Koefisien pada Persamaan Euler pada Analisis Gelombang Pendek
DOI:
https://doi.org/10.5614/jts.2006.13.4.2Keywords:
Persamaan euler, Persamaan gelombang Airy, Kecepatan horisontal.Abstract
Abstrak. Pada paper ini disajikan hasil penelitian terhadap persamaan Euler. Pada analisis hidrodinamika gelombang pendek, persamaan memberikan distribusi kecepatan horisontal yang seragam pada kedalaman dan panjang gelombang yang terlalu besar. Dengan cara coba-coba diperoleh suatu koefisien pengali pada gaya penggerak, sehingga persamaan memberikan distribusi kecepatan yang sesuai dengan teori gelombang linier, demikian juga dengan panjang gelombangnya. Penggunaan koefisien pada persamaan gelombang Airy, memberikan panjang gelombang yang sangat sesuai dengan panjang gelombang dari teori gelombang linier.Abstract. This paper presents results of research in Euler's equation. The first result is that the equation gives uniformly distributed horizontal velocity in depth. The second is that wave length much longer than wave length of linier wave theory. Applying a coefficient that obtained by trial and error on force term in the equation, so the equation gives horizontal velocities distribution as linier wave does, and so does the wavelength. By using the coefficient in the Airy's wave theory, the equation give the value of wavelength very close to wavelength of linier wave theory.
References
Bredmese, H., Schaffer, H.A. and Madsen, P.A. 2004, "Boussinesq Evolution Equations : Numerical Efficiency, Breaking and Amplitude Dispersion" . Coastal Engineering.
Chen, Y., and P. L.-F. Liu, 1995, "Modified Boussinesq Equations and Associated Parabolic Models for Water Wave Propagation" , J. Fluid Mech., 288.
Dean, Robert G., and Dalrymple, "Water Wave Mechanics for Engineers and Scientists" . Prentice-Hall, Englewood Cliffs, New Jersey.
Gobbi, M. F., and Kirby, J. T., 1998, "A New Boussinesq Type Model for Surface Water Wave" . Ph.D. dissertation of the first author. University of Delaware.
Kirby, J.T., and G. Wei, 1994, "Derivation and Properties of A Fully Nonlinear, Extended Boussinesq Model" , In Proc. IAHR Symposium: Waves - Phys. and Num. Model, Vancouver.
Li, Y. S., Liu, S.-X., Yu, Y.-X., and Lai, G.-Z., 1999, "Numerical Modeling of Boussinesq Equations By Finite Element Method" , J. Coastal Engineering, Elsevier.
Madsen, P. A., R. Murray, and O. R. S",rensen, 1991, "A New Form of Boussinesq Equation With Improved Linear Dispersion Characteristics" . Coastal Engineering 15.
Madsen, P. A., and O. R. S",rensen, 1992, "A New Form of Boussinesq Equation With Improved Linear Dispersion Characteristics" . Part 2. a slowly-varying bathymetry. Coastal Engineering 18.
McCowan, A.D., 1987, "The Range of Application of Boussinesq Type Numerical Short Wave Models" , In Proc. 22nd IAHR Congr.
Meftah, Sorgent, P., and Gami P., 2004, "Linear Analysis of A New Type of Extended Boussinesq Model" . Coastal Engineering.
Nwogu, O., 1993, "An Alternative Form of The Boussinesq Equations for Nearshore Wave Propagation" , J. Waterway, Port, Coast. Ocean Engng. 119.
Schaffer, H. A., P. A. Madsen, 1995, " Further Enhancements of Boussinesq Type Equations" , Coastal Engineering 26 (26).
S",rensen, O.R., Schaffer, H. A. and S",rensen, L.A., 2004, "Boussinesq Modelling Using Unstructural Finite Element Technique" , Coastal Engineering.
Syawaluddin, H., dkk., 2005, "Model Difraksi dengan Persamaan Gelombang Airy yang Disempurnakan" , Thesis S3, Departemen Teknik Sipil, ITB.
Wei, G., J.T. Kirby, S. T. Grilli, and R. Subramanya, 1995, "A Fully Nonlinear Boussinesq Model for Surface Waves" . Part 1, Highly nonlinear unsteady waves. J. Fluid Mech. 294.
