Serdar Beji | Istanbul Technical University (original) (raw)
Papers by Serdar Beji
Advances in Pure Mathematics
Advances in Pure Mathematics
Coastal Engineering Journal
Advances in Pure Mathematics
A fundamental algebraic relationship for a general polynomial of degree n is given and proven by ... more A fundamental algebraic relationship for a general polynomial of degree n is given and proven by mathematical induction. The stated relationship is based on the well-known property of polynomials that the n th-differences of the subsequent values of an n th-order polynomial are constant.
Coastal Engineering Journal
International Journal of Environment and Geoinformatics
The Sea of Marmara, a relatively small basin located between the Black Sea and the Aegean Sea wit... more The Sea of Marmara, a relatively small basin located between the Black Sea and the Aegean Sea with narrow seaways of the Bosphorus and the Dardanelles, has vital importance in coastal and ocean engineering activities due to substantial industrial development surrounding it and related sea traffic. Despite this importance, measurements concerning coastal engineering applications, in particular the wave climate, are quite scarce. Lack of essential data impairs the reliability of engineering works such as breakwaters and coastal protection structure designs. For a period of approximately one year between February 2013 and January 2014 Turkish Petroleum International Company (TPIC) carried out wave and wind measurements in the Sea of Marmara. The data were collected in 30-minute intervals throughout the one year span at the location of 41o04' N and 28o19' E with 50 m water depth. The present work analyses this rather unique data statistically for wind, wave height and energy conditions in the Sea of Marmara.
Coastal Engineering Journal
Coastal Engineering Proceedings
This study investigates fatalities due to rip currents on the Black Sea coast of Istanbul. Result... more This study investigates fatalities due to rip currents on the Black Sea coast of Istanbul. Results include the incidence rate of fatalities from rip currents, their causes, temporal and spatial distributions. The data shows that, nearly 70% of all drowning fatalities are associated with rip currents, and that on the average 33 people reportedly die from rip currents each year in Istanbul Black Sea coast. Thus, considering the wind speeds versus rip current fatalities, about one third of the fatalities occur when the wind speed is between 1.5-2.0 m/s. For the wind speeds 1.0-1.5 m/s the rip current magnitude is not too intense so people consider themselves capable enough to swim but for poor swimmers this is the most dangerous case. Nearly 60% of the fatalities in this wind speed interval is found to be children.
Coastal Engineering Proceedings
A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water dep... more A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water depths is presented. The new KdV type equation contains mixed dispersion and shoaling terms, which extend its applicable range of relative depths to virtually deep waters. The wave equation also satisfies an important consistency condition that there is an exact agreement between the shoaling rate of the equation itself and the rate obtained from the constancy of energy flux. A finite-difference scheme is devised for simulating several linear and nonlinear cases over varying bathymetry. The performance the new KdV type equation is observed to be quite satisfactory.
Coastal Engineering Proceedings
For realistic wave simulations in the nearshore zone besides nonlinear interactions, the dissipat... more For realistic wave simulations in the nearshore zone besides nonlinear interactions, the dissipative effects of wave breaking must also be taken into account. This paper presents the applications of a spectral nonlinear wave model with a dissipative breaking mechanism introduced by Beji and Nadaoka (1997). Results obtained for spectral components are converted to the time series and compared with Beji and Battjes' (1993) laboratory measurements and the field measurements of Nakamura and Katoh (1992) in the surf zone. While the model predicts the spilling-type breaking of irregular waves in acceptable agreement with the measurements in time domain, the agreement is unsatisfactory for plunging-type breakers.
In this work an improved Boussinesq model with a surface pressure term is discretized by a new ap... more In this work an improved Boussinesq model with a surface pressure term is discretized by a new approach. By specifying a single parameter the proposed discretization enables the user to run the program either in the long wave mode without dispersion terms or in the Boussinesq mode. Furthermore, the Boussinesq mode may be run either in the classical Boussinesq mode or in the improved Boussinesq mode by setting the dispersion parameter appropriately. In any one of these modes it is possible to specify a fixed or a moving surface pressure for simulating a moving object on the surface. The numerical model developed here is first tested by comparing the numerically simulated solitary waves with their analytical counterparts. The second test case concerns the comparison of the numerical solutions of moving surface pressures with the analytical solutions of the long wave equations for all possible modes (long wave, classical, and improved Boussinesq).
Http Dx Doi Org 10 1080 0020739920230201, Jul 9, 2006
ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here dea... more ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here deal with certain relationships which hold between the roots of the general cubic equation and other appropriate parameters derived from the same polynomial. Each section is organized in a monotonic sequence; that is, statement, demonstration and verification.
Marmara Denizi'nde olası bir deprem sonucunda oluşabilecek deniz dalgaları, Çınarcık Çukuru'ndan ... more Marmara Denizi'nde olası bir deprem sonucunda oluşabilecek deniz dalgaları, Çınarcık Çukuru'ndan geçen Kuzey Sınır Fayı'nın 6.5, 7.0 ve 7.5 büyüklüğündeki depremlerde kırılma durumları için simüle edilmiş ve bu dalgaların en büyük yükseklikleri ile kıyılara ulaşma süreleri hesaplanmıştır. Elde edilen sonuçlar, hiç bir hesaplama yapılmaksızın ortaya atılan dalga yüksekliği değerlerinin abartılı olduğunu göstermektedir.
Mediterranean Journal of Mathematics, 2008
A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a... more A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel's proof, the method produces no solution for the quintic equation.
International Journal of Mathematical Education in Science and Technology, 1992
ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here dea... more ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here deal with certain relationships which hold between the roots of the general cubic equation and other appropriate parameters derived from the same polynomial. Each section is organized in a monotonic sequence; that is, statement, demonstration and verification.
Coastal Engineering, 1995
ABSTRACT A nonlinearity parameter which is valid for both deep and shallow water waves is introdu... more ABSTRACT A nonlinearity parameter which is valid for both deep and shallow water waves is introduced. The parameter may be regarded as a wave Froude number. A modified form of the Ursell number is also discussed.
Coastal Engineering, 1998
Coastal Engineering, 2013
Water wave dispersion relationship Accurate empirical water wave dispersion formula For water wav... more Water wave dispersion relationship Accurate empirical water wave dispersion formula For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.
Advances in Pure Mathematics
Advances in Pure Mathematics
Coastal Engineering Journal
Advances in Pure Mathematics
A fundamental algebraic relationship for a general polynomial of degree n is given and proven by ... more A fundamental algebraic relationship for a general polynomial of degree n is given and proven by mathematical induction. The stated relationship is based on the well-known property of polynomials that the n th-differences of the subsequent values of an n th-order polynomial are constant.
Coastal Engineering Journal
International Journal of Environment and Geoinformatics
The Sea of Marmara, a relatively small basin located between the Black Sea and the Aegean Sea wit... more The Sea of Marmara, a relatively small basin located between the Black Sea and the Aegean Sea with narrow seaways of the Bosphorus and the Dardanelles, has vital importance in coastal and ocean engineering activities due to substantial industrial development surrounding it and related sea traffic. Despite this importance, measurements concerning coastal engineering applications, in particular the wave climate, are quite scarce. Lack of essential data impairs the reliability of engineering works such as breakwaters and coastal protection structure designs. For a period of approximately one year between February 2013 and January 2014 Turkish Petroleum International Company (TPIC) carried out wave and wind measurements in the Sea of Marmara. The data were collected in 30-minute intervals throughout the one year span at the location of 41o04' N and 28o19' E with 50 m water depth. The present work analyses this rather unique data statistically for wind, wave height and energy conditions in the Sea of Marmara.
Coastal Engineering Journal
Coastal Engineering Proceedings
This study investigates fatalities due to rip currents on the Black Sea coast of Istanbul. Result... more This study investigates fatalities due to rip currents on the Black Sea coast of Istanbul. Results include the incidence rate of fatalities from rip currents, their causes, temporal and spatial distributions. The data shows that, nearly 70% of all drowning fatalities are associated with rip currents, and that on the average 33 people reportedly die from rip currents each year in Istanbul Black Sea coast. Thus, considering the wind speeds versus rip current fatalities, about one third of the fatalities occur when the wind speed is between 1.5-2.0 m/s. For the wind speeds 1.0-1.5 m/s the rip current magnitude is not too intense so people consider themselves capable enough to swim but for poor swimmers this is the most dangerous case. Nearly 60% of the fatalities in this wind speed interval is found to be children.
Coastal Engineering Proceedings
A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water dep... more A Korteweg & de Vries type equation with improved dispersion characteristics for uneven water depths is presented. The new KdV type equation contains mixed dispersion and shoaling terms, which extend its applicable range of relative depths to virtually deep waters. The wave equation also satisfies an important consistency condition that there is an exact agreement between the shoaling rate of the equation itself and the rate obtained from the constancy of energy flux. A finite-difference scheme is devised for simulating several linear and nonlinear cases over varying bathymetry. The performance the new KdV type equation is observed to be quite satisfactory.
Coastal Engineering Proceedings
For realistic wave simulations in the nearshore zone besides nonlinear interactions, the dissipat... more For realistic wave simulations in the nearshore zone besides nonlinear interactions, the dissipative effects of wave breaking must also be taken into account. This paper presents the applications of a spectral nonlinear wave model with a dissipative breaking mechanism introduced by Beji and Nadaoka (1997). Results obtained for spectral components are converted to the time series and compared with Beji and Battjes' (1993) laboratory measurements and the field measurements of Nakamura and Katoh (1992) in the surf zone. While the model predicts the spilling-type breaking of irregular waves in acceptable agreement with the measurements in time domain, the agreement is unsatisfactory for plunging-type breakers.
In this work an improved Boussinesq model with a surface pressure term is discretized by a new ap... more In this work an improved Boussinesq model with a surface pressure term is discretized by a new approach. By specifying a single parameter the proposed discretization enables the user to run the program either in the long wave mode without dispersion terms or in the Boussinesq mode. Furthermore, the Boussinesq mode may be run either in the classical Boussinesq mode or in the improved Boussinesq mode by setting the dispersion parameter appropriately. In any one of these modes it is possible to specify a fixed or a moving surface pressure for simulating a moving object on the surface. The numerical model developed here is first tested by comparing the numerically simulated solitary waves with their analytical counterparts. The second test case concerns the comparison of the numerical solutions of moving surface pressures with the analytical solutions of the long wave equations for all possible modes (long wave, classical, and improved Boussinesq).
Http Dx Doi Org 10 1080 0020739920230201, Jul 9, 2006
ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here dea... more ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here deal with certain relationships which hold between the roots of the general cubic equation and other appropriate parameters derived from the same polynomial. Each section is organized in a monotonic sequence; that is, statement, demonstration and verification.
Marmara Denizi'nde olası bir deprem sonucunda oluşabilecek deniz dalgaları, Çınarcık Çukuru'ndan ... more Marmara Denizi'nde olası bir deprem sonucunda oluşabilecek deniz dalgaları, Çınarcık Çukuru'ndan geçen Kuzey Sınır Fayı'nın 6.5, 7.0 ve 7.5 büyüklüğündeki depremlerde kırılma durumları için simüle edilmiş ve bu dalgaların en büyük yükseklikleri ile kıyılara ulaşma süreleri hesaplanmıştır. Elde edilen sonuçlar, hiç bir hesaplama yapılmaksızın ortaya atılan dalga yüksekliği değerlerinin abartılı olduğunu göstermektedir.
Mediterranean Journal of Mathematics, 2008
A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a... more A unified framework is introduced for obtaining the exact roots of a polynomial by establishing a corresponding polynomial of one degree less. The approach gives the well-known solutions for the second and third degree polynomials and a new solution for the quartic equation, which is different in form from the classical Ferrari-Cardan solution. In accord with Abel's proof, the method produces no solution for the quintic equation.
International Journal of Mathematical Education in Science and Technology, 1992
ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here dea... more ABSTRACT Several investigations on cubic polynomials are presented. The studies reported here deal with certain relationships which hold between the roots of the general cubic equation and other appropriate parameters derived from the same polynomial. Each section is organized in a monotonic sequence; that is, statement, demonstration and verification.
Coastal Engineering, 1995
ABSTRACT A nonlinearity parameter which is valid for both deep and shallow water waves is introdu... more ABSTRACT A nonlinearity parameter which is valid for both deep and shallow water waves is introduced. The parameter may be regarded as a wave Froude number. A modified form of the Ursell number is also discussed.
Coastal Engineering, 1998
Coastal Engineering, 2013
Water wave dispersion relationship Accurate empirical water wave dispersion formula For water wav... more Water wave dispersion relationship Accurate empirical water wave dispersion formula For water waves the transcendental dispersion relationship is solved by iterative methods when wave period and water depth are given and wavelength or wave number is required. A highly accurate explicit approximation to linear dispersion relationship is proposed based on Eckart's explicit relationship. While Eckart's expression is accurate to within 5%, the improved relationship has a maximum relative error of less than 0.05%. A simpler form of the relationship with 0.2% accuracy is also given.