Initial Water Depth Research Articles

Design considerations of constructed wetlands to reduce landfill leachate contamination in tropical regions

In tropical regions, landfill leachate contamination at municipal solid waste disposal sites is a critical issue because of the large volume of highly contaminated leachate formed during the rainy season. We evaluated the efficacy of constructed wetlands (CWs) with the ability to reduce the water volume and pollutant levels to reduce leachate contamination compared to the most commonly used treatment system, stabilization ponds, based on parameters obtained in a field experiment in Thailand. The simulation indicated that CWs had a higher potential to reduce the water volume than stabilization ponds over the course of a year. Scenario evaluations under varying initial water depths, system depths, and area sizes indicated that the CWs could reduce the treatment area to prevent overflow and leachate pollution. In addition, the CWs were estimated to reduce the leachate amount and pollution by 83–100% and 92–99%, respectively. When there is limited land available, deeper CWs can be used to sustainably prevent contamination from leachate overflow. Effectively designed CW systems may be valuable for both reducing the required area and the contamination; therefore, CWs are a promising option for sustainable landfill leachate treatment systems in developing tropical regions.

Effects of initial propagule size and water depth on Butomus umbellatus L. growth and vegetative propagation

Over the last century, flowering rush (Butomus umbellatus L.: Butomaceae) has escaped its native Eurasian range and has become a problematic species in parts of North America. As an aquatic invasive species, flowering rush has degraded wetlands in introduced areas and has interfered with human water usage. Although experimental work has been published regarding the reproductive biology of the species, we found few manipulative experiments aimed at testing ecological attributes of this species in the literature. The research reported here demonstrates that flowering rush is capable of aggressive clonal growth and propagation, whether from vegetative rhizome buds or from fragments of rhizomes themselves. This species was capable of growth along a depth gradient from zero to 132 cm and showed an ability to adjust biomass allocation along that gradient; however, biomass and asexual propagule production declined at depths beyond approximately 50 cm. The combination of regrowth from relatively small propagules, ability to tolerate depths of greater than one meter, and plasticity of biomass allocation along habitat gradients make this species a potential threat in many aquatic and wetland habitats in its introduced range. However, certain aspects of its biomass allocation strategies may enhance chemical control for plants growing at greater depths or those regenerating from rhizome buds, both of which tend to have greater S:R biomass ratios.

An Experimental Study of the Run-Up Process of Breaking Bores Generated by Dam-Break Under Dry- and Wet-Bed Conditions

In this study, a series of dam-break laboratory experiments were carried out to investigate the run-up process of breaking bores under dry- and wet-bed conditions. Detailed measurements were conducted to reveal differences in the run-up hydrodynamic characteristics under these two conditions, e.g. the bore front profile, the maximum run-up height and duration, and the instantaneous bore front velocity. Two successive bores were observed under the wet-bed run-up process, while multiple bores (three bores in general) were generated during the dry-bed run-up process due to the significant bottom friction effect. A linear relationship with the uniform gradient is found between the maximum run-up height and the initial water head for both dry- and wet-bed conditions, indicating that difference in the maximum run-up height between the dry- and specified wet-bed cases or among various wet-bed cases is not sensitive to the initial water head. Under the same initial water head, although the dry-bed run-up process takes a longer duration than that of wet-bed cases, the maximum run-up height is smallest for the dry-bed case and gradually increases with the increase of the initial downstream water depth for wet-bed cases. Under the wet-bed conditions, temporal variation of the bore front run-up velocity can be classified into two stages, i.e. the acceleration stage induced by the relatively large incident bore front water depth (large onshore hydrostatic pressure gradient) and the deceleration stage governed by the offshore-directed gravity force and bottom friction. Nevertheless, due to the small incident bore front water depth, run-up process under the dry-bed conditions does not show the acceleration stage.

Numerical study on characteristics of dam-break wave

The influence of the downstream water depth on dam-break wave is systematically and comparatively studied by simulating the physical experiments in this study. Commercial CFD software package FLOW-3D is chosen as the simulation tool and is validated firstly. Three experimental cases of different initial downstream water depth, including dry-bed case (r = 0), shallow downstream water case (r = 0.1) and deep downstream water case (r = 0.4) carried out by Ozmen-Cagatay and Kocaman (2010) are then simulated. The generation and propagation process of dam-break wave is divided into two and three stages, respectively, for dry-bed and wet-bed cases. And the characteristics of the dam-break wave including free surface profile, wave front velocity, mark point movement and trajectory, interface between upstream and downstream water, bottom resistance and turbulent kinetic energy are compared and analyzed elaborately in each stage for each case. The differences of the characteristics between different downstream water depth cases are achieved and the reasons of the differences are explored, which present a comprehensive understanding of dam-break wave generation and propagation.

An Application of the A-PDA Model For the Interconnected Operation Among Adjacent Blocks of Water Distribution Systems In Case of Emergency

The water distribution system is an important social infrastructure providing customers with stable and safe water supply. The fact, however, is that it is not free from various abnormal situations arising from internal / external factors. In case of a water supply failure due to abnormal situations, the emergency interconnected operation between adjacent blocks in the system is one of the most effective countermeasures. To simulate these types of emergency operations, existing hydraulic analysis models, which are based on the infinite water supply assumption, may simulate unrealistic results such as satisfying sufficient water supply for more demand nodes than actual ones. If they want to have more realistic hydraulic simulation result for these situations, it is required to adopt a new hydraulic analysis which is able to consider insufficient water supply for all demand nodes. Demand Driven Analysis (DDA) and Pressure Driven Analysis (PDA) are most commonly used hydraulic analysis. DDA performs a hydraulic analysis based on the assumption that the demand at demand nodes is always 100% satisfied which derives unrealistic results in abnormal situations. In the case of the PDA, it considers the relationship between hydraulic pressure and available flow rate, which is more reliable than the DDA for abnormal operating conditions. However, since DDA and PDA are basis on the infinite water supply assumption, unrealistic hydraulic analysis results may be obtained when they are applied to the insufficient water supply condition such as the emergency interconnected operation between adjacent blocks due to one or more reservoirs may not be working properly. Therefore, Lee et al. (2018) has proposed the Advanced-Pressure Driven Analysis (A-PDA) applying the concept of limited source to the existing PDA. In this study, we apply the PDA and the A-PDA to simulate the hydraulic condition of the emergency interconnected operation between adjacent blocks for a water supply network in Korea and compare the results from them. The target network supplies water to 84,000 households and it consists of 3 reservoirs, 1,492 nodes, 1,937 pipelines, 8 pumps and 10 interconnected emergency pipes. Each reservoir takes responsible for its individual block. When one of the reservoirs cannot supply water to its individual block, the block will be supplied water through the emergency pipes from the adjacent reservoir. Fig 1 shows the layout of target network and Table 1 shows the properties of each reservoir. To explore the effect of the limited water supply condition, we generate an operation scenario: RES1 stops water supply at 00:00hr (mid night) and RES2 and RES3 supply water to Block1 for the emergency. Then, the PDA and the A-PDA are used to simulate this emergency operating condition. The initial water depth of RES2 and RES3 is 3m and 2.7m, respectively. Fig. 2 shows the available supply ratio (ASR, = available demand/required demand) with time by the PDA and the A-PDA for Block1. The ASR with time by the PDA for Block1 show us that emergency water supply to Block1 from RES2 and RES3 can be maintained through the simulation period even though the ASR are 20% to 40%. On the other hand, The ASR with time by the A-PDA for Block1 show us that the emergency water supply to Block1 ceases after 16:00hr. The reason we obtain two different water supply results for Block1 is due to the assumption of the PDA which is that the amount of water supply is unlimited during the simulation period. In the PDA, the water depth of a reservoir is always maintained at the initial set value so that the amount of water demand at demand nodes should be provided. However, for the emergency operating condition we generate for this study, the amount of water from RES2 and RES3 is insufficient to supply water for the entire network without RES1. As shown in Fig. 3, the water depths of RES2 and RES3 are continuously decreased and RES2 is empty at 16:00hr and RES3 is depleted after 39:00hr. After 16:00hr, RES3 is the only water source for the entire network and Block1 cannot be supplied water from RES3 sufficiently. From this simulation results, the A-PDA simulates this type of the water supply situation more realistic than the PDA does since without RES1, obviously, the entire network cannot be provided with sufficient water from RES2 and RES3. Therefore, in the case of the hydraulic analysis which needs to consider water supply quantity such as the interconnection operation required, the application of the A-PDA model is indispensable. Additionally, the application of the A-PDA can anticipate the possible water supply time and the possible emergency interconnected operating time in the abnormal operating condition, which is impossible to obtain by the existing hydraulic analysis. These two values will be used to design or to establish the emergency operating plan for a water supply network for better service quality.

Study of dam break flow interaction with urban settlements over a sloping channel

This paper describes a dam break experiment on a sloped channel, carried out in a hydraulic flume at UCL for the purpose of computer model validations of extreme events, such as flash floods. An elevated reservoir was situated upstream followed by a 1/20 slope leading up to a flat floodplain. Plexiglas blocks were positioned on the floodplain constituting different urban settlements and creating different obstructions to the flow. The flume was instrumented along its length measuring the change in water depth in the reservoir; the water depth time histories in various locations; the flow patterns and flood front velocity; and lastly the pressure and load on the buildings. The experiments were repeated for different urban settlements, flood intensities (two different initial water depths in the reservoir) and roughness layers along the slope, representative of a vegetated and a non-vegetated hill. In the present study, the experimental results were described qualitatively and compared with theoretical processes and 2D numerical results obtained using OpenFOAM's RAS turbulent model. Water depth, velocity and load measurements were analysed for different cases and it was found that while the 2D model provided a good fit on the slope, the flows generated around the building were more complex 3D formations which lead to inaccuracies. All experiments were repeated multiple times to ensure repeatability and thus the procedure was validated successfully providing a complete dataset that can be used for the validation of computational models for extreme events.

A two-dimensional experimental investigation on the sloshing behavior in a water pool

Studies on the pool sloshing behavior are important for the improved evaluation of energetic potential of a large whole-core-scale molten fuel pool that might be formed during a Core Disruptive Accident (CDA) of Sodium-cooled Fast Reactors (SFR). Motivated to understand the characteristics of this behavior, in this study a series of simulated experiments was conducted by injecting nitrogen gas into a Two-Dimensional (2D) rectangular water pool through a nozzle positioned at the center of pool bottom. To achieve a comprehensive understanding, experimental parameters, including nitrogen gas pressure (∼4.2 bar), initial water depth (∼60 cm), gas injection duration (0.06–0.1 s) along with the nozzle size (10–50 mm), were varied. Through detailed analyses, it is found that under current range of conditions, all the experimental parameters employed are confirmable to have remarkable impact on the sloshing characteristics (e.g. maximum elevation of water level at the pool center and peripheries). The performed analyses also suggest that possibly due to a diminished residence time of the injected-gas in the pool, a limited sloshing intensity is observable as the gas-injection pressure increases. Evidence and fundamental data from our work will be utilized for the empirical-model development as well as the analyses and verifications of future SFR severe accident analysis codes in China.

Experimental Study of the Operational Parameters on Low-cost Single-basin Solar Still in Jessore, Bangladesh

Keeping in mind the growing concern of sustainability, the present study aims to develop a hands-on technique for potable water production by using a portable single-basin solar still, which is constructed with low-cost, locally available and lightweight materials. The performance of single-basin solar still were investigated using different essential operational variables, which include weather condition, water salinity, brine water depth, and addition of glass marbles as energy absorbing material. Ambient weather conditions were found to have direct effect on the productivity of the still. The solar still productivity increased by 29% when a layer of glass marbles was used. The study also showed that the daily water production increased with the decrease in the initial depth of brine water. Estimating a useful life of 4 years of the solar still, an average cost of produced potable water was defined to be BDT 0.35 per lit. In addition, some important water quality parameters were tested and compared with drinking water standard values. The obtained values were found to be in line with the drinking water standards of WHO.Journal of Chemical Engineering, Vol. 29, No. 1, 2017: 3-8

Uncertainty analysis of open channel flow: stochastic approach to Advection–Diffusion equation

In fluid mechanics applications, transport occurs through the combination of advection and diffusion. This paper presents a stochastic approach to describe uncertainty and its propagation based on Advection-Diffusion Equation. To assess the uncertainty in initial water depth, random initial condition is imposed on the framework of 1D open cannel flow. Karhunen–Loeve Expansion is adopted to decompose the uncertain parameter in terms of infinite series containing a set of orthogonal Gaussian random variables. Eigenstrucures of covariance function associated with the random parameter, which play a key role in computing coefficients of the series, are extracted from Fredhulm’s equation. The flow depth is also represented as an infinite series of its moments, obtained via polynomial expansion decomposition in terms of the products of random variables. Coefficients of these series are obtained by a set of recursive equations derived from the ADE. Results highlight the effect of various statistical properties of initial water depth. The mean value and variance for the flow depth are compared with Monte Carlo Simulation as a reliable stochastic approach. It was found that when higher-order approximations are used, KLE results would be as accurate as MCS, however, with much less computational time and effort.

Laboratory investigations of earthquake- and landslide-induced composite surges

Seismic surges and landslides are both major secondary mountain hazards during an earthquake. This paper investigates earthquake- and landslide-induced composite surges through large-scale shaking table water tank model experiments. A series of tests were conducted for various initial water depths, peak ground accelerations, slide impact velocities, and slide volumes. Based on the results of the tests, the effects of these parameters on the maximum wave heights of the earthquake- and landslide-induced composite surges were analyzed. An amplification coefficient of seismic surges was defined, and the prediction equation for the amplification coefficient was developed through non-dimensional multiple linear regression analysis. Then, an empirical equation for the maximum wave heights of the composite surges was developed based on the amplification coefficient and Demirel’s method. This equation provides a calculation method for earthquake- and landslide-induced composite surge waves.

An experimental and numerical study on breather solutions for surface waves in the intermediate water depth

A series of laboratory experiments related to Kuznetsov-Ma breather solution have been performed in a seakeeping wave tank with different initial wave steepness and intermediate water depths. Analysis of the experimental results reveals that the maximum wave height in Kuznetsov-Ma breather solution is normally accompanied with a large crest amplitude, which can be largely reduced with the decreasing water depth due to the slower modulational process and the limited length of wave tank, regardless of the initial nonlinearity. The laboratory observations can be accurately simulated by the high-order spectral model (HOS) if the initial Benjamin-Feir index is not very large as a result of weak nonlinearity and/or decreased water depth. Numerical studies also indicate that in the evolutionary process the amplitude of carrier wave will decrease sharply and a peak frequency downshifting can be detected. If the evolutionary time scale is long enough, the spectrum will eventually evolve into a continuous one with the energy relocated in the lower wave frequency part. For Peregrine breather solution that is a particular case of Kuznetsov-Ma solution, it is found that in some cases a specific phase shift of the initial condition can lead to a longer distance for the wave group to travel to achieve the first maximum amplitude and a larger amplification factor than that predicted by the theoretical solution.

Experimental Study on Dam-Break Hydrodynamic Characteristics Under Different Conditions

In this study, a series of dam-break experiments was carried out to investigate the influence of the initial downstream water depth, water head settings, and upstream reservoir length on the dam-break wave movement. The instantaneous water level and flow velocity were measured at two specified downstream locations. Considering the requirements for precise data measurement with high temporal resolution, the synchronization of different instruments was realized based on high-speed camera recording. Even with the same initial water head setting, the water level and flow velocity variations of the dam-break wave propagating downstream on the wet bed show noteworthy differences in flow characteristics compared to the initial dry bed, caused by the interactions between the upstream and downstream water. Hydrodynamic formulae proposed by Lauber and Hager (1998) [1] are not applicable for the wet-bed condition, although their solution of wave profiles for the initial dry-bed condition performs well at the location farther from the gate. The non-dimensional average front velocity of the wet-bed condition, which mainly depends on the initial water head setting, is smaller than that of the dry-bed case. In addition, the maximum water level and flow velocity at the downstream location are mainly controlled by the initial water head setting, while the duration of the large values is influenced by the reservoir length.

Experimental Investigation of Seismic-Induced Hydrodynamic Pressures on a Vertical Wall under Conditions of Wave Resonance

The distribution of hydrodynamic pressure acting on the structural face of a dam significantly influences the stability of the dam. The present study investigates the development of the hydrodynamic pressure acting on the surface of a dam at different heights with respect to time during earthquakes with different dominant frequencies using a shaking table. The results demonstrate that the variation in the hydrodynamic pressure significantly follows the seismically accelerated wave motion in the absence of resonance. However, under conditions of resonance, the fluctuations in the hydrodynamic pressure exhibit similarities with a sine wave, and the positive peak values present some hysteresis. The experimental pressure values in the absence of resonance present parabolic distributions with respect to the water height that are in good agreement with the corresponding hydrodynamic pressures determined by Westergaard’s equation, while conditions of wave resonance produce a uniform distribution of hydrodynamic pressures with greater values and much longer periods of increased hydrodynamic pressure than the case of nonresonance. In addition, the seismic frequency, fundamental frequency of the reservoir, maximum peak seismic acceleration, and initial water depth are treated as variables. An empirical equation is derived to predict the maximum hydrodynamic pressure in conjunction with wave resonance conditions.

Accounting for the Impact of Management Scenarios on Typha Domingensis (Cattail) in an Everglades Wetland.

The coupled regional simulation model, and the transport and reaction simulation engine were recently adapted to simulate ecology, specifically Typha domingensis (Cattail) dynamics in the Everglades. While Cattail is a native Everglades species, it has become invasive over the years due to an altered habitat over the last few decades, taking over historically Cladium jamaicense (Sawgrass) areas. Two models of different levels of algorithmic complexity were developed in previous studies, and are used here to determine the impact of various management decisions on the average Cattail density within Water Conservation Area 2A in the Everglades. A Global Uncertainty and Sensitivity Analysis was conducted to test the importance of these management scenarios, as well as the effectiveness of using zonal statistics. Management scenarios included high, medium and low initial water depths, soil phosphorus concentrations, initial Cattail and Sawgrass densities, as well as annually alternating water depths and soil phosphorus concentrations, and a steadily decreasing soil phosphorus concentration. Analysis suggests that zonal statistics are good indicators of regional trends, and that high soil phosphorus concentration is a pre-requisite for expansive Cattail growth. It is a complex task to manage Cattail expansion in this region, requiring the close management and monitoring of water depth and soil phosphorus concentration, and possibly other factors not considered in the model complexities. However, this modeling framework with user-definable complexities and management scenarios, can be considered a useful tool in analyzing many more alternatives, which could be used to aid management decisions in the future.

A high-resolution, continuous δ13C record spanning the Ordovician–Silurian boundary on Anticosti Island, eastern Canada

One of the best-exposed and most complete stratigraphic records from paleotropical areas spanning the Ordovician–Silurian (O–S) boundary is located on Anticosti Island, eastern Canada. Our study is the first one to sample strata superbly exposed at low tide along the west coast of Anticosti Island, thus providing a previously unexploited, nearly complete stratigraphic interval (∼300 m) at the O–S boundary for δ13C chemostratigraphy. A new high-resolution δ13C curve with more than 500 data points spaced at every ∼0.5 m has been produced, rectifying important pitfalls of previously published δ13C curves (i.e., low sampling resolution, variable sampling intervals, stratigraphic gaps). This new high-resolution δ13C curve displays a lower and an upper positive Hirnantian Isotope Carbon Excursion (HICE) recognized elsewhere around the globe. The ascending limb of the lower HICE starting from baseline values of +0.5‰ corresponds to the upper 20 m of the late Katian Vauréal Formation, but δ13C peak values of +2.5‰ occur in the lower part of the Hirnantian Ellis Bay Formation. In spite of a δ13C record segmented by a few stratigraphic hiatuses, the upper HICE, with its peak values of +4.5‰, is well recorded in the upper part of the Hirnantian Ellis Bay Formation. When compared with sections from around the globe, our δ13C curve displays a distinct long-term trend with a long sustained lower HICE followed abruptly by the upper HICE and return to baseline values of +0.5‰ prior to the Rhuddanian. The continued descending isotopic trend well into the Becscie Formation suggests that the O–S boundary may occur at a higher stratigraphic level (up to 30 m) than previously interpreted. Active subsidence combined with moderate initial water depths prior to the Hirnantian were key factors controlling the deposition of a thick O–S sedimentary succession with a few hiatuses on Anticosti Island and capturing a comprehensive, reliable δ13C record across this interval.

Examination of a solar desalination system equipped with an air bubble column humidifier, evacuated tube collectors and thermosyphon heat pipes

In this paper, the performance of a novel HDH solar desalination system equipped with a combination of heat pipe (HP), evacuated tube collector (ETC) and air bubble column humidifier is experimentally investigated. This novel HDH system uses advantages of ETC-HP as a highly efficient thermal absorption and conductor device, and at the same time employs the advantages of an air bubble column humidifier, i.e. high interface area and effective mixing in order to heat the water and humidify the air, respectively. The effects of various parameters including incoming air flow rate into the humidifier, initial depth of water in the humidifier, and adding fluids such as oil and water in the space between the ETCs and heat pipes on the system performance were investigated. Results indicate that by adding oil in the space between the ETCs and heat pipes, daily fresh water productivity and daily efficiency increase significantly and reached 6.275kg/day·m2 and 65%, respectively. In addition, the optimum initial water depth in the humidifier is the same as the length of the heat pipe's condenser section in the humidifier. Moreover, daily production slightly increases as the air flow rate increases. The estimated cost of fresh water produced through the HDH system designed is 0.028$/L.

Experimental Investigations of Partial-Breach Dam-Break Flows

AbstractThis paper presents experimental results on partial-breach dam-break flows. Three-dimensional (3D) flood waves resulting from an instantaneous breach of a dam are experimentally investigated by combining different measurement techniques. The dam-break flow is initiated by quickly lifting a gate separating a reservoir and a downstream dry basin. Three different initial upstream water depths are considered. The study utilizes the digital particle tracking velocimetry (DPTV) technique for measuring the free-surface velocity and water depth. Stereoscopic configuration of two high definition video cameras recording the movement of hollow plastic balls enabled measurement of the 3D velocity field and the water-surface elevation in the near field. The pressure head is measured by pressure transducers at various locations. Ultrasonic velocity profilers (UVP) are used to obtain velocity profiles in the emptying reservoir. A simple nondimensional relationship for the variation of water-surface elevation in ...

Entrainment and mixing in unsteady gravity currents

ABSTRACTEntrainment and mixing in lock-exchange gravity currents are investigated by large eddy simulations. Nine cases are analysed, varying the initial excess density driving the motion and the aspect ratio r of the initial water depth to the lock length. Laboratory experiments are also performed and a fair agreement between numerical simulations and measurements is found. Mixing between the gravity current and the ambient fluid, in both the slumping and self-similar phases, is studied for a range of entrainment parameters, gravity current fractional area and using an energy budget method. The entrainment is found to increase as r decreases. The occurrence of irreversible mixing is detected during the entire development of the flow, i.e. both in the slumping and self-similar phases. A higher amount of mixing is observed as r decreases and the initial excess density increases.

Comparison between shallow water and Boussinesq models for predicting cascading dam-break flows

This paper investigates the flood wave propagation between two reservoirs, linked by an open channel with a constant gradient. The dam-break flows are caused by the collapse of the upstream dam. The performance of two mathematical models is evaluated: one is based on the standard shallow water equations, and the other is based on the shallow water Boussinesq equations. Both models are solved numerically herein using a total variation diminishing Lax–Wendroff scheme. Computed results are systematically compared, with the laboratory measurements used as references. In particular, this paper extensively examines the run-up of the flood wave on the downstream dam wall, and its dependence on the bed slope and the initial water depths in the upstream and downstream reservoirs. The findings are useful for analyzing the risk of cascading dam failures. Overall, the Boussinesq model is found to give better agreement with the measurements, as it is capable of capturing the short undulations at the front of the flood bore. The superior performance of the Boussinesq model is more significant at larger downstream water depths.

임계 마름 수심기법을 이용한 지하공간 침수 모의

In this study, a 2D hydrodynamic model equipped with critical dry depth scheme was developed to reproduce the flow over staircase. The channel geometry of hydraulic experiment conducted by Ishigaki et al. was generated in the computational space, and the developed model was validated against flow properties such as discharge, velocity and momentum. In addition, the water surface profile and the velocity distribution evolved in flow over two layers staircases were analyzed. When the initial water depth at the upper floor was 0.3 m, the maximum velocity at lower floor was 4.2 m/s, and the maximum momentum was <TEX>$1.2m^3/s^2$</TEX>, and its conversion to force per unit width was 1.2 kN/m. This value was equivalent to the hydrostatic force with 50 cm water depth, and evacuation became difficult, as proposed by Ishigaki et al. For the flow over staircases connecting two layers, the maximum run-up height in flat part connecting two layers was approximately two times higher than the initial water depth in upper floor, and the rapid shock wave with sharp front and long tail was propagated.