications for bed material transport predictions

Many coastal and estuarine environments are dominated by mixtures of non-cohesive sand and cohesive mud. The migration rate of bedforms, such as ripples and dunes, in these environments is important in determining bed material transport rates to inform and assess numerical models of sediment transport and geomorphology. However, these models tend to ignore parameters describing the physical and biological cohesion (resulting from clay and extracellular polymeric substances, EPS) in natural mixed sediment, largely because of a scarcity of relevant laboratory and field data. To address this gap in knowledge, data were collected on intertidal flats over a spring-neap cycle to determine the bed material transport rates of bedforms in biologically-active mixed sand-mud. Bed cohesive composition changed from below 2 vol% up to 5.4 vol% cohesive clay, as the tide progressed from spring towards neap. The amount of EPS in the bed sediment was found to vary linearly with the clay content. Using multiple linear regression, the transport rate was found to depend on the Shields stress parameter and the bed cohesive clay content. The transport rates decreased with increasing cohesive clay and EPS content, when these contents were below 2.8 vol% and 0.05 wt%, respectively. Above these limits, bedform migration and bed material transport was not detectable by the instruments in the study area. These limits are consistent with recently conducted sand-clay and sand-EPS laboratory experiments on bedform development. This work has important implications for the circumstances under which existing sand-only bedform migration transport formulae may be applied in a mixed sand-clay environment, particularly as 2.8 vol% cohesive clay is well within the commonly adopted definition of “clean sand”

Man-induced regime shifts in small estuaries - II: a comparison of rivers

This is Part II of two papers on man-induced regime shifts in small, narrow, and converging estuaries, with focus on the interaction between effective hydraulic drag, fine sediment import, and tidal amplification, induced by river engineering works, e.g., narrowing and deepening. Paper I describes a simple linear analytical model for the tidal movement in narrow, converging estuaries and a conceptual model on the response of tidal rivers to river engineering works. It is argued that such engineering works may set in motion a snowball effect bringing the river into an alternative steady state. Part II analyses the historic development in tidal range in four rivers, e.g., the Elbe, Ems, Loire, and Scheldt, all in northwest Europe; data are available for many decades, up to a century. We use the analytical model derived in Part I, showing that the effective hydraulic drag in the Ems and Loire has decreased considerably over time, as anticipated in Part I. We did not find evidence that the Upper Sea Scheldt is close to its tipping point towards hyperturbid conditions, but risks have been identified. In the Elbe, tidal reflections against the profound step in bed level around Hamburg seem to have affected the tidal evolution in the last decades. It is emphasized that the conceptual picture sketched in these papers is still hypothetical and needs to be validated, for instance through hind-cast modeling of the evolution of these rivers. This will not be an easy task, as historical data for a proper calibration of the models required are scarce