Energy dissipation in sloshing waves in a rolling rectangular tank — III. Results and applications

The hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank have been investigated. In a sequence of three papers, an analytical technique together with a numerical solution method will be presented to describe the sloshing phenomenon accurately and efficiently. This first paper introduces a linear theory of viscous liquid sloshing and formulates a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. The second paper will describe a solution of the problem in function space by the truncation of infinite series. Boundary conditions are satisfied through the use of Fourier series expansions. However, the no-slip condition at the side walls can also be treated in a least-squares sense.Among the results that will be reported in the third paper are the effects of viscosity on liquid sloshing phenomenon and the dependence of viscous dissipation on the Reynolds and Froude numbers. Furthermore, the influence of the tank aspect ratio on viscous dissipation has been explored. These results demonstrate some unknown features of the functional relationships that exist between the dissipated energy and the Reynolds and Froude numbers. Similarly, the dependence of the dissipated energy on the aspect ratio has been analytically studied. The results obtained agree with the physical laws for the range of parameters investigated.     

The determination of present and possible environmental risks in solid waste dumping site,Tunceli, Turkey

Leachate was a major cause of high risk classification. This landfill was set as one with highest possible risk classification due to high vulnerability of private water wells to contamination from leachate flows. The aim of this study is to determine the present and possible environmental risks of the leachate spreading from solid waste dumping site in Tunceli and offer solutions for those determined environmental risks. For this purpose, the characteristics of the leachate were monitored at two station points detected in the solid waste dumping site for 7 months. The characteristics of the leachate were found for pH between 7.9 and 8.7. Oxidation reduction potential (ORP) occurred between ??143 and ??48 mV while conductivity was between 2.8 and 2.6 mS. Total solid matter (TSM) and suspended solid matter (SSM) were between 1000 and 7000 mg/l, 0.2–22.5 mg/l, respectively, while total volatile solids (TVS) occurred between 300 and 1800 mg/l for the two stations. Alkalinity was approximately between 290 and 5210 mg/l, while biological oxygen demand (BOD₅) and chemical oxygen demand (COD) results were 15–606 mg/l and 60–1160 mg/l, respectively, for two stations in all sampling time. In both stations, orthophosphate, ammonium nitrogen, nitrate, sulfate, and chloride analyses stayed between 3.04 and 921.1 mg/l; 0.29–619.36 mg/l; 8.94–135.04 mg/l; 125.9–1360.9 mg/l and 99.9–1249.9 mg/l, respectively, in 6 months. As a result of the characterization studies obtained from the leachate, it was found that the amounts of water entering into the waste mass and the retention period of the water in the mass were very effective in the temporal character change of the leachate. According to the Discharge Standards for Solid Waste Assessment and Disposal Facilities and Discharge to Waste Water Infrastructure Facilities of waste management regulation, the results were found to be risky. Consequently, the site in question needs to be urgently rehabilitated when considering the environmental risks of the leachate spreading from the site.     

Determination of failure probabilities of flood defence systems with improved dynamic bounds method

In this paper, we describe the computational framework of a novel method for solving the challenging problem of probabilistic finite elements. The method is called Improved Dynamic Bounds (IDB) and was developed recently to improve the efficiency of the dynamic bounds. The IDB is used in finite element numerical models to calculate time-dependent failure analyses of structures. In applications, the IDB can speed up the overall simulation process by several orders of magnitude. In applications controlled by two influential variables (e.g, two-dimensional problem), the computational efficiency is improved by a factor of 769 according to Rajabalinejad (2009). Applications of IDB indicate the method is most efficient for problems where the number of influential variables are limited. This is often the case for geotechnical and coastal flood defence systems. The IDB method is applied in this paper to the 17th Street Flood Wall, a component of the flood defence system (levee infra-structure) that failed during the Hurricane Katrina, to calculate the failure probability of an I-wall.     

Estimation of extreme wave heights using GEOSAT measurements

Satellite technology has yielded a large database of global ocean wave heights which may be used for engineering applications. However, the sampling protocol used by the satellite leads to some difficulties in making use of these data for practical applications. These difficulties and techniques to estimate extreme wave heights using satellite measurements are discussed. Significant wave heights for a 50-year return period are estimated using GEOSAT measurements for several regions around North America. Techniques described here may be used for estimation of wave heights associated with any specified return interval in regions where buoy data are not readily available.     

Modeling wave�Ccurrent bottom boundary layers beneath shoaling and breaking waves

The boundary layer characteristics beneath waves transforming on a natural beach are affected by both waves and wave-induced currents, and their predictability is more difficult and challenging than for those observed over a seabed of uniform depth. In this research, a first-order boundary layer model is developed to investigate the characteristics of bottom boundary layers in a wave–current coexisting environment beneath shoaling and breaking waves. The main difference between the present modeling approach and previous methods is in the mathematical formulation for the mean horizontal pressure gradient term in the governing equations for the cross-shore wave-induced currents. This term is obtained from the wave-averaged momentum equation, and its magnitude depends on the balance between the wave excess momentum flux gradient and the hydrostatic pressure gradient due to spatial variations in the wave field of propagating waves and mean water level fluctuations. A turbulence closure scheme is used with a modified low Reynolds number k-ε model. The model was validated with two published experimental datasets for normally incident shoaling and breaking waves over a sloping seabed. For shoaling waves, model results agree well with data for the instantaneous velocity profiles, oscillatory wave amplitudes, and mean velocity profiles. For breaking waves, a good agreement is obtained between model and data for the vertical distribution of mean shear stress. In particular, the model reproduced the local onshore mean flow near the bottom beneath shoaling waves, and the vertically decreasing pattern of mean shear stress beneath breaking waves. These successful demonstrations for wave–current bottom boundary layers are attributed to a novel formulation of the mean pressure gradient incorporated in the present model. The proposed new formulation plays an important role in modeling the boundary layer characteristics beneath shoaling and breaking waves, and ensuring that the present model is applicable to nearshore sediment transport and morphology evolution.     

On wave–current interaction by the Green–Naghdi equations in shallow water

This work is on the use of the Green–Naghdi (GN) nonlinear wave equations for simulating wave–current interaction in shallow water. The stream-function wave theory is used at the wave-maker boundary to generate nonlinear incident waves to consider the wave–current interaction. The nonlinear GN equations are solved in the time domain by use of the finite-difference method. The model is evaluated with data from three experimental studies. A strong opposing current over a submerged bar is investigated in the first test case. In the second test case, the interaction of waves with a uniform current over flat bottom is considered. In the third case, wave–current interaction over a variable bathymetry with the following and opposing currents is studied. The numerical results obtained by the GN equations are compared with the experimental data and results based on the Boussinesq equations. A good agreement is obtained for the three experimental studies considered for a wide range of wave and current conditions.     

Energy dissipation in sloshing waves in a rolling rectangular tank—I. Mathematical theory

The hydrodynamic aspects of the motion of a viscous fluid having a free surface in a rolling tank have been investigated. In a sequence of three papers, an analytical technique together with a numerical solution method will be presented to describe the sloshing phenomenon accurately and efficiently. This first paper introduces a linear theory of viscous liquid sloshing and formulates a boundary value problem subject to appropriate conditions. Viscosity is included in the problem formulation and its effects are properly accounted for. The second paper will describe a solution of the problem in function space by the truncation of infinite series. Boundary conditions are satisfied through the use of Fourier series expansions. However, the no-slip condition at the side walls can also be treated in a least-squares sense.Among the results that will be reported in the third paper are the effects of viscosity on liquid sloshing phenomenon and the dependence of viscous dissipation on the Reynolds and Froude numbers. Furthermore, the influence of the tank aspect ratio on viscous dissipation has been explored. These results demonstrate some unknown features of the functional relationships that exist between the dissipated energy and the Reynolds and Froude numbers. Similarly, the dependence of the dissipated energy on the aspect ratio has been analytically studied. The results obtained agree with the physical laws for the range of parameters investigated.     

WAVECALC: an Excel-VBA spreadsheet to model the characteristics of fully developed waves and their influence on bottom sediments in different water depths

The generation and growth of waves in deep water is controlled by winds blowing over the sea surface. In fully developed sea states, where winds and waves are in equilibrium, wave parameters may be calculated directly from the wind velocity. We provide an Excel spreadsheet to compute the wave period, length, height and celerity, as well as horizontal and vertical particle velocities for any water depth, bottom slope, and distance below the reference water level. The wave profile and propagation can also be visualized for any water depth, modeling the sea surface change from sinusoidal to trochoidal and finally cnoidal profiles into shallow water. Bedload entrainment is estimated under both the wave crest and the trough, using the horizontal water particle velocity at the top of the boundary layer. The calculations are programmed in an Excel file called WAVECALC, which is available online to authorized users. Although many of the recently published formulas are based on theoretical arguments, the values agree well with several existing theories and limited field and laboratory observations. WAVECALC is a user-friendly program intended for sedimentologists, coastal engineers and oceanographers, as well as marine ecologists and biologists. It provides a rapid means to calculate many wave characteristics required in coastal and shallow marine studies, and can also serve as an educational tool.