Based on the general relationship described by Cheng between the drag coefficient and the Reynolds number of a particle, a new relationship between the Reynolds number and a dimensionless particle parameter is propose...Based on the general relationship described by Cheng between the drag coefficient and the Reynolds number of a particle, a new relationship between the Reynolds number and a dimensionless particle parameter is proposed. Using a trial-and-error procedure to minimize errors, the coefficients were determined and a formula was developed for predicting the settling velocity of natural sediment particles. This formula has higher prediction accuracy than other published formulas and it is applicable to all Reynolds numbers less than 2× 10^5.展开更多
A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximatin...A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton's iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that (1) the set-up and the set-down are both non-monotonic quantities with the wave steepness, and (2) the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.展开更多
Tidal current velocity profile in the near-bed layers has been widely studied. The results showed that velocity profile in the near-bed layer obviously departure from the traditional logarithmic profile, due to the ac...Tidal current velocity profile in the near-bed layers has been widely studied. The results showed that velocity profile in the near-bed layer obviously departure from the traditional logarithmic profile, due to the acceleration or deceleration. Although the logarithmic linear profile can reduce the rate of deviation from this, only it is a lower-order approximate solution. In this paper, considering the unsteady and non-linear features of tidal motion, the double logarithmic profile near-bed layers in estuarine and coastal waters is established on the assumption that the turbulent shear stress along the water depth was parabolic distribution, and on the basis of Prandtl's mixing length theory and yon Karman's self-similar theory. Having been verified the data observed at the West Solent in the south of England, and comparison of the logarithmic linear profile, it found that the double logarithmic profile is more precious than the latter. At last, the discussed results showed that: (1) The parabolic distribution of the tidal shear stresses verified good by the field data and experimental data, can be better reflected the basic features of the tidal shear stress deviating from linear distribution that is downward when to accelerate, upward when to decelerate. (2) The traditional logarithmic velocity profile is the zero-order approximation solution of the double logarithmic profile, the logarithmic linear profile is the first order, and the logarithmic parabolic profile is the second order. (3) Ignoring the conditions of diffusion and convection in the tida movement, the double logarithmic profile can reflect the tidal properties of acceleration or deceleration, so that the calculation of the friction velocity and roughness length are more reasonable. When the acceleration or the deceleration is about zero, the double logarithmic profile becomes the logarithmic profile.展开更多
In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simpl...In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)'s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly varying topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.展开更多
Geomorphometry, the science of digital terrain analysis (DTA), is an important focus of research in both geomorphology and geographical information science (GIS). Given that 70% of China is mountainous, geomorphol...Geomorphometry, the science of digital terrain analysis (DTA), is an important focus of research in both geomorphology and geographical information science (GIS). Given that 70% of China is mountainous, geomorphological research is popular among Chinese schol- ars, and the development of GIS over the last 30 years has led to significant advances in geomorphometric research. In this paper, we review Chinese progress in geomorphometry based on the published literature. There are three major areas of progress: digital terrain modelling methods, DTA methods, and applications of digital terrain models (DTMs). First, traditional vector- and raster-based terrain modelling methods, including the assessment of uncertainty, have received widespread attention. New terrain modelling methods such as unified raster and vector, high-fidelity, and real-time dynamic geographical scene modelling have also attracted research attention and are now a major focus of digital terrain modelling research. Second, in addition to the popular DTA methods based on topographical derivatives geomorphological features, and hydrological factors extracted from DTMs, DTA methods have been extended to include analyses of the structure of underlying strata, ocean surface features and even socioeconomic spatial structures. Third, DTMs have been applied to fields including global climate change, analysis of various typical regions, lunar surface and other related fields. Clearly, Chinese scholars have made significant progress in geomorphometry. Chinese scholars have had the greatest international impact in areas including high-fidelity digital terrain modelling and DTM-based regional geomorphological analysis, particularly in the Loess Plateau and the Tibetan Plateau regions.展开更多
This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and de...This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 40476039)
文摘Based on the general relationship described by Cheng between the drag coefficient and the Reynolds number of a particle, a new relationship between the Reynolds number and a dimensionless particle parameter is proposed. Using a trial-and-error procedure to minimize errors, the coefficients were determined and a formula was developed for predicting the settling velocity of natural sediment particles. This formula has higher prediction accuracy than other published formulas and it is applicable to all Reynolds numbers less than 2× 10^5.
基金The Jiangsu Province Natural Science Foundation for the Young Scholar under contract No.BK20130827the Fundamental Research Funds for the Central Universities of China under contract No.2010B02614+1 种基金the National Natural Science Foundation of China under contract Nos 41076008 and 51009059the Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘A computational method for steady water waves is presented on the basis of potential theory in the physical plane with spatial variables as independent quantities. The finite Fourier series are applied to approximating the free surface and potential function. A set of nonlinear algebraic equations for the Fourier coefficients are derived from the free surface kinetic and dynamic boundary conditions. These algebraic equations are numerically solved through Newton's iterative method, and the iterative stability is further improved by a relaxation technology. The integral properties of steady water waves are numerically analyzed, showing that (1) the set-up and the set-down are both non-monotonic quantities with the wave steepness, and (2) the Fourier spectrum of the free surface is broader than that of the potential function. The latter further leads us to explore a modification for the present method by approximating the free surface and potential function through different Fourier series, with the truncation of the former higher than that of the latter. Numerical tests show that this modification is effective, and can notably reduce the errors of the free surface boundary conditions.
基金The National Natural Science Foundation of China under contract No.50339010the public welfare projects of Water Resources Ministry of China under contract No.200701026the Natural Science Foundation of the Jiangsu Higher Education institutions of China under contract No.09KJA170003
文摘Tidal current velocity profile in the near-bed layers has been widely studied. The results showed that velocity profile in the near-bed layer obviously departure from the traditional logarithmic profile, due to the acceleration or deceleration. Although the logarithmic linear profile can reduce the rate of deviation from this, only it is a lower-order approximate solution. In this paper, considering the unsteady and non-linear features of tidal motion, the double logarithmic profile near-bed layers in estuarine and coastal waters is established on the assumption that the turbulent shear stress along the water depth was parabolic distribution, and on the basis of Prandtl's mixing length theory and yon Karman's self-similar theory. Having been verified the data observed at the West Solent in the south of England, and comparison of the logarithmic linear profile, it found that the double logarithmic profile is more precious than the latter. At last, the discussed results showed that: (1) The parabolic distribution of the tidal shear stresses verified good by the field data and experimental data, can be better reflected the basic features of the tidal shear stress deviating from linear distribution that is downward when to accelerate, upward when to decelerate. (2) The traditional logarithmic velocity profile is the zero-order approximation solution of the double logarithmic profile, the logarithmic linear profile is the first order, and the logarithmic parabolic profile is the second order. (3) Ignoring the conditions of diffusion and convection in the tida movement, the double logarithmic profile can reflect the tidal properties of acceleration or deceleration, so that the calculation of the friction velocity and roughness length are more reasonable. When the acceleration or the deceleration is about zero, the double logarithmic profile becomes the logarithmic profile.
基金Open Fund of Key Laboratory of Coastal Disasters and Defence (Ministry of Education)National Natural Science Foundation of China under contract No. 50779015
文摘In the present paper, by introducing the effective wave elevation, we transform the extended elliptic mild-slope equation with bottom friction, wave breaking and steep or rapidly varying bottom topography to the simplest time-dependent hyperbolic equation. Based on this equation and the empirical nonlinear amplitude dispersion relation proposed by Li et al. (2003), the numerical scheme is established. Error analysis by Taylor expansion method shows that the numerical stability of the present model succeeds the merits in Song et al. (2007)'s model because of the introduced dissipation terms. For the purpose of verifying its performance on wave nonlinearity, rapidly varying topography and wave breaking, the present model is applied to study: (1) wave refraction and diffraction over a submerged elliptic shoal on a slope (Berkhoff et al., 1982); (2) Bragg reflection of monochromatic waves from the sinusoidal ripples (Davies and Heathershaw, 1985); (3) wave transformation near a shore attached breakwater (Watanabe and Maruyama, 1986). Comparisons of the numerical solutions with the experimental or theoretical ones or with those of other models (REF/DIF model and FUNWAVE model) show good results, which indicate that the present model is capable of giving favorably predictions of wave refraction, diffraction, reflection, shoaling, bottom friction, breaking energy dissipation and weak nonlinearity in the near shore zone.
基金Foundation: National Natural Science Foundation of China, No.41671389, No.41631175, No.41601411, No.41371424 PAPD, No. 164320H 116
文摘Geomorphometry, the science of digital terrain analysis (DTA), is an important focus of research in both geomorphology and geographical information science (GIS). Given that 70% of China is mountainous, geomorphological research is popular among Chinese schol- ars, and the development of GIS over the last 30 years has led to significant advances in geomorphometric research. In this paper, we review Chinese progress in geomorphometry based on the published literature. There are three major areas of progress: digital terrain modelling methods, DTA methods, and applications of digital terrain models (DTMs). First, traditional vector- and raster-based terrain modelling methods, including the assessment of uncertainty, have received widespread attention. New terrain modelling methods such as unified raster and vector, high-fidelity, and real-time dynamic geographical scene modelling have also attracted research attention and are now a major focus of digital terrain modelling research. Second, in addition to the popular DTA methods based on topographical derivatives geomorphological features, and hydrological factors extracted from DTMs, DTA methods have been extended to include analyses of the structure of underlying strata, ocean surface features and even socioeconomic spatial structures. Third, DTMs have been applied to fields including global climate change, analysis of various typical regions, lunar surface and other related fields. Clearly, Chinese scholars have made significant progress in geomorphometry. Chinese scholars have had the greatest international impact in areas including high-fidelity digital terrain modelling and DTM-based regional geomorphological analysis, particularly in the Loess Plateau and the Tibetan Plateau regions.
基金supported by Fundamental Research Funds for the Central Universities (Grant No. 2010B02614)Natural Science Foundation of Hohai University (Grant No. 2009423511)+1 种基金National Natural Science Foundation of China (Grant No. 4176008)Priority Academic Program Development of Jiangsu Higher Education Institutions
文摘This paper presents a universal third-order Stokes solution with uniform current. This solution is derived on the basis of potential theory by expanding the free surface and potential function in Fourier series and determining the Fourier coefficients by solving a set of nonlinear algebraic equations through the Taylor expansion and perturbation method. The universal solution is expressed upon the still water depth with the still water level as datum and retains a global perturbation parameter. The wave set-up term generated by the self-interaction of oscillatory waves is explicitly included in the free surface function. With the use of different definitions for the wave celerity, different water levels as the datum, different non-dimensional variables as the perturbation parameter, and different treatments for the total head, the universal solution can be reduced to the existing various Stokes solutions, thus explaining the reasons and the physical significance of different non-periodic terms in them, such as the positive or negative constant term in the free surface expression and the time-or space-proportional term in the potential function.