Instabilities in non-rotating and rotating shallow shear flows

Numerical simulations for the wave radiation effect on the linear and nonlinear instabilities of rotating and non-rotating shallow flows are conducted using shallow-water equations. At a low convective Froude number, the results of the instabilities is a string of eddies. The coalescence between the neighbouring eddies decides the transverse mixing of the shallow shear flow. At a higher convective Froude number, the development of the shear flow is characterized by wave radiation and the production of shocklets. The radiation of waves in the non-rotating shallow flow is a phenomenon analogous to the radiation of sound in gas dynamics. In the rotating flow on the other hand, the shallow-flow instabilities are intensified due to rotational interference within a window of instability over a narrow range of Rossby numbers.     

The generation of residual flows in Norway: an input-output approach

The generation of 35 different kinds of residuals is analyzed by an input-output approach for the Norwegian economy in 1970. The general tendency in the computations is that the final demand category, Export, especially export from the sectors Pulp and paper and Metals and minerals, is the main contributor of the flow of residuals generated each year.     

Laboratory-numerical studies of stratified spin-up flows

The stability of stratified rotating flows is investigated by means of laboratory experiments and numerical simulations in axisymmetric cylindrical and annular containers with both horizontal and sloping bottoms. The baroclinic current is initiated via incremental spin-up/down of a linearly stratified fluid by an abrupt change in the rotation rate of the system. Particular attention is given to the non-linear flow regime (finite Rossby numbers). It is found that axisymmetric spin-up current loses its azimuthal symmetry when the Burger number drops below unity, and breaks into a system of large-scale cyclonic and anticyclonic vortices with predominantly vertical axis of rotation. Eddies always develop at the density fronts formed by the corner regions adjacent to the sidewalls of the container. It is shown that the stability of the spin-up flow is largely affected by the bottom slope and the structure of the bottom boundary layer.     

Optimal abatement of carbon emission flows

We study optimal carbon capture and storage (CCS) from point sources, taking into account damages incurred from the accumulation of carbon in the atmosphere and exhaustibility of fossil fuel reserves. High carbon concentrations call for full CCS, meaning zero net emissions. We identify conditions under which partial or no CCS is optimal. In the absence of CCS the CO2 stock might be inverted U-shaped. With CCS more complicated behavior may arise. It can be optimal to have full capture initially, yielding a decreasing stock, then partial capture while keeping the CO2 stock constant, and a final phase without capture but with an inverted U-shaped CO2 stock. We also introduce the option of adaptation and provide a unified theory regarding the optimal use of CCS and adaptation.     

Characteristics of flow structure of free-surface flow in a partly obstructed open channel with vegetation patch

Free-surface flows over patchy vegetation are common in aquatic environments. In this study, the hydrodynamics of free-surface flow in a rectangular channel with a bed of rigid vegetation-like cylinders occupying half of the channel bed was investigated and interpreted by means of laboratory experiments and numerical simulations. The channel configurations have low width-to-depth aspect ratio (1.235 and 2.153). Experimental results show that the adjustment length for the flow to be fully developed through the vegetation patch in the present study is shorter than observed for large-aspect-ratio channels in other studies. Outside the lateral edge of the vegetation patch, negative velocity gradient (\(\partial \overline{u}/\partial z < 0\)) and a local velocity maximum are observed in the vertical profile of the longitudinal velocity in the near-bed region, corresponding to the negative Reynolds stress (\(- \overline{{u^{\prime}w^{\prime}}} < 0\)) at the same location. Assuming coherent vortices to be the dominant factor influencing the mean flow field, an improved Spalart–Allmaras turbulence model is developed. The model improvement is based on an enhanced turbulence length scale accounting for coherent vortices due to the effect of the porous vegetation canopy and channel bed. This particular flow characteristic is more profound in the case of high vegetation density due to the stronger momentum exchange of horizontal coherent vortices. Numerical simulations confirmed the local maximum velocity and negative gradient in the velocity profile due to the presence of vegetation and bed friction. This in turn supports the physical interpretation of the flow processes in the partly obstructed channel with vegetation patch. In addition, the vertical profile of the longitudinal velocity can also be explained by the vertical behavior of the horizontal coherent vortices based on a theoretical argument.     

Mixing layer in open-channel junction flows

When two open-channel flows merge in a three-branch subcritical junction, a mixing layer appears at the interface between the two inflows. If the width of the downstream channel is equal to the width of each inlet channel, this mixing layer is accelerated and is curved due to the junction geometry. The present work is dedicated to simplified geometries, considering a flat bed and a \(90^{\circ }\) angle where two configurations with different momentum ratios are tested. Due to the complex flow pattern in the junction, the so-called Serret–Frenet frame-axis based on the local direction of the velocity must be employed to characterize the flow pattern and the mixing layer as Cartesian and cylindrical frame-axes are not adapted. The analysis reveals that the centerline of the mixing layer, defined as the location of maximum Reynolds stress and velocity gradient, fairly fits the streamline separating at the upstream corner, even though a slight shift of the mixing layer towards the center of curvature is observed. The shape of the mixing layer appears to be strongly affected by the streamwise acceleration and the complex lateral confinement due to the side walls and the corners of the junction, leading to a streamwise increase of the mean velocity along the centerline and a decrease of the velocity difference. This results in a specific streamwise evolution of the mixing layer width, which reaches a plateau in the downstream region of the junction. Finally, the evaluation of the terms in the Reynolds-Averaged-Navier–Stokes equations reveals that the streamwise and normal acceleration and the pressure gradient remain dominant, which is typical of accelerated and rotational flows.     

Prediction of pollutant dispersion in turbulent two-phase flows

With a growing awareness of water pollution problems, in recent years there has been a considerable increased effort in developing and applying numerical models to predict accurately the contaminant distributions, particularly in free surface flows. This numerical study presents a predictive hydrodynamic model in order to explore the dispersion phenomenon of a pollutant injected from time-dependent sources in a turbulent free surface flow. More precisely, we study the impact of pulsation on the dispersion of an injected material. The air/water interface was modeled with the volume of fluid method and sharpness of the free surface was assured by means of Geo-Reconstruct scheme. The numerical results showed that the pulsation played a dominant role at the early stage of the pollutant transport. It was also observed that the pulsation affected the distribution of the injected material especially near the front and that a major swirling action was developed compared to the constant-rate-injection case.     

Least-inference methods for constructing networks of trophic flows

The construction of material and energy budgets within ecosystems has long been accomplished via manual calculation. Recently, optimization techniques have been adapted to automate the procedure, but these methods require assumptions that may not square with biological reality. Two algorithms are developed to construct ecosystem budgets under minimal inference. Although the methods do not recapitulate the model used to generate the input data, analysis reveals that the results do not differ statistically from networks that were constructed manually.     

Large-scale turbulent structure of uniform shallow free-surface flows

The hydrodynamics of super- and sub-critical shallow uniform free-surface flows are assessed using laboratory experiments aimed at identifying and quantifying flow structure at scales larger than the flow depth. In particular, we provide information on probability distributions of horizontal velocity components, their correlation functions, velocity spectra, and structure functions for the near-water-surface flow region. The data suggest that for the high Froude number flows the structure of the near-surface layer resembles that of two-dimensional turbulence with an inverse energy cascade. In contrast, although large-scale velocity fluctuations were also present in low Froude number flow its behaviour was different, with a direct energy cascade. Based on our results and some published data we suggest a physical explanation for the observed behaviours. The experiments support Jirka’s [Jirka GH (2001) J Hydraul Res 39(6):567–573] hypothesis that secondary instabilities of the base flow may generate large-scale two-dimensional eddies, even in the absence of transverse gradients in the time-averaged flow properties.     

Water sharing agreements sustainable to reduced flows

By signing a water sharing agreement (WSA), countries agree to release an amount of river water in exchange for a negotiated compensation. We examine the vulnerability of such agreements to reduced water flows. Among all WSAs that are acceptable to riparian countries, we find out the one which is self-enforced under the most severe drought scenarios. The so-called upstream incremental WSA assigns to each country its marginal contribution to its followers in the river. Its mirror image, the downstream incremental WSA, is not sustainable to reduced flow at the source. Self-enforcement problems can be solved by setting water releases and compensations contingent to water flow. We apply our analysis to the Aral Sea Basin. We compute the upstream incremental compensations for the Bishkek agreement and asses its vulnerability with historical flows.     

Dike-break induced flows: a simplified model

A simplified model for the prediction of the steady-state outflow through a breach in an inland dike is presented. It consists in the application of the mass and momentum conservation principles to a macroscopic control volume. A proper definition of the shape of the control volume enables to take the main characteristics of the flow into account and thus to compensate for the extreme simplification of the spatial representation of the model. At the breach, a relation derived from the shallow-water equations is used to determine the direction of the flow. Developments have been guided by numerical simulations and results have been compared to experimental data. Both the accuracy and the domain of validity of the simplified model are found satisfactory.     

Water sharing agreements sustainable to reduced flows

By signing a water sharing agreement (WSA), countries agree to release an amount of river water in exchange for a negotiated compensation. We examine the vulnerability of such agreements to reduced water flows. Among all WSAs that are acceptable to riparian countries, we find out the one which is self-enforced under the most severe drought scenarios. The so-called upstream incremental WSA assigns to each country its marginal contribution to its followers in the river. Its mirror image, the downstream incremental WSA, is not sustainable to reduced flow at the source. Self-enforcement problems can be solved by setting water releases and compensations contingent to water flow. We apply our analysis to the Aral Sea Basin. We compute the upstream incremental compensations for the Bishkek agreement and asses its vulnerability with historical flows.     

Mechanism of the intermittent motion of two-phase debris flows

A typical two-phase debris flow exhibits a high and steep flow head consisting of rolling boulders and cobbles with intermittent or fluctuating velocity. The relative motion between the solid phase and the liquid phase is obvious. The motion of a two-phase debris flow depends not only on the rheological properties of the flow, but also on the energy transmission between the solid and liquid phases. Several models have been developed to study two-phase debris flows. An essential shortcoming of most of these models is the omission of the interaction between the two phases and identification of the different roles of the different materials in two-phase debris flows. The tracer particles were used for the velocity of solid phase and the velocity of liquid phase was calculated by the water velocity on the surface of the debris flow in the experiments. This paper analyzed the intermittent feature of two-phase debris flows based on videos of debris flows in the field and flume experiments. The experiments showed that the height of the head of the two-phase debris flow increased gradually in the initiation stage and reached equilibrium at a certain distance from the start of the debris flow. The height growth and the velocity of the flow head showed fluctuating characteristics. Model equations were established and the analyses proved that the average velocity of the two-phase debris flow head was proportional to the flood discharge and inversely proportional to the volume of the debris flow head.     

Effect of environmental flows on deep,anoxic pools

A series of field surveys were carried out on two permanent pools of the upper Glenelg River in SW Victoria, Australia. One was representative of the wider and deeper pools while the other was representative of the more-narrow and shallower pools. Both pools showed a typical seasonal cycle of warm, brackish, oxygen-poor, summer conditions and cool, oxygen-rich, low-salinity, winter conditions. The summer salinity increases were larger than expected, suggesting possible saline groundwater inflow from unidentified springs. Both pools contained anoxic water in their deeper sections but this was permanent only in the deeper pool. A simple model of the flushing rate of such anoxic pools subject to flows, such as environmental flow releases, was developed, based on an energy balance between the potential energy required to lift the anoxic layer and the kinetic energy derived from the river flow. The results were tested against and in agreement with the field measurements. The model also suggests that the anoxic layers are resilient to all but the largest environmental flows.     

Turbulent velocity profile in fully-developed open channel flows

The determination of velocity profile in turbulent narrow open channels is a difficult task due to the significant effects of the anisotropic turbulence that involve the Prandtl’s second type of secondary flow occurring in the cross section. With these currents the maximum velocity appears below the free surface that is called dip phenomenon. The well-known logarithmic law describes the velocity distribution in the inner region of the turbulent boundary layer but it is not adapted to define the velocity profile in the outer region of narrow channels. This paper relies on an analysis of the Navier–Stokes equations and yields a new formulation of the vertical velocity profile in the center region of steady, fully developed turbulent flows in open channels. This formulation is able to predict time averaged primary velocity in the outer region of the turbulent boundary layer for both narrow and wide open channels. The proposed law is based on the knowledge of the aspect ratio and involves a parameter C_Ar depending on the position of the maximum velocity (ξ_dip). ξ_dip may be derived, either from measurements or from an empirical equation given in this paper. A wide range of longitudinal velocity profile data for narrow open channels has been used for validating the model. The agreement between the measured and the computed velocities is rather good, despite the simplification used.