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.     

New approaches to determine the ultimate bearing capacity of shallow foundations based on artificial neural networks and ant colony optimization

In this study, two different approaches are proposed to determine the ultimate bearing capacity of shallow foundations on granular soil. Firstly, an artificial neural network (ANN) model is proposed to predict the ultimate bearing capacity. The performance of the proposed neural model is compared with results of the Adaptive Neuro Fuzzy Inference System, Fuzzy Inference System and ANN, which are taken in literature. It is clearly seen that the performance of the ANN model in our study is better than that of the other prediction methods. Secondly, an improved Meyerhof formula is proposed for the computation of the ultimate bearing capacity by using a parallel ant colony optimization algorithm. The results achieved from the proposed formula are compared with those obtained from the Meyerhof, Hansen and Vesic computation formulas. Simulation results showed that the improved Meyerhof formula gave more accurate results than the other theoretical computation formulas. In conclusion, the improved Meyerhof formula could be successfully used for calculating the ultimate bearing capacity of shallow foundations.     

Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model

This paper describes methods and results of research for incorporating four different parameterized wave breaking and dissipation formulas in a coastal wave prediction model. Two formulations assume the breaking energy dissipation to be limited by the Rayleigh distribution, whereas the other two represent the breaking wave energy by a bore model. These four formulations have been implemented in WABED, a directional spectral wave model based on the wave action balance equation with diffraction, reflection, and wave–current interaction capabilities. Four parameterized wave breaking formulations are evaluated in the present study using two high-quality laboratory data sets. The first data set is from a wave transformation experiment at an idealized inlet entrance, representing four incident irregular waves in a slack tide and two steady-state ebb current conditions. The second data set is from a laboratory study of wave propagation over a complex bathymetry with strong wave-induced currents. Numerical simulation results show that with a proper breaking formulation the wave model can reproduce laboratory data for waves propagating over idealized or complicated bathymetries with ambient currents. The extended Goda wave breaking formulation with a truncated Rayleigh distribution, and the Battjes and Janssen formulation with a bore model produced the best agreement between model and data.     

North Atlantic Oscillation influences on Turkish lake levels

The North Atlantic Oscillation (NAO) is a large‐scale mode of natural climate variability governing the path of Atlantic mid‐latitude storm tracks and precipitation regimes in the Atlantic and Mediterranean sectors. The primary focus of this study is to investigate the variability of lake levels in seven lakes scattered across Turkey using the method of continuous wavelet transforms and global spectra. The long winter (December, January, February and March) lake‐level series and the NAO index (NAOI) series were subjected to wavelet transform. The global wavelet spectrum (energy spectrum of periodicities) of lake levels and winter NAOI anomalies, in most cases, revealed a significant correlation. It was shown that the Tuz, Sapanca, and Uluabat lakes reflect much stronger influences of the NAO than the other four lakes. In contrast, weak correlations were found in the coastal areas of the Mediterranean and eastern Turkey. The periodic structures of Turkish lake levels in relation to the NAO revealed a spectrum between the 1‐year and 10‐year scale level. Although the periodicities of more than 10‐year scale levels were detected, explaining significant relations between the NAO and these long‐term periodicities remains a challenging task. The results of this study are consistent with the earlier studies concerning the teleconnection between the NAO and climate variables in Turkey. Copyright © 2009 John Wiley & Sons, Ltd.     

Nonlinear wave loads on a vertical cylinder

Nonlinear contributions due to elevation of the free surface, the dynamic head, and the second-order velocity potential on the wave loads are presented in closed-form expressions. Such nonlinearities resulting from large-amplitude ocean waves are associated with the irrotational flow interacting with a fixed bottom-mounted vertical cylinder piercing the surface. These are expressed in the form of dynamic, waterline and quadratic forces all of which depend on the square of the wave amplitude. The appropriate modifications are made to both the classical Morison equation and the well-known linear diffraction theory of MacCamy and Fuchs for accounting the second-order effects.A limited comparative study is performed to verify the present theoretical derivations. In general, satisfactory agreements have been obtained with the test results from various laboratory studies by different researchers. However, under certain environmental conditions, some discrepancies still exist with the measured results.     

Energy dissipation in sloshing waves in a rolling rectangular tank—II. Solution method and analysis of numerical technique

In Part I of these series of papers, the complete problem formulation in a linearized form was presented. In order to provide the engineer with an in-depth knowledge about the exact solution of the problem, it is natural and essential to start with a linear solution. This will be the objective of Part II, together with an exposition to the analysis of numerical technique utilized.A truncated infinite Fourier series-type solution is adopted for the linearized boundary value problem. It is shown that such a solution is mathematically consistent and represents the phenomenon properly by satisfying all of the field equations and the imposed boundary conditions. The dependence of the Fourier coefficients on the truncation limit has been investigated. The best lower and upper “cutoff limits” for the truncation of an infinite series are determined. An error analysis of the solution technique is performed.     

Morpho-tectonic evolution of the Marmara Sea inferred from multi-beam bathymetric and seismic data

In an initial stage, the Sea of Marmara developed as a graben and, in due course, considerable volumes of sediments were deposited in this basin. Before 200 ka, a new fault (New Marmara Fault) cutting through the whole basin developed, which postdated large sub-marine land sliding in the western part of the basin. This mass movement created the Western Ridge. The initiation of this strike-slip fault indicates that the extensional stress regime was replaced by a new, shearing stress field. In the eastern part of the Marmara Basin, the New Marmara Fault consists of two branches. The northern one replaces the normal faulting at the bottom of the northeastern slope of the basin. As a result, this slope has been rejuvenated. The southern branch is located along the central axis of the basin, forming the major extension of the North Anatolian Fault Zone within the region. Two restraining bends were formed because of the counterclockwise rotation of that part of the Anatolian Block. This resulted the uplifting of the Eastern Ridge and the formation of the positive flower structure within the Tekirdag Basin. The establishment of the compressional regime around the Sea of Marmara also resulted in the northwest–southeast shortening of the initial Marmara Basin.     

Photometric Imaging with Distributive Solar Analogy

The multicolor light curves (UBVRI) of HU Vir have been analyzed to study starspots for epochs 1987 and 1989. The term 'photometric imaging' has been used for predicting cool surface spots by photometric data. Assuming the number of spots and the area are about the same for the two hemispheres, the distributive solar analogy is introduced as a tool to constrain free values of spot parameters into unique values. Therefore, final fitting parameters are claimed unique in a sense that they are independent of free initial guesses. The light and color variations of HU Vir are better explained without polar spots. Finally, the spots are found to be ∼ 1600 K cooler than the T∼ 5000 K of this cool subgiant and cover ∼ %13.9 of the total surface at ±8.0 degrees from the equator for the epoch 1987. The spots at the epoch 1989 are found to be ∼ 2040 K cooler covering ∼ % 12.7 area at ± 27°.7 latitudes. Problems of photometric imaging and possible solutions with distributive solar analogy have been discussed. This revised version was published online in August 2006 with corrections to the Cover Date.     

Seasonal Analysis of Zoobenthos Associated with a Zostera marina L. Bed in Gulbahce Bay Aegean Sea, Turkey

Abstract. seasonal sampling of three stations in Gulbahce Bay Aegean Sea for the zoobenthic organisms associated with a Zostera marina bed was carried out during 1993–94. Temperature, salinity and oxygen were recorded each sampling period. A total of 7 taxonomic groups were determined: Polychaeta was the dominant group comprising 77 % of the total taxa and individuals, followed by Crustacea, Bivalvia and other groups such as Nemertea. Sipuncula, Turbellaria and Phoronida. Of the 108 taxa encountered, the polychaetes Notomastus latericeus and Caulleriella alata accounted for 49 % of the total populations. The species abundance did not show major changes among seasons, with highest values in fall 982 indiv. ·m^-2 and lowest in spring 754 indiv. ·m^-2. Diversity and evenness of the samples were relatively high and fairly constant, and were affected by the dominance levels of the species.